Logic, Thought, and Action 1

Chapter 1

INTRODUCTION∗

Daniel Vanderveken

In contemporary philosophy as well as in human and cognitive sci-ences, language, thought and action are systematically related. One con-siders that the primary function of language is to enable human speakersnot only to express and communicate their thoughts but also to act inthe world. Thus speakers who communicate are viewed as intentionalagents provided with rationality. By choosing to exchange certain wordsspeakers first of all attempt to perform speech acts of different kinds(acts of utterance, acts of reference and predication, illocutionary andperlocutionary acts) in certain ways (literally or not). They also want tocontribute to conversations whose goal is often to change rather than todescribe the world they live in. So contemporary logic and philosophyof language study both thought and action. Underlying any philosophyof language there is a certain philosophy of mind and action.

The main purpose of this book is to present and discuss major hy-potheses, issues and theories advanced today in the logical and analyticstudy of language, thought and action. One can find in the book majorcontributions by leading scholars of analytic philosophy, logic, formal se-mantics and artificial intelligence. Among fundamental issues discussedin the book let us mention the rationality and freedom of agents, the-oretical and practical reasoning, the logical form of individual and col-lective attitudes and actions, the different kinds of action generation,the nature of cooperation and communication, the felicity conditions of

∗I am very grateful to Springer’s referee whose critical remarks have greatly helped to improvethe book. I also wish to warmly thank my research assistant Florian Ferrand who, with somuch care, has produced the camera ready final typescript and my colleague Geoffrey Vitalefor his invaluable help in correcting the introduction. Most of all I want to express mygratitude to my wife Candida Jaci de Sousa Melo for her constant help and encouragement.Grants from the Social Sciences and Humanities Research Council of Canada and the QuebecFoundation for Research on Society and Culture have facilitated the collective work thatunderpins the publication of the present volume.

D. Vanderveken (ed.), Logic, Thought & Action, 1–24.©c Springer. Printed in The Netherlands.2005

2 LOGIC, THOUGHT AND ACTION

speech acts, the construction and conditions of adequacy of scientifictheories, the structure of propositional contents and their truth condi-tions, illocutionary force, time, aspect and presupposition in meaning,the dialogical approach to logic and the structure of dialogues as well asformal methods needed in logic or artificial intelligence to account forchoice, paradoxes, uncertainty and imprecision.

The book is divided into five parts. The first part, Reason, Actionand Communication, contributes mainly to the general philosophy oflanguage, mind and action, the second, Experience, Truth and Real-ity in Science, to the philosophy of science, the third, Propositions,Thought and Meaning, to the logic of language and formal seman-tics, the fourth, Agency, Dialogue and Games, to the logic of action,dialogues and language games and the last part, Reasoning and Cog-nition in Logic and Artificial Intelligence, to the role and formalmethods of logic and computer science. Many authors participated inthe Decade on Language, Reason and Thought which took place in June1994 at the castle of Cerisy-la-Salle in France. Our dear and regret-ted colleague J-Nicolas Kaufmann to whom this book is dedicated waspresent and very active at that conference. We wish to pay him homage.

According to the Western conception of reason, the proper rationalityof human agents basically rests on their capacity to weight on the scalesof the balance of reason their different beliefs, reasons, desires, intentionsand goals and having deliberated to select the best actions that will al-low them to achieve their goals. The classical model of rationality goesback to Aristotle who claimed that deliberation is about means and notabout ends. So, in the model underlying decision theory, human agentsare supposed to have certain primary desires and well ordered prefer-ences prior to making a deliberation and they reason on the basis ofthese desires and their beliefs about the state of the world in order toform other desires for means of coming to their ends. However it of-ten happens that human agents have relatively inconsistent desires thatcannot all be satisfied. Moreover their preferences are not always well or-dered before deliberation. They often have to choose between conflictingdesires in the process of deliberation. And finally there are the freedomand the weakness of the will. An agent who forms an intention after de-liberation can revise or abandon the intention. Previous desires, beliefsand intentions of agents do not seem to cause their future actions. Howcan we account for such facts in a theory of rationality? Human agentsare by nature social. They share forms of life, speak public languages,create social institutions and act together in the world. What kinds ofspeech acts do they attempt to perform in conversation? How can weexplain in philosophy of mind their collective attitudes and actions and

Introduction 3

their communication abilities? The first part of the book, Reason, Ac-tion and Communication, contains a general philosophical discussionof these important questions.

In Chapter 2, The Balance of Reason, Dascal discusses the ideal ofa perfectly reliable balance of reason, an ideal challenged by scepticism.He shows that the balance metaphor is compatible with two differentconceptions of rationality which are both present in Western thought.The first conception expects the balance of reason to provide conclusivedecisions in every rational deliberation. The second conception acknowl-edges the limits of human reason. It is clearly more appropriate for han-dling uncertainty, revision of intentions and more apt to face scepticism.Leibnitz, one of the most eminent rationalist philosophers, made a sub-stantial contribution to both conceptions of rationality. Dascal discussesin detail his ideas. He shows how Leibniz came to grips with the balancemetaphor. The state of equilibrium of the scales of a balance mirrors theequilibrium of indifference between the arguments for and the argumentsagainst a belief, a decision or an action. Yet an indifference of that kindseems to model arbitrariness rather than rationality. Leibniz, as Dascalstresses, was well aware of the problem. He acknowledged that the bal-ance of reason, when it is conceived as a metric and digital balance, liesopen to the objection raised above, but he worked out another version ofthe balance of reason to circumvent this. We can conceive of a balancewhich permits us to directly compare the “values” of what is placed onthe scales without reducing them to universal measuring units.

A major merit of Dascal’s essay lies in the original response he givesto the new kind of scepticism that pervades the Post-modernist trendtoday. Developing Leibniz’ insights, Dascal shows how Leibniz’ revisedmetaphor of the balance of reason can apply even to what is impon-derable and do justice to the idea that there are reasons (for believing,acting or deciding) which incline without necessitating. A new pictureof reason emerges in which hard rationality represented by algorithmsand soft rationality exemplified by the reasoning of lawyers can be seenas complementary rather than conflictual. Dascal considers foregroundnotions which are proper to the reasoning of lawyers (e.g. presumption,burden of proof) and shows that they anticipate Grice’s theory of con-versation and non monotonic reasoning studied nowadays in ArtificialIntelligence.

In the third chapter, Desire, Deliberation and Action, Searle crit-icizes the classical conception of rationality underlying current analysisof practical reasoning and deliberation in philosophy of mind and in de-cision theory. It is wrong to require of rational agents a satisfiable setof desires. It is also wrong to think that an agent who prior to engag-


ing in a deliberation already has certain primary beliefs and desires isthereby committed to other secondary desires or intentions. There couldbe no logic of practical reasoning stating valid principles of inference un-derlying such commitments of an agent. Searle denounces in detail themistakes of this conception of practical syllogism. He first explains whydesire differs radically from belief in both its logical and phenomeno-logical features. He also briefly describes the nature of intentions andanalyzes the relation between desire and action by discussing the natureof reasons for agents to act. In Dascal’s chapter the digital and metricconception of the balance of reason was shown to be inadequate. Searlegoes further and identifies the source of the trouble. That conceptionrests upon the faulty assumption that we can deal with choice, preferenceand desire without recognizing their intentional character.

