Question

An especially simple class of CNF formulas are those built from Horn clauses. A Horn clause is a clause containing, at most, one positive literal. (A pure Horn clause is a clause containing exactly one positive literal.) Horn clauses form the basis for the computer language Prolog, which allows the programmer to input a set of requirements (specified in formal logic) and to ask the computer to find how to satisfy them all (if possible) - as opposed to the user's having to write out the case analysis. (a) Using the atomic formulas = "Tweety is a penguin," b = "Opus is a penguin," c = "Phoenix is a penguin," d = "Elvis lives!", express "If Tweety is a penguin and Opus is a penguin, and Phoenix is a penguin, then Elvis lives" as a Horn clause. (b) Find a set of Horn clauses logically equivalent to (a A b A c d V e (-a V -e)). Find the shortest such set of clauses. (c) Find all satisfying truth assignments for the following set of Horn clauses: {} Now, show that the following set of Horn clauses is not satisfiable:

          An especially simple class of CNF formulas are those built from Horn clauses. A Horn clause is a clause containing, at most, one positive literal. (A pure Horn clause is a clause containing exactly one positive literal.) Horn clauses form the basis for the computer language Prolog, which allows the programmer to input a set of requirements (specified in formal logic) and to ask the computer to find how to satisfy them all (if possible) - as opposed to the user's having to write out the case analysis.

(a) Using the atomic formulas = "Tweety is a penguin," b = "Opus is a penguin," c = "Phoenix is a penguin," d = "Elvis lives!", express "If Tweety is a penguin and Opus is a penguin, and Phoenix is a penguin, then Elvis lives" as a Horn clause. 
(b) Find a set of Horn clauses logically equivalent to (a A b A c d V e (-a V -e)). Find the shortest such set of clauses. 
(c) Find all satisfying truth assignments for the following set of Horn clauses: {}

Now, show that the following set of Horn clauses is not satisfiable:

6 an especially simple class of cnf formulas are those built from horn clauses a horn clause is a clause containing at most one positive literal a pure horn clause is a clause containing exa 50737

Added by Chase M.

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