The generalised distribution semantics and projective families of distributions

TL;DR

This paper extends the distribution semantics for probabilistic logic programming to a more general framework, characterizing the projective families of distributions it can represent and identifying limitations and capabilities of a restricted logic programming fragment.

Contribution

It introduces a generalized distribution semantics that unifies various probabilistic frameworks and characterizes the projective families representable within it, highlighting its expressive limits.

Findings

Characterizes projective families of distributions in the generalized semantics.

Shows limitations of the semantics in representing certain projective families.

Demonstrates that acyclic determinate logic programs can represent all projective families within the semantics.

Abstract

We generalise the distribution semantics underpinning probabilistic logic programming by distilling its essential concept, the separation of a free random component and a deterministic part. This abstracts the core ideas beyond logic programming as such to encompass frameworks from probabilistic databases, probabilistic finite model theory and discrete lifted Bayesian networks. To demonstrate the usefulness of such a general approach, we completely characterise the projective families of distributions representable in the generalised distribution semantics and we demonstrate both that large classes of interesting projective families cannot be represented in a generalised distribution semantics and that already a very limited fragment of logic programming (acyclic determinate logic programs) in the determinsitic part suffices to represent all those projective families that are representable in the generalised distribution semantics at all.