CSE 505: Class Notes on Semantics of Logic Programs

A program P where no clause body contains a negative literal is called a definite program. In other words, if every clause in a program is a Horn clause, then it is a definite program. The least model of a definite logic program P can be computed as the least fixed point of the immediate consequence operator, TP of P defined as follows. Definition 1 Let M ⊆ P be a set of propositions. Then M ′ = TP(M), the immediate consequence of M is the least set such that: • p ∈M ′ if p ∈M • p ∈M ′ if p :− q1, q2, . . . qn ∈ P and for all 1 ≤ i ≤ n, qi ∈M . In other words, given the propositions that are true (in M) TP computes the set of propositions whose truth follows from the program P.