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We present a generic framework that facilitates object level reasoning with logics that are encoded within the Higher Order Logic theorem proving environment of HOL Light. This involves proving statements in any logic using intuitive…
As reasoning LLMs increasingly trade tokens for accuracy through deliberation, search, and self-correction, a single accuracy score can no longer tell whether those tokens buy useful reasoning, recovery from hard instances, or unnecessary…
Multimodal Large Language Models (MLLMs) have demonstrated remarkable capabilities in document understanding. However, their reasoning processes remain largely black-box, making it difficult to ensure reliability and trustworthiness,…
Recent large-scale language models (LLMs) with long Chain-of-Thought reasoning-such as DeepSeek-R1-have achieved impressive results on Olympiad-level mathematics benchmarks. However, they often rely on a narrow set of strategies and…
Explaining opaque Machine Learning (ML) models is an increasingly relevant problem. Current explanation in AI (XAI) methods suffer several shortcomings, among others an insufficient incorporation of background knowledge, and a lack of…
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,…
We investigate the non-elementary computational complexity of a family of substructural logics without contraction. With the aid of the technique pioneered by Lazi\'c and Schmitz (2015), we show that the deducibility problem for full Lambek…
Most commonly, the Open World Assumption is adopted as a standard strategy for the design, construction and use of ontologies. This strategy limits the inferencing capabilities of any system because non-asserted statements (missing…
In this work, we present a novel approach to ontology reasoning that is based on deep learning rather than logic-based formal reasoning. To this end, we introduce a new model for statistical relational learning that is built upon deep…
In default theories, outliers denote sets of literals featuring unexpected properties. In previous papers, we have defined outliers in default logics and investigated their formal properties. Specifically, we have looked into the…
We introduce proper display calculi for intuitionistic, bi-intuitionistic and classical linear logics with exponentials, which are sound, complete, conservative, and enjoy cut-elimination and subformula property. Based on the same design,…
We provide a version of first-order hybrid tense logic with predicate abstracts and definite descriptions as the only non-rigid terms. It is formalised by means of a tableau calculus working on sat-formulas. A particular theory of DD…
Lehmann and Magidor's rational closure is acknowledged as a landmark in the field of non-monotonic logics and it has also been re-formulated in the context of Description Logics (DLs). We show here how to model a rational form of entailment…
While Chain-of-Thought (CoT) significantly enhances the performance of Large Language Models (LLMs), explicit reasoning chains introduce substantial computational redundancy. Recent latent reasoning methods attempt to mitigate this by…
Linear temporal logic (LTL) is a powerful language for task specification in reinforcement learning, as it allows describing objectives beyond the expressivity of conventional discounted return formulations. Nonetheless, recent works have…
The open-world assumption in model development suggests that a model might lack sufficient information to adequately handle data that is entirely distinct or out of distribution (OOD). While deep learning methods have shown promising…
This paper proposes an alternative to standard first-order logic that seeks greater naturalness, generality, and semantic self-containment. The system removes the first-order restriction, avoids type hierarchies, and dispenses with external…
We propose a procedure for automated implicit inductive theorem proving for equational specifications made of rewrite rules with conditions and constraints. The constraints are interpreted over constructor terms (representing data values),…
We study the problem of learning description logic (DL) ontologies in Angluin et al.'s framework of exact learning via queries. We admit membership queries ("is a given subsumption entailed by the target ontology?") and equivalence queries…
We propose a novel eXplainable AI algorithm to compute faithful, easy-to-understand, and complete global decision rules from local explanations for tabular data by combining XAI methods with closed frequent itemset mining. Our method can be…