1-Resolution - CS 255 Assignment 1: Resolution Theorem...

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CS 255 Assignment 1: Resolution Theorem Prover (15 points) Due: March 2 by start of class You are to do this assignment with a partner of your choice. Both of your names should be on all of your work. Theorem Proving For this assignment you will be building an automated theorem prover. An automated theorem prover is a program that takes in a set of axioms (hypotheses) and a conclusion you want proven. It then automatically applies inference rules to the axioms in order to prove the theorem true or false. Resolution The specific prover you will be building is a resolution theorem prover. It uses only a single rule of inference , called resolution. Using only a single rule greatly simplifies implementation. The use of the resolution rule of inference is greatly eased by representing all well-formed-formulas in conjunctive normal form (CNF). Conjunctive normal form means that the entire list of wffs is one large conjunction (AND) of disjunctions (OR) of literals (boolean symbol or its negation). An example of CNF and terminology: Boolean symbol: a Boolean symbol: b Boolean symbol: c Literal: a Literal: a Literal: b Literal: c Clause: (a b) Clause: (c a ) Sentence in CNF: (a b) (c a’) You can apply resolution if you have two clauses (disjunctions of literals) that contain complementary literals. Complementary literals are negations of each other. The result of resolution is a new clause that contains all the other literals in both clauses. An example of resolution: clause1: (a b c) clause2: (b d e) resolvent: (a c d e)
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In the above example, clause1 and clause2 can be resolved since they contain b and b (order doesn’t matter). The resulting clause (resolvent) includes all the terms in both clauses except for b and b
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1-Resolution - CS 255 Assignment 1: Resolution Theorem...

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