Fixpoint semantics for logic programming a survey

AbstractThe variety of semantical approaches that have been invented for logic programs is quite broad, drawing on classical and many-valued logic, lattice theory, game theory, and topology. One source of this richness is the inherent non-monotonicity of its negation, something that does not have close parallels with the machinery of other programming paradigms. Nonetheless, much of the work on logic programming semantics seems to exist side by side with similar work done for imperative and functional programming, with relatively minimal contact between communities. In this paper we summarize one variety of approaches to the semantics of logic programs: that based on fixpoint theory. We do not attempt to cover much beyond this single area, which is already remarkably fruitful. We hope readers will see parallels with, and the divergences from the better known fixpoint treatments developed for other programming methodologies

The Strict/Tolerant Family Continued: Quantifiers and Modalities

This paper continues my earlier work, which showed there is a broad family of propositional many valued logics that have a strict/tolerant counterpart.  Here we generalize those results from propositional to a range of both modal and quantified many valued logics, providing strict/tolerant counterparts for all.  This paper is not self-contained; some results from earlier papers are called on, and are not reproved here.  The key new machinery added to earlier work, allowing modalities and quantifiers to be handled in similar ways, is the central use of bilattices that are function spaces, and more generally lattices that are function spaces.  Two versions of the central proofs are considered, one at length and the other in outline

The Strict/Tolerant Family Continued: Quantifiers and Modalities

This paper continues my earlier work, which showed there is a broad family of propositional many valued logics that have a strict/tolerant counterpart.  Here we generalize those results from propositional to a range of both modal and quantified many valued logics, providing strict/tolerant counterparts for all.  This paper is not self-contained; some results from earlier papers are called on, and are not reproved here.  The key new machinery added to earlier work, allowing modalities and quantifiers to be handled in similar ways, is the central use of bilattices that are function spaces, and more generally lattices that are function spaces.  Two versions of the central proofs are considered, one at length and the other in outline

Strict/Tolerant Logics Built Using Generalized Weak Kleene Logics

This paper continues my work of [9], which showed there was a broad family of many valued logics that have a strict/tolerant counterpart. Here we consider a generalization of weak Kleene three valued logic, instead of the strong version that was background for that earlier work. We explain the intuition behind that generalization, then determine a subclass of strict/tolerant structures in which a generalization of weak Kleene logic produces the same results that the strong Kleene generalization did. This paper provides much background, but is not self-contained. Some results from [9] are called on, and are not reproved here. [9]  Melvin C. Fitting. “A Family of Strict/Tolerant Logics”. In: Journal of Philosophical Logic (2020). Online. Print publication forthcoming