Coalgebraic Semantics for Probabilistic Logic Programming

TL;DR

This paper introduces a coalgebraic framework for probabilistic logic programming, enabling formal semantics that unify derivation trees and possible worlds interpretations, and extends to weighted logic programming.

Contribution

It develops a novel coalgebraic semantics for probabilistic logic programming, connecting derivation and distribution semantics through functor embeddings.

Findings

Coalgebraic semantics unify derivation and possible worlds interpretations.

The approach generalizes to weighted logic programming.

Provides a formal foundation for probabilistic reasoning in logic programming.

Abstract

Probabilistic logic programming is increasingly important in artificial intelligence and related fields as a formalism to reason about uncertainty. It generalises logic programming with the possibility of annotating clauses with probabilities. This paper proposes a coalgebraic semantics on probabilistic logic programming. Programs are modelled as coalgebras for a certain functor F, and two semantics are given in terms of cofree coalgebras. First, the F-coalgebra yields a semantics in terms of derivation trees. Second, by embedding F into another type G, as cofree G-coalgebra we obtain a `possible worlds' interpretation of programs, from which one may recover the usual distribution semantics of probabilistic logic programming. Furthermore, we show that a similar approach can be used to provide a coalgebraic semantics to weighted logic programming.