M ETHODS OF INFERENCE Hasan Zafari. M ETHODS OF INFERENCE What is reasoning? Inferences with rules...
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METHODS OF INFERENCE Hasan Zafari
M ETHODS OF INFERENCE Hasan Zafari. M ETHODS OF INFERENCE What is reasoning? Inferences with rules trees The inference tree Inference by Inheritance Inference
M ETHODS OF INFERENCE What is reasoning? Inferences with rules
trees The inference tree Inference by Inheritance Inference with
frames Reasoning with semantic networks Reasoning with logic
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KR L ANGUAGES AND N ATURAL L ANGUAGE how is a knowledge
representation language different from natural language e.g.
English, Spanish, German, natural languages are expressive, but
have evolved to meet the needs of communication, rather than
representation the meaning of a sentence depends on the sentence
itself and on the context in which the sentence was spoken e.g.
Look! sharing of knowledge is done without explicit representation
of the knowledge itself and they are ambiguous (e.g. small dogs and
cats)
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G OOD K NOWLEDGE R EPRESENTATION L ANGUAGES combines the best
of natural and formal languages: expressive concise unambiguous
independent of context what you say today will still be
interpretable tomorrow formal the knowledge can be represented in a
format that is suitable for computers effective there is an
inference procedure which can act on it to make new sentences
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R EASONING process of constructing new sentences from old ones
proper reasoning ensures that the new sentences represent facts
that actually follow from the facts that the old sentences
represent this relationship is called entailment and can be
expressed as KB |= alpha knowledge base KB entails the sentence
alpha
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W HAT I NFERENCE M ETHODS DO ? an inference procedure can do
one of two things: given a knowledge base KB, it can derive new
sentences that are (supposedly) entailed by KB KB |-- ==> KB |=
given a knowledge base KB and another sentence alpha, it can report
whether or not alpha is entailed by KB KB ==> KB |= an inference
procedure that generates only entailed sentences is called sound or
truth-preserving the record of operation of a sound inference
procedure is called a proof an inference procedure is complete if
it can find a proof for any sentence that is entailed
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T REES : M AKING D ECISIONS Trees / lattices are useful for
classifying objects in a hierarchical nature. Trees / lattices are
useful for making decisions. We refer to trees / lattices as
structures. Decision trees are useful for representing and
reasoning about knowledge. 7
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D ECISION T REE E XAMPLE 8
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http://en.akinator.com/ 9
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AND-OR T REES AND G OALS 1990s, PROLOG was used for commercial
applications in business and industry. PROLOG uses backward
chaining to divide problems into smaller problems and then solves
them. AND-OR trees also use backward chaining. AND-OR-NOT lattices
use logic gates to describe problems. 10
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I NHERITANCE Inheritance is one of the main kind of reasoning
done in semantic nets The ISA (is a) relation is often used to link
a class and its superclass. Some links (e.g. haspart ) are
inherited along ISA paths The semantics of a semantic net can be
relatively informal or very formal Often defined at the
implementation level Bird Robin Rusty isa Red isa Animal isa Wings
hasPart
Slide 14
I NFERENCE BY I NHERITANCE One of the main types of reasoning
done in a semantic net is the inheritance of values (properties)
along the subclass and instance links. Semantic networks differ in
how they handle the case of inheriting multiple different values.
All possible values are inherited, or Only the lowest value or
values are inherited 14
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M ULTIPLE I NHERITANCE A node can have any number of
superclasses that contain it, enabling a node to inherit properties
from multiple parent nodes and their ancestors in the network. It
can cause conflicting inheritance. Nixon Diamond (two contradictory
inferences from the same data) Person subclass non-pacifist Nixon
RepublicanQuaker pacifist subclass instance R Q N P ? !P
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C ONFLICT RESOLUTION double arrows signify deductive or strict
(i.e., non-defeasible) inferences single arrows signify defeasible
inferences, and strikethrough single arrows signify that the
negation of the pointed formula is defeasibly implied Penguins are
birds (no exceptions); Birds usually fly; and Penguins usually
don't fly. conflict Penguin Bird flies Penguin not-flies According
to the Specificity Principle an inference with a more specific
antecedent overrides a conflicting defeasible inference with a less
specific antecedent.
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F RAMES Frames semantic net with properties A frame represents
an entity as a set of slots (attributes) and associated values A
frame can represent a specific entry, or a general concept Frames
are implicitly associated with one another because the value of a
slot can be another frame Book Frame Slot Filler Title AI. A modern
Approach Author Russell & Norvig Year 2003 3 components of a
frame frame name attributes (slots) values (fillers: list of
values, range, string, etc.)