In Searle’s view, it is a mistake to suppose that the desire must alwaysbe the ground for the reason. An acknowledgement of the facts plusthe agent’s rationality can motivate the internal desire of an action.So the reason can also be the ground for the desire. Among desireindependent reasons Searle considers previous commitments, obligationsand duties of the agent. Searle carefully avoids the common mistake ofassimilating an external reason to a physical cause. He argues thatintentional causation is very different from physical causation. Priorbeliefs, desires and intentions can be reasons for an action. Howeverthey do not really compel the agent to act. There is a certain gap in lifebetween prior intentions and their execution just as there is a certain gapin the process of the deliberation between previous desires and beliefsand the formation of a prior intention. It is remarkable that Searleprovides new and independent reasons for Dascal’s idea (borrowed fromLeibniz) of a desire which inclines without necessitating. Agents arefree. They always have to act on reasons and intentions. So they can beweak. And their weakness of will or akrasia is not to be confused withself-deception. Searle’s chapter ends up with an illuminating account ofthe formal resemblances and differences which exist between weaknessof the will and self-deception.

In order to act together with success several rational agents sharing acommon goal have to cooperate. It is now widely accepted that collec-tive actions are more than the sum of individual actions of their agents.They require of agents a collective intention and a will to cooperate. Butwhat is the very nature of cooperation in collective actions? How canagents share collective attitudes in general and collective intentions inparticular? In the fourth chapter, Two Basic Kinds of Cooperation,Tuomela discusses these important questions for the philosophy of so-cial sciences. According to him one must distinguish a full cooperation

Introduction 5

based on a shared collective goal (the “we” mode) and a weaker kind ofcooperation that reduces to coordination (the “I” mode). While mostcurrent empirical studies concern simple coordination in the “I” mode,Tuomela emphasizes an analysis of full blown cooperation in the “we”mode. He also explains why shared collective goals tend to work betterthan shared private goals in most circumstances. Agents have to cometo an agreement to solve many coordination problems. A logical lessonshould be drawn here : there is no non circular rational solution tosuch problems. Mere private rationality will fail. The same remark canbe made about coordination dilemmas . Developing an argument thatgoes back to Hume, Tuomela shows that only shared collective goals canreliably solve the game in a way satisfactory to all the participants.

Human agents use language in order to coordinate their actions in theworld. They need to communicate their beliefs, desires and intentions inorder to achieve shared collective goals. The basic units of meaning andcommunication are speech acts of the type called by Austin illocutionaryacts. Unlike propositions, such acts have felicity rather than truth con-ditions. In Chapter 5, Speech Acts and Illocutionary Logic, Searleand Vanderveken analyze the logical form of illocutionary acts and theirrelations with other types of speech acts. Elementary illocutionary actssuch as assertions, questions and promises consist of an illocutionaryforce and of a propositional content. Contrary to Frege and Austin whosenotion of force was primitive, Searle and Vanderveken divide forces intoseveral components (illocutionary point, mode of achievement, degree ofstrength, propositional content, preparatory and sincerity conditions).Rather than giving a simple list of actual forces, their speech act the-ory formulates a recursive definition of the set of all possible illocution-ary forces. Moreover they rigorously define the conditions of successfuland non defective performance of elementary illocutionary acts. UnlikeAustin they distinguish between successful utterances which are defec-tive (like promises which are insincere or that the speaker could notkeep) and utterances which are not even successful (like promises to havedone something in the past). They also analyze common illocutionaryforce markers such as verb mood and sentential type and propose a newdeclaratory analysis of performative utterances. Finally they show theimportance of illocutionary logic for the purposes of an adequate generaltheory of meaning and for the foundations of universal grammar. Someillocutionary acts strongly or weakly commit the speaker to others. Itis not possible to perform these illocutionary acts without eo ipso per-forming or being committed to other illocutionary acts. Thus commandscontain orders and weakly commit the speaker to granting permission.One of the main objectives of illocutionary logic is to formulate the basic


laws of illocutionary commitment. Searle and Vanderveken explain basicprinciples of illocutionary commitment. Later in Meaning and SpeechActs (1990-91) Vanderveken has used the resources of proof and modeltheories in order to formulate the laws of a general semantics containingillocutionary logic. Recently he has extended and generalized speech acttheory so as to deal with discourse. In the special issue Searle Withhis Replies in the Revue internationale de philosophie (2001) hehas also shown how to analyze the structure and dynamics of languagegames with a proper linguistic goal.

Verbal exchanges between speakers communicating with each otherare standard cases of collective actions. They often consist in joint collec-tive illocutionary acts like debates, consultations and negotiations thatlast during a certain interval of time in the conversation. In Chapter 6,Comprehension, Communication and Minimal Rationality inthe Tradition of Universal Grammar, Andre Leclerc presents Ar-ńauld and Nicole’ theory of communication. Borrowing from neglectedsources such as La grande perpetuit´´ (1669-1672), Leclerc shows thatArnauld and Nicole were aware of the insufficiency of the code modelof linguistic communication according to which the speaker codes histhoughts into sentences and the hearer decodes them in order to accessthe thoughts of the speaker. They fully realized the need to enrich thismodel with an inferential model of linguistic communication in order toaccount for the role of implicatures, insinuations and presuppositions.Leclerc provides evidence for the claim that Arnauld and Nicole antici-pated Cherniak’s principle of minimal rationality and Grice’s maxim ofquantity. He notices that they linked the maxim of quantity with thespeakers’ lack of logical omniscience. Leclerc does not only make anhistorical study which shows the roots of modern pragmatics, he alsocomments passages which can still teach us something important today.The treatment of metaphors is a case in point. Arnauld and Nicole in-terestingly explain why words could not acquire a metaphorical meaningin metaphors

Human reason fully manifests itself in scientific practice. Humanagents formulate scientific theories in order to describe, explain and pre-dict what is happening in the world they live in. According to empiricismscientific theories must be checked against the facts of our experience.We need to confirm or falsify them by observing the world. In orderto be true, scientific statements must be empirically adequate. Howeverthe meaning of scientific terms and even the interpretation of observa-tion sentences that are used for testing scientific statements are theoryladen and depend on conventions which determine their use in a contextof verification. There is a real construction of models in scientific theo-

Introduction 7

ries. Observable phenomena are explained by reference to unobservableprocesses. Empirically equivalent scientific theories can differ in manyaspects. How can we then relate Experience, Truth and Realityin Science? The second part of book discusses this fundamental ques-tion of the philosophy of science. It raises important issues for currentempiricist, constructivist and realist views of science.

