knowledge representation دكترمحسن كاهاني kahani

Knowledge Representation

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Knowledge and its Meaning

Epistemology Types of Knowledge Knowledge Pyramid



Epistemology the science of knowledge

EPISTEMOLOGY ( Gr. episteme, "knowledge"; logos, "theory"),

branch of philosophy concerned with the theory of knowledge. The main problems with which epistemology is concerned are the definition of knowledge and related concepts, the sources and criteria of knowledge, the kinds of knowledge possible and the degree to which each is certain, and the exact relation between the one who knows and the object known.



Knowledge Definitionsknowlaedge \'nS-lij\ n [ME knowlege, fr. knowlechen to acknowledge, irreg. fr. knowen ] (14c) 1 obs : cognizance 2 a (1) : the fact or condition of knowing something with familiarity gained through experience or

association (2) : acquaintance with or understanding of a science, art, or technique b (1) : the fact or condition of being aware of something (2) : the range of one's information or understanding <answered to the best of my 4> c : the circumstance or condition of apprehending truth or fact through reasoning : cognition d : the fact or condition of having information or of being learned <a man of unusual 4> 3 archaic : sexual intercourse 4 a : the sum of what is known : the body of truth, information, and principles acquired by mankind b archaic : a branch of learning syn knowledge, learning, erudition, scholarship mean what is or can be

known by an individual or by mankind. knowledge applies to facts or ideas acquired by study, investigation, observation, or experience <rich in the knowledge of human nature>. learning applies to knowledge acquired esp. through formal, often advanced, schooling <a book that demonstrates vast learning >. erudition strongly implies the acquiring of profound, recondite, or bookish learning <an erudition unusual even in a scholar>. scholarship implies the possession of learning characteristic of the advanced scholar in a specialized field of study or investigation <a work of first-rate literary scholarship >.

[Merriam-Webster, 1994]



Types of Knowledge

a priori knowledge comes before knowledge perceived through senses considered to be universally true

a posteriori knowledge knowledge verifiable through the senses may not always be reliable

procedural knowledge knowing how to do something

declarative knowledge knowing that something is true or false

tacit knowledge knowledge not easily expressed by language



Knowledge in Expert Systems

Conventional Programming

Knowledge-Based Systems

Algorithms

+ Data Structures

= Programs

Knowledge

+ Inference

= Expert System



Review of Knowledge Representation Criteria

Definition of Knowledge Representation: A formalism for representing in a computer,

facts and other kinds of knowledge about a subject or specialty such that these facts and knowledge can be used in reasoning.



Criteria of Adequacy:Metaphysical Adequacy

The representation scheme cannot contradict the actual, real world circumstance, either by ignoring certain things that actually happen or by allowing things to happen that do not.

An expert system is a representation of the real world, therefore it must reflect the real world.



Epistemic Adequacy

The K.R. scheme must be able to represent facts, usually about individuals and their relations and attributes.



Heuristic Adequacy

The K.R. scheme must be able to express the reasoning used to solve a problem. Probably the most difficult of these criteria to meet.



Computational Tractability

The K.R. scheme must be able to manipulate the representation using a computer system.



Expressiveness

These criteria are "nice", but not necessary. Adequacy criteria are necessary



Lack of Ambiguity

only one interpretation



Clarity

Can humans understand what is being said as well as the computer?

Can take this further: we would like the use of the KR to increase or clarify our knowledge of the domain.



Uniformity

Able to handle all types of knowledge we need to represent in a uniform fashion.

Difficult to represent every type of knowledge (heuristic vs fact, etc) in a different manner.



Notational convenience

does the knowledge fit the representation?

is the developer comfortable with the

representation scheme?



Declarativeness not procedural, "processing" should not change or

impact the meaning. A representation is declarative if:

the meanings of the statements are independent of the use made of the statements

referential transparency also exists. Referential transparency exists when equivalent expressions can always be substituted for one another while preserving the truth value of the statements in which they occur.



