Related papers: Hypertableau Reasoning for Description Logics

Understanding the uncertainty in large language model (LLM) explanations is important for evaluating their faithfulness and reasoning consistency, and thus provides insights into the reliability of LLM's output regarding a question. In this…

One of the main reasons to employ a description logic such as EL or EL++ is the fact that it has efficient, polynomial-time algorithmic properties such as deciding consistency and inferring subsumption. However, simply by adding negation of…

Currently, there is a significant amount of research being conducted in the field of artificial intelligence to improve the explainability and interpretability of deep learning models. It is found that if end-users understand the reason for…

In this paper we present tableau proof systems for various justification logics. We show that the tableau systems are sound and complete with respect to Mkrtychev models. In order to prove the completeness of the tableaux, we give a…

Deep learning has become the dominant approach for creating high capacity, scalable models across diverse data modalities. However, because these models rely on a large number of learned parameters, tightly couple feature extraction with…

Logical reasoning is a critical component of Large Language Models (LLMs), and substantial research efforts in recent years have aimed to enhance their deductive reasoning capabilities. However, existing deductive reasoning benchmarks,…

Large language models suffer from content effects in reasoning tasks, particularly in multi-lingual contexts. We introduce a novel method that reduces these biases through explicit structural abstraction that transforms syllogisms into…

Integrating large language models (LLMs) with rule-based reasoning offers a powerful solution for improving the flexibility and reliability of Knowledge Base Completion (KBC). Traditional rule-based KBC methods offer verifiable reasoning…

The logic of bunched implications (BI) is a substructural logic that forms the backbone of separation logic, the much studied logic for reasoning about heap-manipulating programs. Although the proof theory and metatheory of BI are…

This paper presents general syntactic conditions ensuring the strong normalization and the logical consistency of the Calculus of Algebraic Constructions, an extension of the Calculus of Constructions with functions and predicates defined…

Table Question Answering (TableQA) poses a significant challenge for large language models (LLMs) because conventional linearization of tables often disrupts the two-dimensional relationships intrinsic to structured data. Existing methods,…

Qualitative reasoning involves expressing and deriving knowledge based on qualitative terms such as natural language expressions, rather than strict mathematical quantities. Well over 40 qualitative calculi have been proposed so far, mostly…

In this paper we provide an alternative semantics for Equilibrium Logic and its monotonic basis, the logic of Here-and-There (also known as G\"odel's G3 logic) that relies on the idea of "denotation" of a formula, that is, a function that…

We introduce an extension of Strategy Logic for the imperfect-information setting, called SLii, and study its model-checking problem. As this logic naturally captures multi-player games with imperfect information, the problem turns out to…

A non-deterministic call-by-need lambda-calculus \calc with case, constructors, letrec and a (non-deterministic) erratic choice, based on rewriting rules is investigated. A standard reduction is defined as a variant of left-most outermost…

Multimodal reasoning has emerged as a powerful framework for enhancing reasoning capabilities of reasoning models. While multi-turn table reasoning methods have improved reasoning accuracy through tool use and reward modeling, they rely on…

The ubiquity and value of tables as semi-structured data across various domains necessitate advanced methods for understanding their complexity and vast amounts of information. Despite the impressive capabilities of large language models…

Description logics are a powerful tool for describing ontological knowledge bases. That is, they give a factual account of the world in terms of individuals, concepts and relations. In the presence of uncertainty, such factual accounts are…

It is widely acknowledged that function symbols are an important feature in answer set programming, as they make modeling easier, increase the expressive power, and allow us to deal with infinite domains. The main issue with their…

Tabled logic programming is receiving increasing attention in the Logic Programming community. It avoids many of the shortcomings of SLD execution and provides a more flexible and often extremely efficient execution mechanism for logic…