MT-PDCL: A Measure-Theoretic Framework for Probabilistic Logic Programming

A recent publication on arXiv (2608.13018) presents Measure-Theoretic Probabilistic Definite Clause Logic (MT-PDCL), a fundamental framework that broadens the scope of probabilistic logic programming into continuous domains. Traditional frameworks depend on converting logic programs into discrete propositional forms, which limits precise inference to finite and discrete probability distributions. MT-PDCL overcomes this limitation by clearly defining stochastic variables within bounded index domains and incorporating standard Borel σ-algebras into the interpretation space, enabling logical variables to function directly within continuous measurable spaces. Building on Continuous Distribution Semantics, MT-PDCL represents probabilistic rules as independent causal events. Instead of using finite boolean circuits for aggregation, it establishes declarative entailment through precise Lebesgue integration. This paper is a new submission and can be accessed via the provided URL.