Knowledge Representation Methods

Production Rules Structured Objects

Semantic Nets Frames

Logic



Production Rule Representations

Consists of <condition,action> pairs Agent checks if a condition holds

If so, the production rule “fires” and the action is carried out This is a recognize-act cycle

Given a new situation (state) Multiple production rules will fire at once Call this the conflict set Agent must choose from this set

Call this conflict resolution Production system is any agent

Which performs using recognize-act cycles



Case Studies Production Rules sample domains

e.g. theorem proving, determination of prime numbers, distinction of objects (e.g. types of fruit, trees vs. telephone poles, churches vs. houses, animal species)

suitability of production rules basic production rules

no salience, certainty factors, arithmetic rules in ES/KBS

salience, certainty factors, arithmetic e.g. CLIPS, Jess

enhanced rules procedural constructs

e.g. loops objects

e.g. COOL, Java objects fuzzy logic

e.g. FuzzyCLIPS, FuzzyJ



Advantages of Production Rules

simple and easy to understand straightforward implementation

in computers possible formal foundations for some

variants



Problems with Production Rules

simple implementations are very inefficient

some types of knowledge are not easily expressed in such rules

large sets of rules become difficult to understand and maintain



Semantic Nets graphical representation for propositional information originally developed by M. R. Quillian as a model for

human memory labeled, directed graph nodes represent objects, concepts, or situations

labels indicate the name nodes can be instances (individual objects) or classes

(generic nodes) links represent relationships

the relationships contain the structural information of the knowledge to be represented

the label indicates the type of the relationship



Example



Relationships without relationships, knowledge is an unrelated

collection of facts reasoning about these facts is not very interesting

inductive reasoning is possible relationships express structure in the collection of

facts this allows the generation of meaningful new

knowledge generation of new facts generation of new relationships



Types of Relationships relationships can be arbitrarily defined by the

knowledge engineer allows great flexibility for reasoning, the inference mechanism must know how

relationships can be used to generate new knowledge inference methods may have to be specified for every

relationship frequently used relationships

IS-A relates an instance (individual node) to a class (generic

node) AKO (a-kind-of)

relates one class (subclass) to another class (superclass)



Objects and Attributes

attributes provide more detailed information on nodes in a semantic network often expressed as properties

combination of attribute and value attributes can be expressed as relationships

e.g. has-attribute



Implementation Questions simple and efficient representation schemes for

semantic nets tables that list all objects and their properties tables or linked lists for relationships

conversion into different representation methods predicate logic

nodes correspond variables or constants links correspond to predicates

propositional logic nodes and links have to be translated into propositional

variables and properly combined with logical connectives



OAV-Triples object-attribute-value triplets

can be used to characterize the knowledge in a semantic net

quickly leads to huge tables

Object Attribute Value

Astérix profession warrior

Obélix size extra large

Idéfix size petite

Panoramix wisdom infinite



Problems Semantic Nets expressiveness

no internal structure of nodes relationships between multiple nodes no easy way to represent heuristic information extensions are possible, but cumbersome best suited for binary relationships

efficiency may result in large sets of nodes and links search may lead to combinatorial explosion

especially for queries with negative results usability

lack of standards for link types naming of nodes

classes, instances



Frame represents related knowledge about a subject

provides default values for most slots frames are organized hierarchically

allows the use of inheritance knowledge is usually organized according to cause and effect

relationships slots can contain all kinds of items

rules, facts, images, video, comments, debugging info, questions, hypotheses, other frames

slots can also have procedural attachments procedures that are invoked in specific situations involving a

particular slot on creation, modification, removal of the slot value



Simple Frame ExampleSlot Name Filler

name Astérix

height small

weight low

profession warrior

armor helmet

intelligence very high

marital status presumed single



Overview of Frame Structure two basic elements: slots and facets (fillers, values, etc.); typically have parent and offspring slots

used to establish a property inheritance hierarchy (e.g., specialization-of)

descriptive slots contain declarative information or data (static knowledge)

procedural attachments contain functions which can direct the reasoning process (dynamic

knowledge) (e.g., "activate a certain rule if a value exceeds a given level")

data-driven, event-driven ( bottom-up reasoning) expectation-drive or top-down reasoning pointers to related frames/scripts - can be used to transfer control to

a more appropriate frame



Slots each slot contains one or more facets facets may take the following forms:

values default

used if there is not other value present range

what kind of information can appear in the slot if-added

procedural attachment which specifies an action to be taken when a value in the slot is added or modified (data-driven, event-driven or bottom-up reasoning)

if-needed procedural attachment which triggers a procedure which goes out to get information

which the slot doesn't have (expectation-driven; top-down reasoning) other

may contain frames, rules, semantic networks, or other types of knowledge

[Rogers 1999]



