tic properties interpretation In this question, we will explore the seman- of propositional Horn clauses. For any set of clauses S, define Is to be the that satisfies an atom p if and only if S = p. • Show that if S is a set of positive Horn clauses, then Is = S. • Give an example of a set of clauses S where Is S. Suppose that S is a set of positive Horn clauses and that c is a negative Horn clause. Show that if Is c then SU{c} is unsatisfiable. Suppose that S is a set of positive Horn clauses and that T is a set of negative ones. Using part (c), show that if SU{c} is satisfiable for every c E T, then SUT is satisfiable also. • In the propositional case, the normal Prolog interpreter can be thought of as taking a set of positive Horn clauses S (the program) and a single negative clause c (the query) and determining whether or not SU{c} is satisfiable. Use part (d) to conclude that Prolog can be used to test the satisfiability of an arbitrary set of Horn Clauses.

tic properties interpretation In this question, we will explore the seman- of propositional Horn clauses. For any set of clauses S, define Is to be the that satisfies an atom p if and only if S = p. • Show that if S is a set of positive Horn clauses, then Is = S. • Give an example of a set of clauses S where Is S. Suppose that S is a set of positive Horn clauses and that c is a negative Horn clause. Show that if Is c then SU{c} is unsatisfiable. Suppose that S is a set of positive Horn clauses and that T is a set of negative ones. Using part (c), show that if SU{c} is satisfiable for every c E T, then SUT is satisfiable also. • In the propositional case, the normal Prolog interpreter can be thought of as taking a set of positive Horn clauses S (the program) and a single negative clause c (the query) and determining whether or not SU{c} is satisfiable. Use part (d) to conclude that Prolog can be used to test the satisfiability of an arbitrary set of Horn Clauses.

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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