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CPE/CSC 481: Knowledge-Based Systems Dr. Franz J. Kurfess Computer Science Department Cal Poly © 2002 Franz J. Kurfess Logic and Reasoning 1 Course Overview Introduction Knowledge Semantic Nets, Frames, Logic Reasoning with Uncertainty Probability, Bayesian Decision Making Expert and Inference Predicate Logic, Inference Methods, Resolution Reasoning Representation System Design CLIPS Overview Concepts, Notation, Usage Pattern Matching Variables, Functions, Expressions, Constraints Expert System Implementation Salience, Rete Algorithm Expert System Examples Conclusions and Outlook ES Life Cycle © 2002 Franz J. Kurfess Logic and Reasoning 2 Overview Logic and Reasoning Motivation Knowledge Representation and Reasoning Methods Objectives Knowledge logic as prototypical reasoning system syntax and semantics validity and satisfiability logic languages Reasoning and Reasoning Methods propositional and predicate calculus inference methods © 2002 Franz J. Kurfess Production Rules Semantic Nets Schemata and Frames Logic Important Concepts and Terms Chapter Summary Logic and Reasoning 3 Logistics Term Project Lab and Homework Assignments Exams Grading © 2002 Franz J. Kurfess Logic and Reasoning 4 Bridge-In © 2002 Franz J. Kurfess Logic and Reasoning 5 Pre-Test © 2002 Franz J. Kurfess Logic and Reasoning 6 Motivation © 2002 Franz J. Kurfess Logic and Reasoning 7 Objectives © 2002 Franz J. Kurfess Logic and Reasoning 8 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 ¥x Robin(x) -> HasWings(x) © 2002 Franz J. Kurfess of an inference rule gives: Logic and Reasoning 11 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 © 2002 Franz J. Kurfess Logic and Reasoning 12 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. © 2002 Franz J. Kurfess Logic and Reasoning 13 Summary of Logic Languages propositional 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 logic degree of truth degree of belief [0..1] © 2002 Franz J. Kurfess Logic and Reasoning 14 Propositional Logic Syntax Semantics Validity and Inference Models Inference Rules Complexity © 2002 Franz J. Kurfess Logic and Reasoning 15 Syntax symbols constants True, False propositional symbols P, Q, … logical connectives logical conjunction , disjunction , negation , implication , equivalence parentheses , sentences constructed from simple sentences conjunction, disjunction, implication, equivalence, negation © 2002 Franz J. Kurfess Logic and Reasoning 16 BNF Grammar Propositional Logic Sentence AtomicSentence ComplexSentence AtomicSentence | ComplexSentence True | False | P | Q | R | ... (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 © 2002 Franz J. Kurfess Logic and Reasoning 17 Semantics interpretation of the propositional symbols and constants symbols can be any arbitrary fact 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 specification frequently © 2002 Franz J. Kurfess of the logical connectives explicitly via truth tables Logic and Reasoning 18 Truth Tables for Connectives P Q False False True True False True False True © 2002 Franz J. Kurfess P PQ PQ PQ PQ True True False False False False False True False True True True True True False True True False False True Logic and Reasoning 19 Validity and Inference truth tables can be used to test sentences for validity one row for each possible combination of truth values for the symbols in the sentence the final value must be True for every sentence © 2002 Franz J. Kurfess Logic and Reasoning 20 Inference Rules more efficient than truth tables © 2002 Franz J. Kurfess Logic and Reasoning 26 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) © 2002 Franz J. Kurfess Logic and Reasoning 27 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. © 2002 Franz J. Kurfess Logic and Reasoning cannot conclude that Bacon wrote Hamlet. 