UGC NET CSE | Junet 2015 | Part 3 | Question: 24

Question

Which one of the following is true?

• A. The resolvent of two Horn clauses is not a Horn clause
• B. The resolvent of two Horn clauses is a Horn clause
• C. If we resolve a negated goal G against a fact or rule A to get clause C then C has positive literal or non-null goal
• D. If we resolve a negated goal G against a fact or rule A to get clause C then C has positive literal or null goal

Answer 1

Answer B

If you resolve Horn clauses A and B to get clause C, then the positive literal of A will resolve against a negative literal in B, so the only positive literal left in C is the one from B (if any). Thus, the resolvent of two Horn clauses is a Horn clause.

 If you resolve a negated goal G against a fact or rule A to get clause C, the positive literal in A resolves against a negative literal in G. Thus C has no positive literal, and thus is either a negated goal or the null clause

This link is good one... https://cs.nyu.edu/courses/spring02/G22.2560-001/horn.html

Answer 2

option B is true 

Horn clauses play a basic role in constructive logic and computational logic. They are important in automated theorem proving by first-order resolution, because the resolvent of two Horn clauses is itself a Horn clause, and the resolvent of a goal clause and a definite clause is a goal clause. These properties of Horn clauses can lead to greater efficiencies in proving a theorem (represented as the negation of a goal clause).

A Horn clause is a logic disjunction of literals, where at most one of the literals is positive, and all the others are negative. It is named after Alfred Horn who described them in an article in 1951.

A Horn clause with exactly one positive literal is a definite clause; a definite clause with no negative literals is sometimes called a “fact”; and a Horn clause without a positive literal is sometimes called a goal clause. These three kinds of Horn clauses are illustrated in the following propositional example:

definite clause: {\displaystyle \neg p\lor \neg q\vee \cdots \vee \neg t\vee u}

fact: {\displaystyle u}

goal clause: {\displaystyle \neg p\lor \neg q\vee \cdots \vee \neg t}