Usage of Frames

filling slots in frames can inherit the value directly can get a default value these two are relatively inexpensive can derive information through the attached

procedures (or methods) that also take advantage of current context (slot-specific heuristics)

filling in slots also confirms that frame or script is appropriate for this particular situation

[Rogers 1999]



Restaurant Frame Example

generic template for restaurants different types default values

script for a typical sequence of activities at a restaurant



Generic Restaurant FrameGeneric RESTAURANT Frame

Specialization-of: Business-EstablishmentTypes: range: (Cafeteria, Fast-Food, Seat-Yourself, Wait-To-Be-Seated) default: Seat-Yourself if-needed: IF plastic-orange-counter THEN Fast-Food, IF stack-of-trays THEN Cafeteria, IF wait-for-waitress-sign or reservations-made THEN Wait-To-Be-Seated, OTHERWISE Seat-Yourself.Location: range: an ADDRESS if-needed: (Look at the MENU)Name: if-needed: (Look at the MENU)Food-Style: range: (Burgers, Chinese, American, Seafood, French) default: American if-added: (Update Alternatives of Restaurant)Times-of-Operation: range: a Time-of-Day default: open evenings except MondaysPayment-Form: range: (Cash, CreditCard, Check, Washing-Dishes-Script)Event-Sequence: default: Eat-at-Restaurant ScriptAlternatives: range: all restaurants with same Foodstyle if-needed: (Find all Restaurants with the same Foodstyle)



Frame Advantages

fairly intuitive for many applications similar to human knowledge organization suitable for causal knowledge easier to understand than logic or rules

very flexible



Frame Problems it is tempting to use frames as definitions of concepts

not appropriate because there may be valid instances of a concept that do not fit the stereotype

exceptions can be used to overcome this can get very messy

inheritance not all properties of a class stereotype should be

propagated to subclasses alteration of slots can have unintended consequences in

subclasses



Introduction to Logic

expresses knowledge in a particular mathematical notation

All birds have wings --> x. Bird(x) -> HasWings(x) rules of inference

guarantee that, given true facts or premises, the new facts or premises derived by applying the rules are also true

All robins are birds --> x Robin(x) -> Bird(x) given these two facts, application of an inference rule gives:

x Robin(x) -> HasWings(x)



Logic and Knowledge rules of inference act on the superficial structure or syntax

of the first 2 formulas doesn't say anything about the meaning of birds and robins could have substituted mammals and elephants etc.

major advantages of this approach deductions are guaranteed to be correct to an extent that

other representation schemes have not yet reached easy to automate derivation of new facts

problems computational efficiency uncertain, incomplete, imprecise knowledge



Summary of Logic Languages propositional logic

facts true/false/unknown

first-order logic facts, objects, relations true/false/unknown

temporal logic facts, objects, relations, times true/false/unknown

probability theory facts degree of belief [0..1]

fuzzy logic degree of truth degree of belief [0..1]



Syntax of Propositional Logic

A BNF (Backus-Naur Form) grammar of sentences in propositional logic

Sentence -> AtomicSentence | ComplexSentence

AtomicSentence -> True | False | P | Q | R | ...

ComplexSentence -> (Sentence)

| Sentence Connective Sentence

| ~Sentence

Connective -> ^ | V | <=> | =>



Inference Rules

more efficient than truth tables



Modus Ponens

eliminates =>

(X => Y), X

______________

Y If it rains, then the streets will be wet. It is raining. Infer the conclusion: The streets will be wet.

(affirms the antecedent)



Modus tollens (X => Y), ~Y _______________ ¬ X

If it rains, then the streets will be wet. The streets are not wet. Infer the conclusion: It is not raining.

NOTE: Avoid the fallacy of affirming the consequent: If it rains, then the streets will be wet. The streets are wet. cannot conclude that it is raining.

If Bacon wrote Hamlet, then Bacon was a great writer. Bacon was a great writer. cannot conclude that Bacon wrote Hamlet.