28 Syllogism chain implications to deduce a conclusion) (X => Y), (Y => Z) _____________________ (X => Z) © 2002 Franz J. Kurfess Logic and Reasoning 29 More Inference Rules and-elimination and-introduction or-introduction double-negation unit elimination resolution © 2002 Franz J. Kurfess Logic and Reasoning 30 Resolution (X v Y), (~Y v Z) _________________ (X v Z) basis for the inference mechanism in the Prolog language and some theorem provers © 2002 Franz J. Kurfess Logic and Reasoning 31 Complexity issues table enumerates 2n rows of the table for any proof involving n symbol truth 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) © 2002 Franz J. Kurfess Logic and Reasoning 32 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 atoms not every knowledge base can be written as a collection of Horn sentences © 2002 Franz J. Kurfess Logic and Reasoning 33 Reasoning in Knowledge-Based Systems shallow and deep reasoning forward and backward chaining alternative inference methods metaknowledge © 2002 Franz J. Kurfess Logic and Reasoning 34 Shallow and Deep Reasoning shallow also called experiential reasoning aims at describing aspects of the world heuristically short inference chains possibly complex rules deep reasoning reasoning also called causal reasoning aims at building a model of the world that behaves like the “real thing” long inference chains often simple rules that describe cause and effect relationships © 2002 Franz J. Kurfess Logic and Reasoning 35 Examples Shallow and Deep Reasoning shallow reasoning IF a car has a good battery good spark plugs gas good tires THEN the car can move deep reasoning IF the battery is good THEN there is electricity IF there is electricity AND good spark plugs THEN the spark plugs will fire IF the spark plugs fire AND there is gas THEN the engine will run IF the engine runs AND there are good tires THEN the car can move © 2002 Franz J. Kurfess Logic and Reasoning 36 Forward Chaining given a set of basic facts, we try to derive a conclusion from these facts example: What can we conjecture about Clyde? IF elephant(x) THEN mammal(x) IF mammal(x) THEN animal(x) elephant (Clyde) modus ponens: IF p THEN q p q © 2002 Franz J. Kurfess unification: find compatible values for variables Logic and Reasoning 37 Forward Chaining Example IF elephant(x) THEN mammal(x) unification: IF mammal(x) THEN animal(x) find compatible values for variables elephant(Clyde) modus ponens: IF p THEN q p q IF elephant( x ) THEN mammal( x ) elephant (Clyde) © 2002 Franz J. Kurfess Logic and Reasoning 38 Forward Chaining Example IF elephant(x) THEN mammal(x) unification: IF mammal(x) THEN animal(x) find compatible values for variables elephant(Clyde) modus ponens: IF p THEN q p q IF elephant(Clyde) THEN mammal(Clyde) elephant (Clyde) © 2002 Franz J. Kurfess Logic and Reasoning 39 Forward Chaining Example IF elephant(x) THEN mammal(x) unification: IF mammal(x) THEN animal(x) find compatible values for variables elephant(Clyde) modus ponens: IF p THEN q p q IF mammal( x ) THEN animal( x ) IF elephant(Clyde) THEN mammal(Clyde) elephant (Clyde) © 2002 Franz J. Kurfess Logic and Reasoning 40 Forward Chaining Example IF elephant(x) THEN mammal(x) unification: IF mammal(x) THEN animal(x) find compatible values for variables elephant(Clyde) modus ponens: IF p THEN q p q IF mammal(Clyde) THEN animal(Clyde) IF elephant(Clyde) THEN mammal(Clyde) elephant (Clyde) © 2002 Franz J. Kurfess Logic and Reasoning 41 Forward Chaining Example IF elephant(x) THEN mammal(x) unification: IF mammal(x) THEN animal(x) find compatible values for variables elephant(Clyde) modus ponens: IF p THEN q p animal( q x ) IF mammal(Clyde) THEN animal(Clyde) IF elephant(Clyde) THEN mammal(Clyde) elephant (Clyde) © 2002 Franz J. Kurfess Logic and Reasoning 42 Forward Chaining Example IF elephant(x) THEN mammal(x) unification: IF mammal(x) THEN animal(x) find compatible values for variables elephant(Clyde) modus ponens: IF p THEN q p animal(Clyde) q IF mammal(Clyde) THEN animal(Clyde) IF elephant(Clyde) THEN mammal(Clyde) elephant (Clyde) © 2002 Franz J. Kurfess Logic and Reasoning 43 Backward Chaining © 2002 Franz J. Kurfess Logic and Reasoning 44 Backward Chaining try to find supportive evidence (i.e. facts) for a hypothesis example: Is there evidence that Clyde is an animal? IF elephant(x) THEN mammal(x) IF mammal(x) THEN animal(x) elephant (Clyde) modus ponens: IF p THEN q p q © 2002 Franz J. Kurfess unification: find compatible values for variables Logic and Reasoning 45 Backward