In Chapter 7, Truth and Reference, Lauener opposes to physicalrealism a pragmatic kind of relativism in the conception of truth and on-tology. According to the received view, the question of meaning is priorto the question of truth. Before asking whether an assertive utterance istrue or false, one has to understand the meaning of that utterance. Sincemeaning depends on sense and reference, one is led to think that refer-ence precedes truth. Tarski’s definition of truth reinforces the receivedview. Tarski equates truth with satisfaction by all sequences of objectsof the domain. Quine however in Pursuit of Truth (1990) claims thattruth precedes reference. Lauener criticizes Quine’s claim and showsthat reference plays a primordial role in the determination of truth con-ditions. According to him even the meaning of observation sentences isirreducible to stimulus meaning. Their use and interpretation in a con-text depend on both the senses and denotations of their terms which arerelative to a given linguistic system and conceptual scheme. Scientificactivity moreover requires rule governed intentional illocutionary actssuch as assertions, conjectures, conventions and agreements that cannotbe accounted for in an austere extensional ontology.

Lauener’s objection to the priority of truth over reference leads togeneral conclusions which are independent of that issue. Quine upholdsscientific realism and physicalism as far as truth is concerned, while headvocates relativism as regards to ontology. Lauener questions the com-patibility of these two positions. Quine himself was fully aware of theproblem. Lauener does not try to reconcile realism for truth with rela-tivism for ontology. He advocates relativism in both cases, but the kindof relativism that he advocates has nothing to do with cultural or subjec-tive relativism. Lauener does not so much challenge realism as he doesthe holistic view of science as a language-theory conglomerate conceivedas a constantly evolving whole. Lauener is not opposed to realism butrather to holism in science and universalism in logic (the view of logicas a language as opposed to the view of logic as a calculus). Lauenerdoes not really advocate a relativistic ontology. He rather advocates apluralistic ontology : “Since a new domain of values for the variables ispresupposed for each context I advocate a pluralistic conception of ontol-ogy in contrast to Quine who postulates a unique universe by requiringus to quantify uniformly over everything that exists . . . according to my


method of systematic relativization to contexts (of action), we create re-ality sectors by employing specific conceptual schemes through which wedescribe the world.”. Lauener’s argument for the recognition of regionalontologies is based on philosophical considerations.

It is very interesting to notice that in the next chapter Michel Ghinsadvances an independent argument supporting the claim that we need tocircumscribe domains in science on the basis of purely scientific consid-erations. This spontaneous convergence between two chapters is worthstressing. In Chapter 8, Empirical Versus Theoretical Existenceand Truth, Michel Ghins mainly argues in favour of a specific, selectiveand moderate version of scientific realism in accordance with the com-mon use of the terms “existence” and “truth” in ordinary speech. Theactual presence of an object in sensory perception and the permanenceof some of its characteristics during an interval of time jointly consti-tute a sufficient condition, a “criterion”, of existence of that object inscientific activity as well as in everyday experience. These features alsoground the truth of statements about ordinary observable objects andof some physical laws connected to experience. So scientific statementscan be accepted as true when they are inductively well established in acertain limited domain of experience.

Ghins illustrates his version of scientific realism by considering thetwo particular examples of electromagnetic and gravitational fields andcrystalline spheres in ancient astronomy. As one might expect, his crite-rion supports the existence of the fields but not of the spheres. HermanWeyl had already compared the different observable manifestations ofan electric field with different perceptions of an ordinary object and ar-gued that if we see forces as corresponding to perceptions and differentcharges as corresponding to different positions of the observers, we areentitled to attribute objective reality to electric fields. Ghins takes ad-vantage of Weyl’s analogy and goes further. Sharing Kant’s criterion ofreality (“[reality is] that which is connected with perception according tolaws”), Ghins shows that we have good grounds to consider as laws notonly true physical statements like the three famous Newtonian laws butalso mathematical laws of classical mechanics of point-like masses whichrestrict the domain in which Newton’s laws are true. Such an extensionof the coverage of the concept of law is by no means a trivial matter.It enables Ghins to answer Popper’s objection according to which lim-iting a theory to a given domain would be tantamount to protecting itagainst adverse evidence. It also provides an independent support forLauener’s position on the question as to whether human knowledge is an“amorphous and unified language-theory” or as a constellation of sepa-rate theories, each endowed with its own language and its own ontology.

Introduction 9

The scientist’s preference for simpler theories is often seen as springingfrom aesthetic or pragmatic considerations which have nothing to withwhat reality is like. Ghins debunks this view and shows that simplicity isa reliable guide for those who want to know what there is. The oppositeview leads to counter-intuitive consequence.

In Chapter 9, Michel Ghins on the Empirical Versus the Theo-retical, Bas van Fraassen replies to Ghins’ ideas on existence and truthin science. van Fraassen basically agrees with Ghins on the central roleof experience, the need to reject the myth of the given and the hope foran empiricist philosophy of science. However as regards existence andtruth van Fraassen considers that one must sharply separate questionsof epistemology from questions of semantics and ontology. Sensory per-ception and invariance are not a necessary condition of existence. Ghinsdoes not give a criterion of existence strictly speaking. He only offers apartial criterion of legitimacy for assertions of existence of certain ob-jects of reference that we can observe. But perhaps there also exist inthe world other sorts of entities which are “transient”, “invisible” and“intangible”. This is not an issue of semantics but of ontology. Is Ghins’epistemic principle right? van Fraassen does not give an answer to thequestion. Both Ghins and van Fraassen view reality from the standpointof experience. According to Ghins, proponents of a scientific theory arecommitted to believing in the existence of all entities among those pos-tulated that bear a certain relationship to what can be experienced.Directly observable ones are not privileged. Van Fraassen’s empiricismis less moderate. Proponents of a scientific theory are only committedto believing in the existence of observable entities.

In contemporary philosophy of language, mind and action, proposi-tions are not only senses of sentences provided with truth conditions.They are also contents of human conceptual thoughts like illocution-ary acts (assertions, questions, promises) and attitudes (beliefs, de-sires, intentions). The third part of the book deals with Propositions,Thought and Meaning. The double nature of propositions imposesnew criteria of material and formal adequacy on the logic of proposi-tions and formal semantics. One can no longer identify so called strictlyequivalent propositions having the same truth conditions. They are notthe senses of synonymous sentences, just as they are not the contentsof the same thoughts. Moreover human agents are not perfectly ratio-nal in thinking and speaking. They do not make all valid inferences.They can assert and believe necessarily false propositions. So we needvery fine criteria of propositional identity in logic. It is important totake into account the creative as well as the restricted cognitive abilitiesof human agents. It is also important to consider tense and aspect as


well as presupposition accommodation and assignment of scope in theunderstanding of truth conditions. For that purpose, we need a betterexplication of truth conditions with an account of aspect, tense and pre-supposition. We also need to take into account the illocutionary forcesof utterances. Part three of the book contains logical contributions onthe matter.

