An effective fixpoint semantics for linear logic programs

An effective fixpoint semantics for linear logic programs

In this paper we investigate the theoretical foundation of a new bottom-up semantics for linear logic programs, and more precisely for the fragment of LinLog (Andreoli, 1992) that consists of the language LO (Andreoli & Pareschi, 1991) enriched with the constant 1. We use constraints to symbolically and finitely represent possibly infinite collections of provable goals. We define a fixpoint sem...

A Fixpoint Semantics for Disjunctive Logic Programs

D We present a fixpoint semantics for disjunctive logic programs. We extend the concept of the Herbrand base of a logic program to consist of all positive clauses that may be formed using the atoms in the Herbrand base. A monotonic closure operator is defined, operating on the lattice formed by the power set of the extended Herbrand base. The closure operator is shown to achieve a least fixpoin...

Unfolding, Procedural and Fixpoint Semantics of Logic Programs

In this paper, we propose new notions related to unfolding semantics which clarify the relationship between procedural and fixpoint semantics of logic programs. We introduce 3 main new ideas : the unfolding rule has an associativity property that ensures the adequacy of unfolding semantics with the procedural semantics the uniformly fair computation rules which guarantees strong procedural equi...

Fixpoint Semantics for a Fragment of First-Order Linear Logic

In this paper we investigate the theoretical foundation of a bottom-up, xpoint semantics for a subset of Girard's linear logic [Gir87]. More precisely, we consider a rst-order formulation of a fragment of LinLog [And92] including multiplicative disjunction and universal quanti cation over goals. The semantics is de ned by means of a xpoint operator which is monotonic and continuous over an exte...

Unfolding and Fixpoint Semantics of Concurrent Constraint Logic Programs