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
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In this question, we will explore the seman-
tic properties of propositional Horn clauses. For any set of clauses S, define Is to be the
interpretation 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.
Transcribed Image Text:In this question, we will explore the seman- tic properties of propositional Horn clauses. For any set of clauses S, define Is to be the interpretation 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.
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