In Chapter 10, Propositional Identity, Truth According to Pred-ication and Strong Implication, Daniel Vanderveken enriches theformal ontology of the theory of sense and denotation of Frege andChurch. His main purpose is to formulate a natural logic of propo-sitions that explains their double nature by taking into considerationthe acts of reference and predication that speakers make in expressingpropositions. According to his analysis, each proposition is composedof atomic propositions (each predicating a single attribute of objectsof reference under concepts). Human agents do not know actual deno-tations of most propositional constituents. Various objects could fallunder many concepts or could have certain properties in a given cir-cumstance. So they also ignore in which possible circumstances atomicpropositions are true. Most could be true in many different sets of pos-sible circumstances given the various denotations that their attributeand concepts could have in the reality. For that reason atomic proposi-tions have possible in addition to actual Carnapian truth conditions. Foreach proposition one can distinguish as many possible truth conditionsas there are distinct sets of possible circumstances where that proposi-tion would be true if its propositional constituents had such and suchpossible denotations in the reality. In understanding a proposition wejust know that its truth in a circumstance is compatible with certainpossible denotation assignments to its propositional constituents and in-compatible with others. So logic has to distinguish propositions whoseexpression requires different acts of predication as well as those whosetruth is not compatible with the same possible denotation assignmentsto their constituents. Consequently, not all necessarily false propositionshave the same cognitive value. Some are pure contradictions that we apriori know to be false in apprehending their logical form. We cannotbelieve them. One can define the notion of truth according to a speaker,distinguish subjective from objective possibilities and formulate adequateprinciples of epistemic logic in predicative propositional logic.

As Vanderveken points out, the set of propositions is provided with arelation of strong implication that is much finer than strict implication.Strong implication is a relation of partial order which is paraconsistent,finite, decidable and a priori known. In the second part of the chapterVanderveken proceeds to the predicative analysis of modal and temporal

Introduction 11

propositions of the logic of ramified time. He uses the resources of modeltheory and formulates a powerful axiomatic system. He also enumeratesvalid laws for propositional identity and strong implication. And hecompares his logic with intensional and hyperintensional logics, the logicof analytic implication and that of relevance.

In predicating a property of an object a speaker expressing a proposi-tional content can view the represented fact in different ways as a state,an event or an unfinished process. There are different ontological cat-egories of fact. Having aspectualized the predication, the speaker hasto insert the represented fact into his own time reference, which is dis-tinct from the external time reference of the calendar. Verbal aspectand tense are fundamental to the understanding of truth conditions ofelementary propositions. Their semantic analysis requires a logical cal-culus. In the late seventies Rohrer edited two collective books presentinga rigorous logical treatment of tense and aspect showing how one canrepresent in Montague grammar the temporal structure of verbs andhow verbal meaning interacts with the meaning of tense forms and tem-poral adverbs. In Chapter 11, Reasoning and Aspectual-TemporalCalculus, Jean-Pierre Descles analyzes aspect and time within the the-óretical framework of cognitive applicative grammar which is an exten-sion of Shaumyan’s Universal Applicative Grammar incorporating com-binatory logic and topology. Descles analyses fundamental concepts ofáspectuality: state, event, process, resultative state by means of topo-logical notions. He uses open and closed intervals of instants for givinga semantic interpretation of aspectual concepts. Aspectual operatorsare obtained by an abstraction process from semantic interpretations.Curry’s combinatory logic is used to build abstract aspectual operators.

Both the Montagovian and cognitive applicative approaches are rootedin Church’s lambda calculus as regards logic and focus on intervals asregards semantics. Yet there are important differences between the twoapproaches. In “Universal Grammar” Montague interprets indirectlysentences of natural language via their translation into a formal ob-ject language of intensional logic for which he builds a truth conditionalmodel-theoretical semantics. In his Cognitive Applicative Grammar, De-scles starts with defining a quasi-topological model of speech operations.Ńext he expresses model-theoretical concepts in terms of operators ofcombinatory logic. His formal language is not an object language relatedto natural language via translation. It is a meta-language which serves todescribe natural language. Yet both approaches share a central concernfor aspectual reasoning. In a natural deduction style Descles formulates´principles of valid inferences that enable us to derive from the sentence“This morning, the hunter killed the deer” conclusions like “Therefore


the deer was killed this morning”, “Now, the deer is dead” and “Yes-terday, the deer was alive” An interesting feature of Descles’ approach´lies in his concern for the speaking act as well as for the dynamics ofmeaning. He analyzes intricate connections between aspectual-temporalconditions and the learning of lexical predicates. His approach aims atshedding light on the interaction of language activities with other cog-nitive activities such as perception and action. Descles also shows thatápplicative grammar can accommodate speech acts in its own way.

The problems raised by presupposition have been a challenge for logi-cians, linguists and philosophers of language for almost a century. Thecurrent notion of presupposition is ambiguous; among pieces of informa-tion which are not explicitly stated but taken for granted, one shoulddistinguish between what is “induced” or “triggered” by lexical items orsyntactic constructions, and what is “already given” but “not marked”because of background knowledge. In Chapter 12, Presupposition,Projection and Transparency in Attitude Contexts, Rob van derSandt advocates an unified account of presuppositions which establishesa straightforward connection between the two kinds of phenomena. Thecentral tenet of his anaphoric theory of presupposition is that one singleprocess underlies both the process of anaphoric binding and the processof presupposition resolution. He treats all presuppositions as anaphoricexpressions which are bound by some previously established antecedent.van der Sandt acknowledges that sometimes the so called antecedent ofthe presupposition is missing and has to be supplied by some kind ofaccommodation. But, contrary to others, he imposes a new constrainton accommodation. When no antecedent is in the offing, accommo-dation has to insert an identifiable object which can then function asantecedent for the presuppositional anaphor. Accommodation appliesto discourse structures. This leads van der Sandt to work out a theoryof presupposition in the framework of Kamp’s Discourse RepresentationTheory. Using discourse representation structures he constructs a classof conditions that encode anaphoric material.

Accommodation is implemented by a projection algorithm. When itis applied to a modal sentence containing a definite description, thatalgorithm yields either the wide or the narrow scope reading of the de-scription. This depends on the level at which the accommodation ismade. Just as Descles offered a dynamic conception of disambiguation,´van der Sandt gives us a dynamic account of the contrasts betweenwide scope and narrow scope, or de re and de dicto readings. His pro-jection mechanism has a greater explanatory power than the standardRussellian theory of descriptions. On Russell’s account, there is no wayto project a description in the consequent of a conditional to its an-

Introduction 13

tecedent. According to van der Sandt such a projection is possible. Arethere truth value gaps in the case of presupposition failure? Kamp andReyle’ standard verification conditions for discourse representation sidewith Russell. van der Sandt revises verification conditions in such away that no truth value is assigned when an presuppositional anaphorcan neither be bound nor accommodated. This is a significant improve-ment in accordance with the Frege-Strawson theory. At the end, vander Sandt comes to grips with very difficult problems which arise whenthe pragmatic distinction between the first person and the third personinteract with the semantic distinction between de re and de dicto. Heshows how his theory can solve recalcitrant puzzles mentioned by Kripkeand Heim for the presuppositional adverb “too.”

