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© 2002 Franz J. Kurfess Logic and Reasoning 1 CPE/CSC 481: Knowledge-Based Systems Dr. Franz J. Kurfess Computer Science Department Cal Poly.

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Presentation on theme: "© 2002 Franz J. Kurfess Logic and Reasoning 1 CPE/CSC 481: Knowledge-Based Systems Dr. Franz J. Kurfess Computer Science Department Cal Poly."— Presentation transcript:

1 © 2002 Franz J. Kurfess Logic and Reasoning 1 CPE/CSC 481: Knowledge-Based Systems Dr. Franz J. Kurfess Computer Science Department Cal Poly

2 © 2002 Franz J. Kurfess Logic and Reasoning 2 Course Overview u Introduction u Knowledge Representation u Semantic Nets, Frames, Logic u Reasoning and Inference u Predicate Logic, Inference Methods, Resolution u Reasoning with Uncertainty u Probability, Bayesian Decision Making u Expert System Design u ES Life Cycle u CLIPS Overview u Concepts, Notation, Usage u Pattern Matching u Variables, Functions, Expressions, Constraints u Expert System Implementation u Salience, Rete Algorithm u Expert System Examples u Conclusions and Outlook

3 © 2002 Franz J. Kurfess Logic and Reasoning 3 Overview Logic and Reasoning u Motivation u Objectives u Knowledge and Reasoning u logic as prototypical reasoning system u syntax and semantics u validity and satisfiability u logic languages u Reasoning Methods u propositional and predicate calculus u inference methods u Knowledge Representation and Reasoning Methods u Production Rules u Semantic Nets u Schemata and Frames u Logic u Important Concepts and Terms u Chapter Summary

4 © 2002 Franz J. Kurfess Logic and Reasoning 4 Logistics u Term Project u Lab and Homework Assignments u Exams u Grading

5 © 2002 Franz J. Kurfess Logic and Reasoning 5 Bridge-In

6 © 2002 Franz J. Kurfess Logic and Reasoning 6 Pre-Test

7 © 2002 Franz J. Kurfess Logic and Reasoning 7 Motivation

8 © 2002 Franz J. Kurfess Logic and Reasoning 8 Objectives

9 © 2002 Franz J. Kurfess Logic and Reasoning 9 Evaluation Criteria

10 © 2002 Franz J. Kurfess Logic and Reasoning 10 Chapter Introduction u Review of relevant concepts u Overview new topics u Terminology

11 © 2002 Franz J. Kurfess Logic and Reasoning 11 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)

12 © 2002 Franz J. Kurfess Logic and Reasoning 12 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

13 © 2002 Franz J. Kurfess Logic and Reasoning 13 Validity and Satisfiability  a sentence is valid or necessarily true if and only if it is true under all possible interpretations in all possible worlds  also called a tautology IsBird(Robin) V ~IsBird(Robin) Stench[1,1] V ~Stench[1,1] OpenArea[square in front of me] V Wall[square in front of me]  is NOT a tautology!  assumes every square has either a wall or an open area, so not true for all worlds "If every square has either a wall or an open area in it, then OpenArea[square in front of me] V Wall[square in front of me]"  is a tautology...  a sentence is satisfiable iff there is some interpretation in some world for which it is true  a sentence that is not satisfiable is unsatisfiable (also known as a contradiction):  It is raining and it is not raining.

14 © 2002 Franz J. Kurfess Logic and Reasoning 14 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]

15 © 2002 Franz J. Kurfess Logic and Reasoning 15 Propositional Logic u Syntax u Semantics u Validity and Inference u Models u Inference Rules u Complexity

16 © 2002 Franz J. Kurfess Logic and Reasoning 16 Syntax u symbols  logical constants True, False  propositional symbols P, Q, … u logical connectives u conjunction , disjunction , u negation , u implication , equivalence  u parentheses ,  u sentences u constructed from simple sentences u conjunction, disjunction, implication, equivalence, negation

17 © 2002 Franz J. Kurfess Logic and Reasoning 17 BNF Grammar Propositional Logic Sentence  AtomicSentence | ComplexSentence AtomicSentence  True | False | P | Q | R |... ComplexSentence  (Sentence ) | Sentence Connective Sentence |  Sentence Connective   |  |  |  ambiguities are resolved through precedence      or parentheses e.g.  P  Q  R  S is equivalent to (  P)  (Q  R))  S

18 © 2002 Franz J. Kurfess Logic and Reasoning 18 Semantics u interpretation of the propositional symbols and constants u symbols can be any arbitrary fact u sentences consisting of only a propositional symbols are satisfiable, but not valid  the constants True and False have a fixed interpretation  True indicates that the world is as stated  False indicates that the world is not as stated u specification of the logical connectives u frequently explicitly via truth tables

19 © 2002 Franz J. Kurfess Logic and Reasoning 19 Truth Tables for Connectives  P True True False False P  Q False True P  Q False True P  Q True False True P  Q True False True Q False True False True P False True

20 © 2002 Franz J. Kurfess Logic and Reasoning 20 Validity and Inference u truth tables can be used to test sentences for validity u one row for each possible combination of truth values for the symbols in the sentence  the final value must be True for every sentence

21 © 2002 Franz J. Kurfess Logic and Reasoning 21 Propositional Calculus  properly formed statements that are either True or False  syntax  logical constants, True and False  proposition symbols such as P and Q  logical connectives: and ^, or V, equivalence, implies => and not ~  parentheses to indicate complex sentences  sentences in this language are created through application of the following rules  True and False are each (atomic) sentences  Propositional symbols such as P or Q are each (atomic) sentences  Enclosing symbols and connective in parentheses yields (complex) sentences, e.g., (P ^ Q)

22 © 2002 Franz J. Kurfess Logic and Reasoning 22 Complex Sentences  Combining simpler sentences with logical connectives yields complex sentences  conjunction  sentence whose main connective