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Abstract

In analogy to the Davis-Putnam procedure we develop a new procedure for
computing stable models of propositional normal disjunctive logic programs,
using case analysis and simplification. Our procedure enumerates all stable
models without repetition and without the need for a minimality check. Since it
is not necessary to store the set of stable models explicitly, the procedure
runs in polynomial space. We allow clauses with empty heads, in order to
represent truth or falsity of a proposition as a one-literal clause. In
particular, a clause of form $\mathop\sim A\rightarrow$ expresses that~$A$ is
constrained to be true, without providing a justification for~$A$. Adding this
clause to a program restricts its stable models to those containing~$A$,
without introducing new stable models. Together with $A\rightarrow$ this
provides the basis for case analysis. We present our procedure as a set of
rules which transform a program into a set of solved forms, which resembles the
standard method for presenting unification algorithms. Rules are sound in the
sense that they preserve the set of stable models. A subset of the rules is
shown to be complete in the sense that for each stable model a solved form can
be obtained. The method allows for concise presentation, flexible choice of a
control strategy and simple correctness proofs."