# The generalised distribution semantics and projective families of distributions

arXiv: https://arxiv.org/abs/2211.06751 · HTML: https://mlsanity.com/paper/2211.06751/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 28 references that are in the map.
- First posted on arXiv 12 Nov 2022.

## Builds on (most cited first, 8 of 8)

- [An asymptotic analysis of probabilistic logic programming, with implications for expressing projective families of distributions](https://mlsanity.com/paper/2102.08777/) (2021)
- [Weighted Model Counting in FO2 with Cardinality Constraints and Counting Quantifiers: A Closed Form Formula](https://mlsanity.com/paper/2110.05992/) (2021)
- [Inference, Learning, and Population Size: Projectivity for SRL Models](https://mlsanity.com/paper/1807.00564/) (2018)
- [A Complete Characterization of Projectivity for Statistical Relational Models](https://mlsanity.com/paper/2004.10984/) (2020)
- [On Projectivity in Markov Logic Networks](https://mlsanity.com/paper/2204.04009/) (2022)
- [The Complexity of Bayesian Networks Specified by Propositional and Relational Languages](https://mlsanity.com/paper/1612.01120/) (2016)
- [Projectivity revisited](https://mlsanity.com/paper/2207.00625/) (2022)
- [Probabilistic Disjunctive Logic Programming](https://mlsanity.com/paper/1302.3592/) (2013)

## Abstract (arXiv)

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.