Jeroen Spaans

Pascal Kettmann, Hannes Strass, Jesse Heyninck et al.

In logic programming, negation can be interpreted in various ways. Probably best known is the concept of "negation as failure", where "$\mathit{not}\, p$" is true if we have no evidence for $p$. On the other hand, strong negation requires that we have evidence for $p$ being false. Defining semantics for logic programs containing both kinds of negation is a challenging task, and this becomes even more challenging when combining this with other extensions of logic programming, e.g. fuzziness. In this work, we use the framework of approximating fixpoint theory to formulate well-behaved semantics for fuzzy logic programs containing both "by-failure" and strong negation. We show that this framework generalizes several existing semantics as well as giving rise to a host of new semantics.

Jeroen Spaans, Jesse Heyninck

Constraint Logic Programming (CLP) is a logic programming formalism used to solve problems requiring the consideration of constraints, like resource allocation and automated planning and scheduling. It has previously been extended in various directions, for example to support fuzzy constraint satisfaction, uncertainty, or negation, with different notions of semiring being used as a unifying abstraction for these generalizations. None of these extensions have studied clauses with negation allowed in the body. We investigate an extension of CLP which unifies many of these extensions and allows negation in the body. We provide semantics for such programs, using the framework of approximation fixpoint theory, and give a detailed overview of the impacts of properties of the semirings on the resulting semantics. As such, we provide a unifying framework that captures existing approaches and allows extending them with a more expressive language.