The concept of assertion has played a crucial role in the developmentof contemporary logic. It took time for logicians and philosophers toclarify the role of assertion in formalization. In Chapter 13 The Limitsof a Logical Treatment of Assertion Denis Vernant considers thatany logical treatment of assertion is limited because the concept requiresa pragmatic analysis. The first part of Vernant’s contribution analysesRussell’s account of assertion from the Principles of Mathematicsto Principia Mathematica , while emphasizing its characteristic apor-ias. Vernant carefully reconstructs successive stages of Russell’s thoughton the matter. The second part deals with the pragmatic treatment ofassertion which began with Frege’s Logische Untersuchungen andwas to continue with Searle’s definition of assertive speech acts and theformulation by Searle and Vanderveken of illocutionary logic. Vernantdefends a solution which is based on Frege’s account but which goes muchbeyond it. Assertion like judgment is well the acknowledgment of thetruth of propositional content. Vernant shows that the new treatment ofassertion as an illocutionary act (and not a mental state) removes Rus-sell’s aporias. Frege only dealt with propositional negation. However,there is another negation, called illocutionary negation, which applies toforce. As Searle and Vanderveken pointed out, the point of an act ofillocutionary denegation is to make it explicit that the speaker does notperform a certain illocutionary act. So one must distinguish between theassertion of the negation of a proposition and the illocutionary denega-tion of that assertion. Vernant shows that already in 1904 Russell hadanticipated illocutionary negation in his treatment of what he called de-nial. Russell’s insistence on denial as the expression of disbelief showsthat he had understood the pragmatic complexity of assertion. At theend, Vernant criticizes current speech act theory for neglecting interac-tions and conversational exchanges between speakers and makes a pleafor a multi-agent speech act theory. Speakers perform their assertions


and other individual illocutionary acts with the intention of contribut-ing to the conversation in which they participate. By pointing out thedialogical function of illocutionary acts Vernant shares actual concernsin a more general speech act theory adequate for dialogue analysis.

As Wittgenstein pointed out, meaning and use are inseparable. Hu-man speakers are agents sharing forms of life whose language-gamesserve to allow them to act in the world. Their verbal and non verbalactions are internally related. Human agents first of all make voluntarymovements of their own body. In oral speech they emit sounds. Theirbasic intentional actions generate others in various ways (causally, con-ventionally, simply, etc.) How do agents succeed to bring about factsin the world? What is the causal and temporal order prevailing in theworld in which they act? As Belnap pointed out, the logic of actionrequires a theory of branching time with an open future as well as atheory of games involving histories that represent possible courses ofhistory of the world. Such a theory is compatible with indeterminism.How can we formally account for the freedom of will and the intention-ality, capacities and rationality of human agents? The fourth part ofthe book deals with Agency, Dialogue and Games. It is concernedwith questions such as: What is the nature of agency? How can weexplicate free choice, action in the present and in the future, mentalcausation, success and failure and action generation? What is the na-ture of basic actions? In language use, speakers make utterances, actsof reference and predication, they express propositional contents withforces and perform illocutionary acts which have perlocutionary effectson the audience? How do they succeed in doing all this? Is there anirreducible pragmatic aspect in predication and discourse? What is thelogical structure of a dialogue? The first contribution by Paul Loren-zen to dialogical logic appeared more than fifty years ago. Since thendifferent dialogical systems and related research programmes have beendeveloped. Is there a general framework for the study of the variousinteractions between dialogue and logic? What kind of rationality doagents manifest in practising language-games? How can they reach out-comes given their knowledge and other attitudes?

In a recent book Facing the Future Agents and Choices in OurIndeterminist World (2000), Nuel Belnap and co-authors have out-lined a logic of agency which accommodates both causality and inde-terminism in a conception of ramified time where the set of moments oftime is a tree-like frame. There is a single causal route to the past butthere are multiple future routes. So agents are free: their actions arenot determined. In the indeterminist theory of ramified time momentsrepresenting complete possible states of the actual world are instanta-

Introduction 15

neously world-wide super-events. Because of the global nature of thesecausal relata (the instantaneous moments), there is a world-wide matterof action at a distance in the logic of agency with branching time. Thetheory remains non relativistic and commits us to an account of action-outcomes that makes them instantaneously world-wide. However it isclear that both our freedom and our actions are local matter. They aremade up of events here now that have no effect on very distant regionsof the universe. In Chapter 14, Agents and Agency in BranchingSpace Times, Nuel Belnap shows how to improve the logic of agencyby using the theory of branching space-times which can account for localindeterminism. For that purpose the cosmological model proposed byEinstein and Minkowski is an invaluable source of insight. This modelin which action at a distance is abandoned forces us to reconsider ourconception of an event. As Belnap observes, “a causally ordered his-torical course of events can no longer be conceived as a linear orderof momentary super-events. Instead, a history is a relativistic space-time that consists in a manifold of point-events bound together by aMinkowski-style causal ordering that allows that some pairs of pointsevents are space-liked related”. So the theory of branching space timesbetter articulates better the indeterminist causal structure of the world.In that theory causal relata are point events which are limited in bothtime-like and space-like dimensions. Now indeterminism and free willare not global but local. Because the theory of branching space times isboth indeterminist and relativist, it is a much better theoretical appa-ratus for the purpose of the logic of agency. As Belnap shows, logic cannow more finely identify persisting agents and also describe their choicesconcerning the immediate future.

Belnap begins his chapter by explaining his basic ideas about choiceand agency in branching time. Next he presents the theory of branchingspace-times. And then he considers how the two theories can be com-bined. He discusses new interesting postulates that the logic of agencycould adopt as regards the nature of agents, their free choice and howthey do things in branching space-times. Belnap’s investigations couldlead us to an important new theory of games in branching space timesthat would describe, as he says, “with utmost seriousness the causalstructure of the players and the plays in a fashion that sharply sepa-rates (as von Neumann’s theory does not) causal and epistemic con-siderations” One of Belnap’s new postulate characterizes causation inbranching space-times. Using the notion of transition between an initialevent and a scattered outcome event together with the notion of causalloci, Belnap defines the notion of joint responsibility of two agents. Heconcedes that his account does not cover joint action which requires the


additional concept of joint intention. Belnap’s account of action in termsof causation does not consider at all the intentions of agents. The mainobjective of the next chapter is to take them into account.

