To Make a Molecular Theorem Prover Lee InHee

To Make a Molecular Theorem Prover Lee, In-Hee

Resolution Refutation l Problem: l Turn A→B into ¬A∨B, add R as ¬R l l If we resolve ¬A∨B and A∨C, we get B∨C

R is True!

Predicate Calculus l Symbols and terms ¨ Truth symbol: TRUE and FALSE ¨ Constant symbol < Ex) John, Bill, etc. ¨ Variable symbol < Ex) x, y, etc. ¨ Function symbol < Ex) distance. Between, father. Of, etc. ¨ Function expression < Ex) father. Of(John, Bill), distance. Between(x, N. Y), etc. ¨ Term: either a constant, variable or function expression ¨

Predicate Calculus l Example sentences in predicate calculus ¨ All human die. < ¨ Sam is not John’s brother. < ¨ John has a sister. <

Instantiation and Generalization l Universal instantiation ¨ Variable-constant ¨ l Existential generalization ¨ Constant-to-variable ¨

Unification To resolve two clauses, we may need to substitute some variables with other variables or constants l The process of doing an appropriate substitution is called unification l Notation: (to substitute with)/(to be substituted) l Example l l

Resolution in Predicate Calculus l Package delivery robot knows that 1. “All of the packages in room 27 are smaller than any of the ones in room 28. 2. Package A is either in room 27 or in room 28 (but it doesn’t know which). 3. Package B is in room 27. 4. Package B is not smaller than package A. ” ¨ Is package A in room 27?

Resolution in Predicate Calculus l From the fact that A and B is package, we get ¨ l From 1. ¨ From 2. l From 3. l From 4. l Negation of the question, l

Discussion Topic l Problem encoding ¨ As usual? l Unification ¨ Make all possible unification? l Solution detection ¨ Depends on encoding