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Introduction to Knowledge Representation and Navya Nyaya
Dr. Shrinivasa Varakhedi
Motivation
Knowledge Representation is a multi-disciplinary subject that applies theories and techniques from different fields
1. Logic – that provides Formal Structures for representation and rules of inference
2. Ontology – defines the kinds of things that exist in the application domain
3. Epistemology – that provides a base for knowledge representation and its implementation.
Where Navya Nyaya system has a lot to contribute and participate in Knowledge revolution.
Knowledge Representation Language
A KRL is a way of writing down beliefs (or other kinds of mental states) Not really a language, any more than a programming language is. Needs to be
– Very expressive: In it, we need to be able to express anything we want.
– What might some possibilities be?
KRL Candidates: NL ?Expressive! Suitably declarative
But: – Ambiguous
» No need do give eg. !– Context-dependent meanings
» Pronouns, unspecified relations – In other words, a KR language should represent facts in form that expresses what they mean afterthey have been understood.
KRL
IT should be
Expressive (Readable by domain expert)
Unambiguous
Context-independent
Compositional
Computable
Actual KRLs
There have been various candidates proposed for KRLs over the years. One set of proposals is that formal logicbe used as a basic framework for such languages.
Logic consists of – A language
» which tells us how to build up sentences in the language (i.e., syntax)
» and what those sentences mean (i.e, semantics) – An inference procedure
» Which tells us which sentences are valid inferences from other sentences
Alternatives? Conceptual Graphs
A knowledge representation language is a way to encode mental states.
Conceptual graphs (CGs) are a system of logic based on the existential graphs of Charles Sanders Peirce and the semantic networks of artificial intelligence. They express meaning in a form that is logically precise, humanly readable, and computationally tractable. With their direct mapping to language, conceptual graphs serve as an intermediate language for translating computer-oriented formalisms to and from natural languages. With their graphic representation, they serve as a readable, but formal design and specification language. CGs have been implemented in a variety of projects for information retrieval, database design, expert systems, and natural language processing.
Conceptual Graphs
Conceptual Graph is complete bipartite oriented graph, where each node is either a concept or a relation between two concepts, there is one or two edges each going to concepts, and each concept may represent another conceptual graph
dog brownhas
John is going to Boston by a bus.
CGExpr & NNExpr
[Go]- (Agnt)®[Person: John] (Dest)®[City: Boston] (Inst)®[Bus].
Gamanam - kartA – John- Karma – Boston- Karanam - Bus
Tom believes that Mary wants to marry Sailor.
CGE & NNE
[Person: Tom]¬(Expr)¬[Believe]®(Thme)- [Proposition: [Person: Mary *x]¬(Expr)¬[Want]®(Thme)- [Situation: [?x]¬(Agnt)¬[Marry]®(Thme)®[Sailor] ]]. Sva-kartrka-Sailor-karmaka-vivAha—viSayaka-icChA-prakAraka-Mary-visheSyaka—jnAnavAn Tom. Svam = Mary.
Navya Nyaya Language
Navya Nyaya system of Logic has developed a Language for representing knowledge1. Close to NL 2. It is NOT a meta-language or Artificial L, but a Restricted Language based on Sanskrit3. Well defined Technical Terms 4. Six basic Relations 5. Expressive of all types of different cognitions
Six Basic Relations
AdhAra-Adheya-bhAvaNirUpya-nirUpaka-bhAvaPratiyogi-anuyogi-bhAva (Sambandha)Pratiyogi-anuyogi-bhAva (AbhAva)ViSayatAAvacCedakatAPratibandhakatA
Unique Features of NNL
Difference in Perception and other cognitions– Uddeshya-vidheya-bhAva– “Mountain has fire” is a perception that grasps both
the contents simultaneously.– “Mountain has fire” is an inference which attributes
only “fire” to the mountain already known fact.This distinction is present even in the Language
usages.
Unique features of NL (contd)
Verbal cognition that has been generated by Sentence is distinct in its form. - “Pot is red” – expression means that “Pot” is identical with “Red”.- On the other hand the perception senses the Pot as having Red-color – as “Pot has Redness”
Such subtle distinctions make a lot differences.
Differences & commonality of True and false Cognitions
In NNL you can express a cognition with out revealing its truth or falsity– “Here is a silver” – simply `rajata-viSayaka-jnAnam.