Chaining Example IF elephant(x) THEN mammal(x) unification: IF mammal(x) THEN animal(x) find compatible values for variables elephant(Clyde) modus ponens: IF p THEN q p q animal(Clyde) IF mammal( © 2002 Franz J. Kurfess x ? ) THEN animal( x ) Logic and Reasoning 46 Backward Chaining Example IF elephant(x) THEN mammal(x) unification: IF mammal(x) THEN animal(x) find compatible values for variables elephant(Clyde) modus ponens: IF p THEN q p q animal(Clyde) ? IF mammal(Clyde) THEN animal(Clyde) © 2002 Franz J. Kurfess Logic and Reasoning 47 Backward Chaining Example IF elephant(x) THEN mammal(x) unification: IF mammal(x) THEN animal(x) find compatible values for variables elephant(Clyde) modus ponens: IF p THEN q p animal(Clyde) q ? IF mammal(Clyde) THEN animal(Clyde) IF elephant( © 2002 Franz J. Kurfess x ) THEN mammal( x ? ) Logic and Reasoning 48 Backward Chaining Example IF elephant(x) THEN mammal(x) unification: IF mammal(x) THEN animal(x) find compatible values for variables elephant(Clyde) modus ponens: IF p THEN q p animal(Clyde) q ? IF mammal(Clyde) THEN animal(Clyde) ? IF elephant(Clyde) THEN mammal(Clyde) © 2002 Franz J. Kurfess Logic and Reasoning 49 Backward Chaining Example IF elephant(x) THEN mammal(x) unification: IF mammal(x) THEN animal(x) find compatible values for variables elephant(Clyde) modus ponens: IF p THEN q p animal(Clyde) q ? IF mammal(Clyde) THEN animal(Clyde) ? IF elephant(Clyde) THEN mammal(Clyde) elephant ( © 2002 Franz J. Kurfess x ) ? Logic and Reasoning 50 Backward Chaining Example IF elephant(x) THEN mammal(x) unification: IF mammal(x) THEN animal(x) find compatible values for variables elephant(Clyde) modus ponens: IF p THEN q p animal(Clyde) q IF mammal(Clyde) THEN animal(Clyde) IF elephant(Clyde) THEN mammal(Clyde) elephant (Clyde) © 2002 Franz J. Kurfess Logic and Reasoning 51 Forward vs. Backward Chaining Forward Chaining Backward Chaining planning, control diagnosis data-driven goal-driven (hypothesis) bottom-up reasoning top-down reasoning find possible conclusions supported by given facts similar to breadth-first search antecedents (LHS) control evaluation find facts that support a given hypothesis © 2002 Franz J. Kurfess similar to depth-first search consequents (RHS) control evaluation Logic and Reasoning 52 Alternative Inference Methods © 2002 Franz J. Kurfess Logic and Reasoning 53 Metaknowledge © 2002 Franz J. Kurfess Logic and Reasoning 54 Post-Test © 2002 Franz J. Kurfess Logic and Reasoning 55 Use of References [Giarratano & Riley 1998] [Russell & Norvig 1995] [Jackson 1999] [Durkin 1994] [Giarratano & Riley 1998] © 2002 Franz J. Kurfess Logic and Reasoning 57 References [Altenkrüger & Büttner] Doris Altenkrüger and Winfried Büttner. Wissensbasierte Systems Architektur, Enwicklung, Echtzeit-Anwendungen. Vieweg Verlag, 1992. [Awad 1996] Elias Awad. Building Expert Systems - Principles, Procedures, and Applications. West Publishing, Minneapolis/St. Paul, MN, 1996. [Bibel 1993] Wolfgang Bibel with Steffen Höldobler and Torsten Schaub. Wissensrepräsentation und Inferenz - Eine grundlegende Einführung. Vieweg Verlag, 1993. [Durkin 1994] John Durkin. Expert Systems - Design and Development. Prentice Hall, Englewood Cliffs, NJ, 1994. [Giarratano & Riley 1998] Joseph Giarratano and Gary Riley. Expert Systems - Principles and Programming. 3rd ed., PWS Publishing, Boston, MA, 1998 [Jackson, 1999] Peter Jackson. Introduction to Expert Systems. 3rd ed., Addison-Wesley, 1999. [Russell & Norvig 1995] Stuart Russell and Peter Norvig, Artificial Intelligence - A Modern Approach. Prentice Hall, 1995. © 2002 Franz J. Kurfess Logic and Reasoning 58 Important Concepts and Terms agent automated reasoning belief network cognitive science computer science hidden Markov model intelligence knowledge representation linguistics Lisp logic machine learning microworlds © 2002 Franz J. Kurfess natural language processing neural network predicate logic propositional logic rational agent rationality Turing test Logic and Reasoning 59 Summary Chapter-Topic © 2002 Franz J. Kurfess Logic and Reasoning 60 © 2002 Franz J. Kurfess Logic and Reasoning 61
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