In Chapter 15, Attempt, Success and Action Generation, DanielVanderveken presents a logic of agency where intentional actions are pri-mary as in contemporary philosophy. In his view, any action that anagent performs unintentionally could in principle have been attempted.Moreover any unintentional action of an agent is generated by an inten-tional action of that agent. As strictly equivalent propositions are notthe contents of the same attitudes, the logic of agency should distin-guish intentional actions whose contents are different. For that purposeVanderveken uses the resources of the predicative modal and temporalpropositional logic presented in Chapter 9. His main purpose now is toenrich the logic of action thanks to a new account of attempt and actiongeneration. Unlike prior intentions which are mental states, attempts aremental actions of a very specific kind that Vanderveken analyzes: theyare personal, intrinsically intentional, free and also successful. (Whoevertries to make an attempt makes that attempt). Like intentions attemptshave strong propositional content conditions. They are directed towardsthe present or the future, etc. Vanderveken explicates model theoret-ically these features within ramified time. As before, coinstantaneousmoments are logically related in models by virtue of actions of agentsat these moments. Now, moments of time and histories are also logi-cally related by virtue of attempts of agents. Attempts have conditionsof achievement. Human agents sometimes attempt to do impossiblethings. However they are rational and cannot attempt to do what theybelieve to be impossible. Thanks to his account of subjective possibili-ties, Vanderveken can deal with unachievable attempts. To each agentand moment there always corresponds in each model a non empty set ofcoinstantaneous moments which are compatible according to that agentwith the achievement of his attempts at that moment.

He proceeds to a unified explication of attempt and action. In orderthat an agent succeed in doing things it is not enough that he try andthat these things occur. It is also necessary that they occur because ofhis attempt. Vanderveken uses the counterfactual conditional in order todefine intentional causation and intentional actions. He explicates howattempts can succeed or fail, which attempts are the most basic actionsand how they generate all other actions. Not all unintended effects ofintentional actions are contents of unintentional actions, only those thatare historically contingent and that the agent could have intended. Somany events which happen to us in our life (e.g. our mistakes) arenot really actions. Vanderveken accounts for the minimal rationality of

Introduction 17

agents in explaining action generation. Agents cannot try to do thingsthat they know to be impossible or necessary. Moreover agents have tominimally coordinate their knowledge and volition in trying to act inthe world. He states the basic valid laws of his logic of action.

In the usual account of one-place predication where a general termserves to attribute a property to a particular of an independently givendomain of objects, one takes for granted a conceptual framework whichuses, among others, the metaphysics of substance and attribute, andwhich is, furthermore, dependent on the availability of individuated ob-jects. In Chapter 16, Pragmatic and Semiotic Prerequisites forPredication: A Dialogical Model, Kuno Lorenz considers the pre-propositional state where the task to utter a sentence and express aproposition is still to be achieved. He gives a rational reconstructionof the prerequisites for predication within a novel conceptual frame-work, a dialogical model, that is partly derived from ideas of Peirce andWittgenstein. By relating the both pragmatic and semiotic approachesof Peirce and Wittgenstein to a dialogical methodology, Lorenz presentsa sequence of nested dialogical constructions. His purpose is to lead usfrom modeling simple activity to modeling the growth of more complexactivities up to elementary verbal utterances.

Lorenz uses dialogue, conceived as a generalized language-game, asa means of inquiry. Emulating Nelson Goodman’s spirit he says thatneither particulars nor properties exist out there. Lorenz argues thatthe contrast between individuals and universals is not something thatwe discover by observing the world. It emerges from a process of ob-jectivation which is part of the acquisition of action competence. Thisprocess is best understood if we look at it from the perspective of theagent-patient opposition. The agent performs the token of an action andlooks at it from the I-perspective. For him, action is a means to reacha goal. The patient recognizes an action-type and looks at it in a You-perspective. For him, action is an object among others. One has learnedan action when one is able to go back and forth from one perspective tothe other. This shift of perspective is exemplified in dialogue. Lorenzshows how the move of objectivation from action as a means to action asan object is accompanied by a split of the action into action particularswhose invariants may be treated as kernels of universalia and respec-tive wholes which are closures of the actualization of singularia. Kernelsand closure taken together (form and matter in the tradition) make upa particular within a situation. Hence particulars, for Kuno Lorenz, arethe product of a dialogical construction. As he puts it, “particulars maybe considered to be half thought and half action”.


A major innovation of Lorenz lies in the role he gives to the dia-logical structure of utterances. He distinguishes between two differentfunctions in acts expressing elementary propositions: the significativefunction of showing and the communicative function of saying. Com-munication takes place between the two protagonists of the utterance. Inhis view, when a speaker makes an act of reference, he shows somethingto a hearer. Similarly when he predicates an attribute, he does that fora hearer. And even the ostensive function can involve a communicativecomponent. Lorenz’ account of predication is fine-grained. His concep-tual framework enables him to distinguish between part, whole, aspectand phase. He give an account not only of familiar elementary proposi-tions in which a universal is predicated of a particular but also of otherpropositions in which a particular is seen as a part of a whole. Lorenz’analysis of predication covers both the class-membership predication andthe mereological predication. This is a remarkable advance.

The dialogical approach to logic and the theory of language gamesare part of the dynamic turn that logic took over the last thirty years.In Chapter 17, On How to Be a Dialogician, Shahid Rahman andLaurent Keiff present an overview on recent development on dia-logues and games. Their aim is to present the main features of thedialogical approach to logic. The authors distinguish three main ap-proaches following two targets: (1) the constructivist approach of PaulLorenzen and Kuno Lorenz (1978) and (2) the game-theoretical approachof Jaakko Hintikka (1996) aim to study the dialogical (or argumentative)structure of logic. (3) The argumentation theory approach of Else Barthand Erik Krabbe (1982) is concerned with the logic and mathematicsof dialogues and argumentation. It links dialogical logic with informallogic (Chaim Perelman, Stephen Toulmin). Now two very importantlines of research attempt to combine the lines of the two groups: (4)the approach of Johan van Benthem (2001-04) aims to study interestinginterfaces between logic and games as model for dynamic many-agentactivities and (5) Henry Prakken, Gerard Vreeswijk (1999) and ArnoLodder stress the argumentative structure of non-monotonic reasoning.Rahman & Keiff describe main innovations of the dynamic approachfrom the standpoint of dialogical logic.