Syllogism

chain implications to deduce a conclusion)

(X => Y), (Y => Z)

_____________________

(X => Z)



Resolution

(X v Y), (~Y v Z)

_________________

(X v Z) basis for the inference mechanism in the Prolog

language and some theorem provers



Complexity issues truth table enumerates 2n rows of the table for any proof

involving n symbol it is complete computation time is exponential in n

checking a set of sentences for satisfiability is NP-complete but there are some circumstances where the proof only involves

a small subset of the KB, so can do some of the work in polynomial time

if a KB is monotonic (i.e., even if we add new sentences to a KB, all the sentences entailed by the original KB are still entailed by the new larger KB), then you can apply an inference rule locally (i.e., don't have to go checking the entire KB)



Predicate Logic

new concepts (in addition to propositional logic) complex objects

terms relations

predicates quantifiers

syntax semantics inference rules usage



Objects

distinguishable things in the real world people, cars, computers, programs, ...

frequently includes concepts colors, stories, light, money, love, ...

properties describe specific aspects of objects

green, round, heavy, visible, can be used to distinguish between objects



Relations

establish connections between objects relations can be defined by the designer or user

neighbor, successor, next to, taller than, younger than, …

functions are a special type of relation non-ambiguous: only one output for a given

input



Syntax also based on sentences, but more complex

sentences can contain terms, which represent objects constant symbols: A, B, C, Franz, Square1,3, … stand for unique objects ( in a specific context)

predicate symbols: Adjacent-To, Younger-Than, ... describes relations between objects

function symbols: Father-Of, Square-Position, … the given object is related to exactly one other object



Semantics provided by interpretations for the basic constructs

usually suggested by meaningful names constants

the interpretation identifies the object in the real world predicate symbols

the interpretation specifies the particular relation in a model may be explicitly defined through the set of tuples of objects that satisfy the

relation function symbols

identifies the object referred to by a tuple of objects may be defined implicitly through other functions, or explicitly through tables



Terms logical expressions that specify objects constants and variables are terms more complex terms are constructed from function

symbols and simpler terms, enclosed in parentheses basically a complicated name of an object

semantics is constructed from the basic components, and the definition of the functions involved either through explicit descriptions (e.g. table), or

via other functions



Unification an operation that tries to find consistent variable bindings

(substitutions) for two terms a substitution is the simultaneous replacement of variable

instances by terms, providing a “binding” for the variable without unification, the matching between rules would be

restricted to constants often used together with the resolution inference rule unification itself is a very powerful and possibly complex

operation in many practical implementations, restrictions are imposed

e.g. substitutions may occur only in one direction (“matching”)



Atomic Sentences

state facts about objects and their relations specified through predicates and terms

the predicate identifies the relation, the terms identify the objects that have the relation

an atomic sentence is true if the relation between the objects holds this can be verified by looking it up in the set of

tuples that define the relation



Complex Sentences

logical connectives can be used to build more complex sentences

semantics is specified as in propositional logic



Quantifiers

can be used to express properties of collections of objects eliminates the need to explicitly enumerate all

objects predicate logic uses two quantifiers

universal quantifier

existential quantifier



Universal Quantification

states that a predicate P is holds for all objects x in the universe under discourse x P(x)

the sentence is true if and only if all the individual sentences where the variable x is replaced by the individual objects it can stand for are true



Existential Quantification

states that a predicate P holds for some objects in the universe x P(x)

the sentence is true if and only if there is at least one true individual sentence where the variable x is replaced by the individual objects it can stand for



Horn clauses or sentences

class of sentences for which a polynomial-time inference procedure exists P1 P2 ... Pn => Q

where Pi and Q are non-negated atomic sentences

not every knowledge base can be written as a collection of Horn sentences

Horn clauses are essentially rules of the form If P1 P2 ... Pn then Q



Comparison Between Knowledge

Representation Schemes



Similarity Despite everything, there are many similarities

between the three knowledge representation schemes.

All express a binary relationship between two objects: entity-attribute-triples in production rules, instance-slot-filler in structured objects, and relationship between two parameters in predicate logic.



Similarity Production rules and structured objects are considered

more object centered, while logic is considered more relationship centered, but we can map from one to the other.