At the same time you have devices to show the difference between them.– On a shell – shukti-niStha-visheSyatA-nirUpita-rajatatva-
niStha-prakAratAkam jnAnam.– In a silver shop – rajata-niStha- shukti-niStha-visheSyatA-
nirUpita-rajatatva-niStha-prakAratAkam jnAnam
Distinction among contents of cognitions
NNL makes clear distinction among the contents of a cognition.Every cognition objectifies three type of contents– VisheSya– PrakAra– SamsargaApart from this you may find even more subtle distinction
with mode of these types of Contents.“Floor has chair and table” Vs “Chair-possessing floor has table”
AdhAra-Adheya-bhAva(Relation of locus-located)
Pot has colorPot has waterWater has tasteFloor has absence of Pot
In all these examples the two things are related with the relation of AdhAra-adheya-bhAva.
All the properties will have this link with their locus.
NirUpya-nirUpaka-bhAva
Rama is son of DasharathaSita is wife of RamaVishvamitra is guru of Rama and Lakshmana
Here the relational properties can not be understood with out their counter-relatives.
These counter-relatives are NirUpakas.All relational properties will have this link with their co-
relatives.
Pratiyogi-anuyogi-bhAva
Face has similarity of moon.
In this example, “similarity” has two relatives :Face & Moon.Face is anuyogi of similarityMoon is pratiyogi of similarity
AbhAva-pratiyogi
To describe absence of something, NN-ontology force you to accept a category called “absence”.“Pot is absent in the room” – means absence of pot is present in the room.
Here “Pot’ is pratiyogi = absentee and “room” is anuyogi = location of absence.
AvacCedaka – Concept of limiter
To show clear distinction in different cognitions and their forms, a new concept called “avacCedaka” is introduced by NN. This relation reduces ambiguity.Simple example :
“Pot has red-color” – inherence“Pot has water” - contact
Some expressions with modern notations
[samavAya]-(avacCinna)-[[[Gandhtva]-(avacCinna)-[[Gandha]-(niStha)-[AdheytA]]]]-(nirUpita)-[adhikaraNatA]-(vatI)-[PrthivI]
Several such examples are worked out.Let’s see the computability of Cg and similar
expressions…..(Of course NNL gets thru this test)
A monkey scratches its ear with a pawn.
.
monkey scratchagent object ear
instrument
pawpart of
part of
Conceptual Graphs
FOPL transformation to CG– for each node predicate– general concept variable, specific concept atom
type:instance type(instance) – relation n-ary predicat relation(in1, in2, …, inn) with
arguments conncecting neighbouring concepts– CG is existencionally quantified conjunction of these predicates
X (dog(emma) color(emma,X) brown(X)) dog:Emmabrown
has
FOPL transformation to CG– for each node predicate– general concept variable, specific concept atom
type:instance type(instance) – relation n-ary predicat relation(in1, in2, …, inn) with
arguments conncecting neighbouring concepts– CG is existencionally quantified conjunction of these predicates
X (dog(emma) color(emma,X) brown(X))
The CG Inference Task
Given: an initial scenario CGa query (= unknown node in the scenario)
Find: a sequence of joins which instantiate that node (answer the query)
objperson:joe necktieagnt buy:b01
buy:b01
inst
?
Scenario:
Query:
Goal: find ?
(“what is the instrument of the buy?” Ans: $10)
Inference using Joins
objperson:joe necktiebuy:b01agnt
inst
?
Query: inst(b1,X)?Query: “What is the instrument of the buy?” (Ans: $10)
objperson physobjbuy:*xagnt
inst
money:@?
valueposs
schema for buy(x) is
inst
money:@?
valueposs
necktie:*x
value
schema for necktie(x) is
$10
worn-by
person
money:$10
worn-by
person
Ans: $10!
An alternative sequence of joins
objperson:joe necktiebuy:b01agnt
inst
?
Query: inst(b1,X)?
objperson physobjbuy:*xagnt
inst
money:@?
valueposs
schema for buy(x) is
inst
money:@?
valueposs
person:*x
part
head
part
body
schema for person(x) is
part
head
part
body
schema for head(x) is
head has hair
shaperound
has hair
shaperound
money:*x carry-in wallet
schema for money(x) is
carry-in wallet
CG and NNL - complimentary
CG has been found to be similar one to NN.CG can be extended on the basis of NN featuresNNL with modern symbols and notations could be tested on Intelligent systems.A Student pilot project is already undertaken.A serious study in this direction is yet to be made.