Decomposed Entailment for Factuality Checking and Hallucination Detection

The reliability of Large Language Models (LLMs) is often compromised by factual inconsistencies, including hallucinations---cases where generated content is not supported by the underlying source. We present HallDetect, a lightweight, reference-free, and black-box framework for hallucination detection that we evaluate not only on summarization but across a broader range of source-grounded generation settings. HallDetect builds on decomposition-based factuality evaluation: generated content is decomposed into atomic claims, each verified by a compact encoder-based entailment model through a contrastive formulation over a multi-scale library of source chunks, and aggregated with an asymmetric score in which a single confidently contradicted claim flags the response. Under a controlled protocol in which all methods share the same 4-bit quantized backbones and consumer-grade hardware budget, HallDetect outperforms comparably resourced generative and embedding-based baselines on three of four benchmarks while remaining stable across backbone families, and yields a claim-to-span audit trail that localizes each error.

Towards Non-Monotonic Entailment in Propositional Defeasible Standpoint Logic

Recent work in defeasible reasoning has seen notions of preferential semantics and entailment in the style of Kraus et al. applied to modal logics. However, work in this field has focussed primarily on satisfiability checking, and monotonic notions of entailment, which may be inferentially weak. One particular modal logic where this has been introduced is propositional standpoint logics, where modalities can express the views of different viewpoints. This has resulted in the formalisation of propositional defeasible standpoint logic (PDSL). In this paper, we propose a means of lifting the class of (non-monotonic) rational entailment relations from traditional KLM-style reasoning to a fragment of PDSL. In order to do so, we extend the expressivity of PDSL via situated standpoint conditionals, allowing us to talk about a defeasible conditional holding in the context of a given standpoint. This allows us to re-characterise the syntax of PDSL in terms of situated conditionals, and shows that a large fragment of PDSL is expressible as a set of situated conditionals. We then focus on characterising non-monotonic entailment in this fragment, defining a method to transport any ranking-based entailment relation from the propositional case into the PDSL case. This is first described in the general case and then considered in the specific cases of rational and lexicographic closures, providing a faithful translation of each inference into PDSL. We also show that entailment-checking in this fragment of PDSL can be done largely using algorithms from the propositional case, while preserving complexity bounds.

On the Complexity of Entailment for Cumulative Propositional Dependence Logics

This paper establishes and proves complexity results for entailment for cumulative propositional dependence logic and for cumulative propositional logic with team semantics. As recently shown, cumulative logics are famously characterised by System~C and exactly captured by the cumulative models of Kraus, Lehmann and Magidor. This gives rise to the entailment problem via relational models, which is specifically considered here.