They give a new content to key logical notions. There are illocutionaryforce symbols in the object language of dialogical logic. The two play-ers (proponent and opponent) perform illocutionary acts with variousforces in contributing to possible dialogues of dialogic. The first utter-ance is an assertion by the proponent which fixes the thesis in question.That assertion is defective if the speaker cannot defend its propositionalcontent so as to win the game. Other moves have the forces of attacks

Introduction 19

and defence. An attack is a demand for a new assertion. A defence isa response to an attack that justifies a previous assertion. The secondutterance has to be an attack by the opponent. The third can be a de-fence or a counterattack of the proponent. And so on. In dialogical logicas in Frege’s Begriffschrift force is part of meaning. Utterances serveto perform illocutions with different forces and conditional as well ascategorical assertions. Particle rules determine how one can attack anddefend formulas containing logical constants, whereas structural rulesdetermine the general course of a dialogue. Dialogical logic can for-mulate different logical systems by changing only the set of structuralrules while keeping the same particle rules. It can also formulate differ-ent logics by introducing new particles. Thus classical and intuitionisticlogics differ dialogically by a single structural rule determining to whichattacks one may respond. The dialogical approach to logic makes it sim-ple to formulate new logics by a systematic variation and combinationof structural and particle rules. Notice that the structural rules deter-mine how to label formulas — number of the move, player (proponentor opponent), formula, name of move (attack or defence) — and how tooperate with these labelled formulae.

The thesis advanced is valid when the proponent has a formal win-ning strategy : when he can succeed in defending that thesis against allpossible allowed criticisms by the opponent. Rahman and Keiff showthat the dialogical and classical notions of validity are equivalent un-der definite conditions. Like in illocutionary and paraconsistent logics,speakers can assert in paraconsistent dialogic incompatible propositionswithout asserting everything. Certain kinds of inconsistency are for-bidden by dialogical logic. Like relevant logic connexive dialogic candiscriminate trivially true conditionals from those where a determinatekind of meaning links the antecedent to the consequent. Each modallogic is distinguished by the characteristic properties of its accessibilityrelation between possible worlds. In dialogic accessibility relations aredefined by structural rules specifying which contexts are accessible froma given context. Authors show the great expressive power of dialogicas a frame by presenting a dialogical treatment of non normal logics inwhich the law of necessitation does not hold. At the end, they advocatepluralism versus monism in logic.

In Chapter 18, Some Games Logic Plays, Pietarinen takes a game-theoretical look at the semantics of logic. Game-theoretical semanticshas been studied from both logical and linguistic perspectives. Pietari-nen shows that it may be pushed into new directions by exploiting theressources of the theory of games. He focuses on issues that are of com-mon interest for logical semantics and game theory. Among such topics


Pietarinen discusses concurrent versus sequential decisions, imperfectversus perfect and complete versus incomplete information. Further-more, he draws comparisons between teams that communicate and teamsthat do not communicate, agents’ short-term memory dysfunctions suchas forgetting of actions and of previous information, screening and sig-nalling, and partial and complete interpretations. Finally, Pietarinenaddresses the relevance of these games to pragmatics and its precursoryideas in Peirce’s pragmaticism.

The common reference point is provided by Independence-Friendly(IF) logics which were introduced by Hintikka in the early 1990s. Incontrast to the traditional conception of logic, the flow of informationfrom one logically active component to another in formulas of IF logicsmay be interrupted. This gives rise to imperfect information in semanticgames. It is worth investigating, as Pietarinen does, in which sensesgame-theoretical approaches throw light on pragmatically constrainedphenomena such as anaphora. Following Hintikka’s idea that languagederives much of its force from the actual content of strategies, Pietarinenextends the semantic game framework to hyper-extensive forms whereone can speak about strategies themselves in the context of semanticgames that are played in a move-by-move fashion. He further arguesthat Peirce’s pragmatic and interactive study of assertions antedatesnot only the account of strategic meaning, but also Grice’s programmeon conversational aspects of logic.

The borderline between decision theory and game theory is one of themore lively areas of research today in the philosophy of action. Over thelast ten years, the economist Robert Aumann renewed epistemic logic byhis account of common knowledge and philosophers and logicians suchas Cristina Bicchieri, Richard Jeffrey, Wlodeck Rabinowicz and JordanHoward Sobel made decisive contributions to the analysis of rationalaction. In Chapter 19 Backward Induction Without Tears? Sobelfocuses on a kind of game whose solution hinges on a pattern of reasoningwhich is well known in inductive logic : backward induction. The rules ofthe game under scrutiny are described in the following passage : “X andY are at a table on which there are dollars coins. In round one, X canappropriate one coin, or two. Coins she appropriates are removed fromthe table to be delivered when the game is over. If she takes two, thegame is over, she gets these, and Y gets nothing. If she takes just one,there is a second round in which Y chooses one coin or two. Dependingon his choice there may be a third round in which it is X’s turn to choose,and so on until a player takes two coins, or there is just one coin left andthe player whose turn it is takes it.”

Introduction 21

Sobel distinguishes between weak and strong solutions to a game. Aweak solution shows that players who satisfy certain conditions resolvea game somehow without explaining how. On the contrary, a strong so-lution shows how players reach the outcome. Conditions determine thelevel of rationality ascribed to the gameplayers. Game theorists disagreeabout rationality which should be granted to players even in a theorywhich is intended to reflect the behaviour of idealized players. Considerthe backward-induction terminating game described above. The ques-tion arises whether ideally rational and informed players in that gamesatisfy a strong knowledge condition. Rabinowicz would give a negativeanswer. He claims that it is not reasonable to expect the players to bestubbornly confident in their beliefs and incorruptible in their disposi-tions to rational behaviour. On the contrary Sobel says that once wehave granted that the gameplayers are resiliently rational, we should alsoadmit that past irrationality would not exert a corrupting influence onpresent play. Even though he does not share Rabinowicz’s view, Sobelwonders about the possibility of finding an intermediate solution whichwould be less demanding than his initial condition — the condition ofknowledge compounded robustly forward of resilient rationality — butwhich nevertheless “would enable reasoning on X’s part to her choiceto take both coins and end the game” He argues that ideally rationaland well informed players in the game would not have a strong solu-tion to the game unless they satisfied demanding subjunctive conditions(involving counterfactual conditionals) which are not significantly dif-ferent from “knowledge compounded robustly forward of resilient ratio-nality”. One can find in Sobel’s contribution original and deep ideas onideal game-theoretic rationality. Thus he investigates the consequencesof holding prescience as being an ingredient of game-theoretical rational-ity.

Reasoning and computation play a fundamental role in mathemat-ics and science. A primary purpose of logic is to state principles ofvalid inference and to formulate logical systems where as many logicaltruths as possible are provable by effective methods. The last part ofthe book, Reasoning and Computation in Logic and ArtificialIntelligence, contains discussions on the matter. It is well known thatmaterial and strict implication, which are central notions for the veryanalysis of entailment and valid reasoning, lead to paradoxical laws intraditional logic. Among so-called paradoxes of implication there is, forexample, the law that a contradiction implies any sentence whatsoever.Do inconsistent theories really commit their proponents to asserting ev-erything? This part of the book presents paraconsistent and relevantlogics which advocate like intuitionist logic rival conceptions of impli-


cation and of valid reasoning. It also discusses important issues forartificial intelligence. Human agents take decisions and act in situa-tions where they have an imperfect knowledge of what is happening andthey do many things while relying on imprecise perceptions. They arenot certain of data and they can revise their conclusions. Which newmethods should logic and artificial intelligence use in order to deal withuncertainty and imprecision in computing data?

