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Formally specifying, let alone verifying, properties of systems involving multiple programming languages is inherently challenging. We introduce Heterogeneous Dynamic Logic (HDL), a framework for combining reasoning principles from distinct…
Propositional logics in general, considered as a set of sentences, can be undecidable even if they have "nice" representations, e.g., are given by a calculus. Even decidable propositional logics can be computationally complex (e.g., already…
Logical frameworks provide natural and direct ways of specifying and reasoning within deductive systems. The logical framework LF and subsequent developments focus on finitary proof systems, making the formalization of circular proof…
The paper proposes a new knowledge representation language, called DLP<, which extends disjunctive logic programming (with strong negation) by inheritance. The addition of inheritance enhances the knowledge modeling features of the language…
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…
The development of highly fluent large language models (LLMs) has prompted increased interest in assessing their reasoning and problem-solving capabilities. We investigate whether several LLMs can solve a classic type of deductive reasoning…
Large Language Models (LLMs) have shown human-like reasoning abilities but still struggle with complex logical problems. This paper introduces a novel framework, Logic-LM, which integrates LLMs with symbolic solvers to improve logical…
Large Language Models (LLMs) suffer from critical reasoning gaps, including a tendency to hallucinate and poor accuracy in classifying logical fallacies. This limitation stems from their default System 1 processing, which is fast and…
In this paper a conditional logic is defined and studied. This conditional logic, DmBL, is constructed as a deterministic counterpart to the Bayesian conditional. The logic is unrestricted, so that any logical operations are allowed. A…
Safeguarding vision-language models (VLMs) is a critical challenge, as existing methods often suffer from over-defense, which harms utility, or rely on shallow alignment, failing to detect complex threats that require deep reasoning. To…
Inductive reasoning is an essential capability for large language models (LLMs) to achieve higher intelligence, which requires the model to generalize rules from observed facts and then apply them to unseen examples. We present MIRAGE, a…
In this work we study a rational extension $SROEL^R T$ of the low complexity description logic SROEL, which underlies the OWL EL ontology language. The extension involves a typicality operator T, whose semantics is based on Lehmann and…
While large language models (LLMs) leverage both knowledge and reasoning during inference, the capacity to distinguish between them plays a pivotal role in model analysis, interpretability, and development. Inspired by dual-system cognitive…
While Large Language Models (LLMs) demonstrate exceptional performance in surface-level text generation, their nature in handling complex multi-step reasoning tasks often remains one of ``statistical fitting'' rather than systematic logical…
Dynamic Topological Logic ($\mathcal{DTL}$) is a combination of $\mathcal{S}${\em 4}, under its topological interpretation, and the temporal logic $\mathcal{LTL}$ interpreted over the natural numbers. $\mathcal{DTL}$ is used to reason about…
Studies have underscored how, regardless of the recent breakthrough and swift advances in AI research, even state-of-the-art Large Language models (LLMs) continue to struggle when performing logical and mathematical reasoning. The results…
Large Language Models (LLMs) have rapidly transformed the landscape of artificial intelligence, enabling natural language interfaces and dynamic orchestration of software components. However, their reliance on probabilistic inference limits…
In order to automate verification process, regulatory rules written in natural language need to be translated into a format that machines can understand. However, none of the existing formalisms can fully represent the elements that appear…
Large Language Models (LLMs) have been widely adopted in ranking systems such as information retrieval (IR) systems and recommender systems (RSs). To alleviate the latency of auto-regressive decoding, some studies explore the single (first)…
The use of large language models either as decision support systems, or in agentic workflows, is rapidly transforming the digital ecosystem. However, the understanding of LLM decision-making under uncertainty remains limited. We study LLM…