Predicate logic makes is easier to represent non-binary relationships, other formalisms require the creation of a linking entity.

Frames overcome some of the complexity by grouping like information together).



Similarity

With respect to the first three criteria (metaphysical, epsitemic, and heuristic) each representation scheme is adequate.

With respect to the fourth criteria (computational tractability), Predicate logic has some unique qualities (discuss shortly).



Production Rules

High notational convenience. Programmers are very comfortable working

with production rules. More expert systems have used production rules

than other knowledge representation schemes



Structured Objects

The biggest problem is default reasoning, which creates a great deal of trouble. the ability to "inherit properties" from object

more highly placed in the hierarchy Ironically, the ability to handle default

reasoning was part of the initial attraction of these representation



Structured Objects

When we attempt to implement "exception processing" we lose the ability to express universal truths!

Not much use to have a knowledge base that cannot express universal truths within its domain!

Best problems such as taxonomizing.



Predicate Logic

Special issues with respect to computational tractability.

We limit Logic Representation to Horn Clauses so that logic more computationally tractable.

The question is whether or not we lost "expressiveness" by limiting to Horn clauses.



Predicate Logic

Limit predicate calculus in two ways:

1. only one literal on the left hand side of the clause

2. cannot have negated literals



Predicate Logic - One Problem:

Treat negation as failure. conclude that a literal is false unless we show it to be

true. This a closed world assumption

when all our predicates are taken together we know the necessary conditions for the truth of the predicate.

This seems reasonable, but consider trying to enumerate the conditions for things like: birds that don't fly, etc.



Predicate Logic

With negation as failure must know how our knowledge base is going to be

used (what sort of deductions it must make) so that we present the predicates properly (we may need to order them in a particular way).

Difficult to envision every eventuality. Loose the declarative nature of logic. Can no longer interpret the knowledge "neutrally".



Predicate Logic - Second Problem:

Lose the non-monotonic nature of the reasoning process. In a monotonic system if a certain conclusion can be

drawn from a body of evidence, then adding to the evidence cannot prevent the conclusion from being drawn.

KB |- P then KB + delta |- P for any delta. By interpreting negation as failure, we lose the non-

monotonic nature that classical logic allows us.



Predicate Logic

Structured objects using an inheritance property appear to avoid this issue, but the problems of default values in reasoning leads to another set of problems.

With respect to Predicate Logic, can conclude that its expressiveness is adequate, but be aware of the limitations.



Predicate Logic There are similar problems with the other knowledge

representation schemes with respect to negation. What is meant by the absence of a relationship

between to objects in a semantic network? Is there NO relationship or simply lack of knowledge

about the existence of a relationship. With the closed-world assumption, the lack of link

means that the relationship does not exist.



Choosing a way to represent knowledge

The nature of the search space

The nature of the data

The nature of the knowledge




If some basic problem solving approach will work (i.e. a brute force approach that explicitly examines all alternatives), then use it! If the problem space is relatively small and data

and rules are reliable, exhaustive search via Prolog or Lisp may be best.




Consider ways to factor the search space. ”Pruning" branches that are unlikely Decomposing the domain into independent

components that can be processes separately



The nature of the data

If the data has some inherent structure to it, you may be able to fit it to a structured object representation easily.

Static knowledge is generally easier to use with structured objects than dynamic knowledge (dynamic knowledge changes during the execution of the program).



The nature of the data Consider use multiple representation schemes to

represent all of the knowledge. Be careful how you organize the knowledge in the

knowledge base. ”Declarativeness", is rarely achieved. Therefore, when executing the system, the ordering of

knowledge within the knowledge base may affect the solution, certainly the solution path.



The nature of the knowledge

Is the reasoning along the lines of

this and that and this other thing suggest A production rules with certainty factors are in

order

Or is it more categorical as with standard logic



Summary Despite all the work being done on knowledge

representation, there is relatively little advice on how to pick a knowledge representation scheme.

Even when using a shell, do not ignore the differences between knowledge representation schemes, otherwise you may end up with an unusable expert systems.

knowledge representation دكترمحسن كاهاني kahani

Documents

criteria of knowledge

theory of knowledge

knowledge logos

knowledge representation

kinds of knowledge possible

bookish learning

real world circumstance

heuristic adequacythe