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F EATURES OF F RAME R EPRESENTATION More natural support of
values than semantic nets (each slots has constraints describing
legal values that a slot can take) Can be easily implemented using
object-oriented programming techniques Inheritance is easily
controlled
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I NHERITANCE Similar to Object-Oriented programming paradigm
Hotel Room what room where hotel contains hotel chair hotel phone
hotel bed Hotel Chair what chair height 20-40cm legs 4 Hotel Phone
what phone billing guest Hotel Bed what bed size king part mattress
Mattress price 100$
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: FrameNet 21
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I NFERENCE WITH FRAMES 22
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Reasoning with semantic networks - Knowledge explicitly
represented in a semantic network can be used to infer additional
facts which are NOT explicitly represented (1) Inferences may rely
on rules of common sense e.g.,For all objects X, Y, and Z if X is
on Y and Y is left of Z then X is left of Z in the example network
cup-1 is on saucer-1 and saucer-1 is left of teapot-1 it follows
the above general rule, then: cup-1 is left of teapot-1
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Inferences based on transitivity - Relationship is a is
transitive if X is a Y and Y is a Z then X is a Z holds for all
distinct objects X, Y and Z - Relationship part of is
transitive
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- Relationship supported by is transitive, allowing the
inference shown by the dotted line in the following semantic
network fragment - However, the relationship is on (i.e., resting
directly on) is not transitive cup-1 is on saucer-1 and saucer-1 is
on table-1 but cup-1 is not on table-1 - Relationships among people
brother of is transitive but not father of
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Inference based on inheritance - A node inherits information
from its related more general node - Add a general object node,
other nodes inherit its properties - Eases the task of coding
knowledge - Automatically infer information about related objects
in hierarchy Example: attribute purpose is inherited
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Inferences based on transitivity and inheritance Two steps
involved in the inference shown by the dotted line: Step 1.
inference based on transitivity Step 2. inference based on
inheritance
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Dealing with exceptions - Inheritance is a default mechanism
and exceptions do occur Canary Bird Wings Fly IS-A HAS TRAVEL
Tweety IS-A Penguin IS-A Animal Air BREATHE From the above semantic
network, it can be inferred that: Canary is a animal, Tweety is a
bird, Tweety is a animal, Penguin is a bird, Penguin is a animal,
Penguin travel fly ... IS-A
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- If an attributes value is explicitly represented in a
semantic net, it takes priority over the value that would otherwise
by inherited Step 1. Account for exceptions on local basis Step 2.
Link new node with information that over-ride the incorrectly
inherited information CanaryBird Wings Fly IS-A HAS TRAVEL Tweety
IS-A Penguin IS-A Animal Air BREATHE IS-A Walk TRAVEL
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S EMANTIC N ET O PERATION Bird Fly How do you travel? Fly
TRAVEL User How do you travel? Tweety How do you travel? Canary How
do you travel? Bird Fly TRAVEL Fly User
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A DVANTAGES & D ISADVANTAGES Advantages Explicit and
succinct Reduced search time Inheritance Has correspondence with
human memory Disadvantages No interpretation standards Invalid
inferences Combinatorial explosion: if a relation is false many or
all of the relations in the network must be examined.
Slide 32
Expert Systems: Principles and Programming, Fourth Edition32
Rules of Inference
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R EASONING WITH L OGIC
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Expert Systems: Principles and Programming, Fourth Edition34
Truth Table Modus Ponens
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Expert Systems: Principles and Programming, Fourth Edition35
Types of Logic Deduction reasoning where conclusions must follow
from premises Induction inference is from the specific case to the
general Analogy inferring conclusions based on similarities with
other situations Abduction reasoning back from a true condition to
the premises that may have caused the condition
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Expert Systems: Principles and Programming, Fourth Edition36
Deductive Logic Argument group of statements where the last is
justified on the basis of the previous ones Deductive logic can
determine the validity of an argument. Syllogism has two premises
and one conclusion Deductive argument conclusions reached by
following true premises must themselves be true
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Expert Systems: Principles and Programming, Fourth Edition37
Syllogisms vs. Rules Syllogism: All basketball players are tall.
Jason is a basketball player. Jason is tall. IF-THEN rule: IF All
basketball players are tall and Jason is a basketball player THEN
Jason is tall.
Comparing abduction, deduction, and induction Deduction: major
premise: All balls in the box are black minor premise: These balls
are from the box conclusion: These balls are black Abduction: rule:
All balls in the box are black observation: These balls are black
explanation: These balls are from the box Induction: case: These
balls are from the box observation: These balls are black
hypothesized rule: All ball in the box are black 40 A => B A
--------- B A => B B ------------- Possibly A Whenever A then B
------------- Possibly A => B Deduction reasons from causes to
effects Abduction reasons from effects to causes Induction reasons
from specific cases to general rules