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The projection lemma (often also referred to as the elimination lemma) is one of the most powerful and useful tools in the context of linear matrix inequalities for system analysis and control. In its traditional formulation, the projection…

Large language models (LLMs) are widely used to evaluate the quality of LLM generations and responses, but this leads to significant challenges: high API costs, uncertain reliability, inflexible pipelines, and inherent biases. To address…

Scaling arguments provide valuable analysis tools across physics and complex systems yet are often employed as one generic method, without explicit reference to the various mathematical concepts underlying them. A careful understanding of…

Large language models (LLMs) are increasingly explored as general-purpose reasoners, particularly in agentic contexts. However, their outputs remain prone to mathematical and logical errors. This is especially challenging in open-ended…

We are interested in understanding how well Transformer language models (TLMs) can perform reasoning tasks when trained on knowledge encoded in the form of natural language. We investigate their systematic generalization abilities on a…

We propose relational linear programming, a simple framework for combing linear programs (LPs) and logic programs. A relational linear program (RLP) is a declarative LP template defining the objective and the constraints through the logical…

The logic programming paradigm provides the basis for a new intensional view of higher-order notions. This view is realized primarily by employing the terms of a typed lambda calculus as representational devices and by using a richer form…

Large language models (LLMs) have achieved significant performance in various natural language reasoning tasks. However, they still struggle with performing first-order logic reasoning over formal logical theories expressed in natural…

Large Language Models (LLMs) are often described as instances of foundation models that possess strong generalization obeying scaling laws, and therefore transfer robustly across various conditions in few- or zero-shot manner. Such claims…

Answer Set Programming (ASP) is a prominent rule-based language for knowledge representation and reasoning with roots in logic programming and non-monotonic reasoning. The aim to capture the essence of removing (ir)relevant details in ASP…

We present a family of logics for reasoning about agents' positions and motion in the plane which have several potential applications in the area of multi-agent systems (MAS), such as multi-agent planning and robotics. The most general…

We study a synthetic corpus based approach for language models (LMs) to acquire logical deductive reasoning ability. The previous studies generated deduction examples using specific sets of deduction rules. However, these rules were limited…

We propose a purely extensional semantics for higher-order logic programming. In this semantics program predicates denote sets of ordered tuples, and two predicates are equal iff they are equal as sets. Moreover, every program has a unique…

Mathematical reasoning is one of the crucial abilities of general artificial intelligence, which requires machines to master mathematical logic and knowledge from solving problems. However, existing approaches are not transparent (thus not…

Large language models (LLMs) often struggle with complex logical reasoning due to logical inconsistencies and the inherent difficulty of such reasoning. We use Lean, a theorem proving framework, to address these challenges. By formalizing…

We propose a modular method for proving termination of general logic programs (i.e., logic programs with negation). It is based on the notion of acceptable programs, but it allows us to prove termination in a truly modular way. We consider…

We discuss proving correctness and completeness of definite clause logic programs. We propose a method for proving completeness, while for proving correctness we employ a method which should be well known but is often neglected. Also, we…

In large language models (LLMs), code and reasoning reinforce each other: code offers an abstract, modular, and logic-driven structure that supports reasoning, while reasoning translates high-level goals into smaller, executable steps that…

Logical reasoning is essential for large language models (LLMs) to ensure accurate and coherent inference. However, LLMs struggle with reasoning order variations and fail to generalize across logically equivalent transformations. LLMs often…

To appear in Theory and Practice of Logic Programming (TPLP). In this paper we propose an extension of logic programming (LP) where each default literal derived from the well-founded model is associated to a justification represented as an…