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We present a novel reasoning calculus for the description logic SHOIQ^+---a knowledge representation formalism with applications in areas such as the Semantic Web. Unnecessary nondeterminism and the construction of large models are two…
The theory of regular cost functions is a quantitative extension to the classical notion of regularity. A cost function associates to each input a non-negative integer value (or infinity), as opposed to languages which only associate to…
While it was defined long ago, the extension of CTL with quantification over atomic propositions has never been studied extensively. Considering two different semantics (depending whether propositional quantification refers to the Kripke…
Answering conjunctive queries (CQs) over a set of facts extended with existential rules is a prominent problem in knowledge representation and databases. This problem can be solved using the chase algorithm, which extends the given set of…
Recent advances in large language models (LLMs) have made reasoning a central benchmark for evaluating intelligence. While prior surveys focus on efficiency by examining how to shorten reasoning chains or reduce computation, this view…
Recent Large Multimodal Models have demonstrated remarkable reasoning capabilities, especially in solving complex mathematical problems and realizing accurate spatial perception. Our key insight is that these emerging abilities can…
In this note we suggest that difficulties encountered in natural language semantics are, for the most part, due to the use of mere symbol manipulation systems that are devoid of any content. In such systems, where there is hardly any link…
Ontology-based query answering (OBQA) asks whether a Boolean conjunctive query is satisfied by all models of a logical theory consisting of a relational database paired with an ontology. The introduction of existential rules (i.e., Datalog…
Reasoning is essential for large language models (LLMs), especially in complex tasks such as mathematical problem solving. However, multimodal reasoning still faces challenges in modality alignment and training scalability, as many existing…
The Semantic Web ontology language OWL 2 DL comes with a variety of language features that enable sophisticated and practically useful modeling. However, the use of these features has been severely restricted in order to retain decidability…
Modal separability for modal fixpoint formulae is the problem to decide for two given modal fixpoint formulae $\varphi,\varphi'$ whether there is a modal formula $\psi$ that separates them, in the sense that $\varphi\models\psi$ and…
Formalisms based on temporal logics interpreted over finite strict linear orders, known in the literature as finite traces, have been used for temporal specification in automated planning, process modelling, (runtime) verification and…
We study fragments of first-order logic and of least fixed point logic that allow only unary negation: negation of formulas with at most one free variable. These logics generalize many interesting known formalisms, including modal logic and…
Legal reasoning requires both precise interpretation of statutory language and consistent application of complex rules, presenting significant challenges for AI systems. This paper introduces a modular multi-agent framework that decomposes…
Language models have recently advanced into the realm of reasoning, yet it is through multimodal reasoning that we can fully unlock the potential to achieve more comprehensive, human-like cognitive capabilities. This survey provides a…
We propose a framework grounded in Logic Programming for representing and reasoning about business processes from both the procedural and ontological point of views. In particular, our goal is threefold: (1) define a logical language and a…
Existing multimodal reasoning approaches predominantly follow two paradigms: converting visual inputs into text prior to reasoning, or performing end-to-end reasoning within a unified vision-language representation space. Despite their…
Reasoning has emerged as a pivotal capability in Large Language Models (LLMs). Through Reinforcement Learning (RL), typically Group Relative Policy Optimization (GRPO), these models are able to solve complex tasks such as mathematics and…
We consider the satisfiability problem for the two-variable fragment of the first-order logic extended with modulo counting quantifiers and interpreted over finite words or trees. We prove a small-model property of this logic, which gives a…
The W3C Web Ontology Language (OWL) is a powerful knowledge representation formalism at the basis of many semantic-centric applications. Since its unrestricted usage makes reasoning undecidable already in case of very simple tasks,…