Syntax and semantics of multi-adjoint normal logic programming

TL;DR

This paper introduces multi-adjoint normal logic programming, extending the framework with a negation operator and providing conditions for stable model existence and uniqueness within a convex algebraic setting.

Contribution

It extends multi-adjoint logic programming by incorporating negation and offers semantic conditions for stable model existence and uniqueness.

Findings

Provided syntax and semantics for multi-adjoint normal logic programming.

Established sufficient conditions for stable model existence.

Identified conditions for the unicity of stable models.

Abstract

Multi-adjoint logic programming is a general framework with interesting features, which involves other positive logic programming frameworks such as monotonic and residuated logic programming, generalized annotated logic programs, fuzzy logic programming and possibilistic logic programming. One of the most interesting extensions of this framework is the possibility of considering a negation operator in the logic programs, which will improve its flexibility and the range of real applications. This paper introduces multi-adjoint normal logic programming, which is an extension of multi-adjoint logic programming including a negation operator in the underlying lattice. Beside the introduction of the syntax and semantics of this paradigm, we will provide sufficient conditions for the existence of stable models defined on a convex compact set of a euclidean space. Finally, we will consider a particular algebraic structure in which sufficient conditions can be given in order to ensure the unicity of stable models of multi-adjoint normal logic programs.