Developing insights due to Vasilev and Jaskowski, da Costa and Asenjoínvented paraconsistent logic. In Chapter 20, On the Usefulnessof Paraconsistent Logic, Newton da Costa, Jean-Yves Beziau andÓtavio Bueno examine intuitive motivations to develop a paraconsistentlogic. These motivations are formally developed using semantic methodswhere in particular, bivaluations and truth-tables are used to character-ize paraconsistent logic. The authors then discuss the way in whichparaconsistent logic, as opposed to classical logic, demarcates inconsis-tency from triviality. (A theory is trivial when every sentence in thetheory’s language is a theorem.) They also examine why in paraconsis-tent logic one cannot infer everything from a contradiction.

As a result, paraconsistent logic opens up the possibility of investigat-ing the domain of what is inconsistent but not trivial. Why is it desirableto rescue inconsistent theories from the wreck? The reason is that inpractice we live with inconsistent theories. From 1870 to 1895 Cantorderived important theorems of set theory from two quite obvious princi-ples: the postulate of extensionality and the postulate of comprehension.Yet around 1902, Zermelo and Russell discovered a hidden inconsistencyin the second principle. However when the shaky foundations of set the-ory were brought to light, mathematicians and logicians did not abandonthe whole body of set theory. They decided instead to search for a wayof correcting the faulty postulate and found several solutions (Russell’stheory of types, Zermelo’s separation axiom etc. . . ) This historical factshows that an inconsistent theory can be useful, that working mathe-maticians do not derive anything whatever from an inconsistency andthat we need a logic if we want to continue to use reasoning duringthe span of time which elapses after the discovery of an inconsistencyand before the discovery of a solution which removes the inconsistency.Inventors of paraconsistent logic intended to provide such a logic. daCosta, Beziau and Bueno briefly consider applications of paraconsistent´logic to various domains. In mathematics they consider the formulationof set theory, in artificial intelligence the construction of expert systems,and in philosophy theories of belief change and rationality. With thesemotivations and applications in hand, the usefulness and legitimacy ofparaconsistent logic become hard to deny.

Introduction 23

According to relevance logic what is unsettling about so-called para-doxes of implication is that in each of them the antecedent seems irrele-vant to the consequent. Following ideas of precursors such as Ackermannand Anderson & Belnap, relevance logicians tend to reject laws that com-mit fallacies of relevance. The most basic system of relevance logic isthe system B+ that Paul Gochet, Pascal Gribomont and Didier Rosettoconsider in Chapter 21, Algorithms for Relevant Logic. Their mainpurpose is to investigate whether the connection method can be extendedto that basic system of relevance logic. A connection proof proceeds likea refutation constructed by tableaux or sequents. It starts with the de-nial of the formula to be proven and attempts to establish by applyingreduction rules which stepwise decompose the initial formula that sucha denial leads to a contradiction. The connection method which hasbeen recently extended to modal and intuitionistic logic is much moreefficient than the sequent calculi and tableau method. So it is very use-ful to extend it to other non classical logics especially to those used inartificial intelligence. Gochet, Gribomont and Rosetto begin their chap-ter by presenting the basic axiomatic system B+ of relevant logic. Theyalso briefly present Bloesch’s tableau method for B+ and next adaptWallen’s connection method to the system B+. The authors give a de-cision procedure which provides finite models for any satisfiable formulaof system B+. They also prove the soundness and the completeness oftheir extension. This is an important logical result.

Extensional languages with a pure denotational semantics are of avery limited interest in cognitive science. Intensional object languagesare needed in artificial intelligence as well as in philosophical logic andsemantics to deal with thoughts of agents who are often uncertain. How-ever, many natural intensional properties existing in artificial and nat-ural languages are hard to compute in the algorithmic way. In Chapter22, Logic, Randomness and Cognition, Michel de Rougemont showsthat randomized algorithms are necessary to represent well intensionsand to verify some specific relations in computer science. There are twomain intensional aspects to take into consideration in artificial intelli-gence namely the complexity and the reliability of data. When data areuncertain, the advantage of randomized algorithms is very clear accord-ing to de Rougemont for both the uncertainty and complexity can thenbe improved in the computation. Rougemont concentrates on the reli-ability of queries in order to illustrate this advantage. This importantcontribution to “exact philosophy” fits in with the previous chapter inwhich complexity issues were also raised.

Perceptions play a key role in human recognition, attitudes and ac-tion. In Chapter 23, Computing with Numbers to Computing


with Words — From Manipulation of Measurements to Ma-nipulation of Perceptions, Lofti Zadeh provides the foundations of acomputational theory of perception based on the methodology of com-puting with words. There is a deep-seated tradition in computer scienceof striving for progression from perceptions to measurements, and fromthe use of words to the use of numbers. Why and when, then, shouldwe compute with words and perceptions? As Zadeh points out, there isno other option when precision is desired but the needed information isnot available. Moreover when precision is not needed, the tolerance forimprecision can be exploited to achieve tractability, robustness, simplic-ity and low solution cost. Notice that human agents have a remarkablecapability for performing a wide variety of actions without any need formeasurements and computations. In carrying out actions like parkinga car and driving, we employ perceptions — rather than measurements— of distance, direction, speed, count, likelihood and intent.

Because of the bounded ability of sensory organs to resolve detail,perceptions are intrinsically imprecise. In Zadeh’s view, perceived val-ues of attributes are fuzzy and granular — a granule being a clump ofvalues drawn together by indistinguishability, similarity, proximity orfunctionality. In this perspective, a natural language is a useful sys-tem for describing perceptions. In Zadeh’s methodology, computationwith perceptions amounts to computing with words and sentences drawnfrom natural language labelling and describing perceptions. Computingwith words and perceptions provides a basis for an important generaliza-tion of probability theory. Zadeh’s point of departure is the assumptionthat subjective probabilities are, basically, perceptions of likelihood. Akey consequence of this assumption is that subjective probabilities aref-granular rather than numerical, as they are assumed to be in the stan-dard bivalent logic of probability theory. In the final analysis, Zadeh’stheory could open the door to adding to any measurement-based theorythe capability to operate on perception-based information.

Fuzzy logic, even more than relevant and paraconsistent logics, had toovercome deep-seated prejudices and hostility. Nowadays the hostilityhas vanished and the merits of fuzzy logic have been widely recognized.Like other non-standard logics, fuzzy logic brings together concern forlogic, for thought and for action.

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REASON, ACTIONAND COMMUNICATION

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Logic, Thought, and Action 1