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Legal reasoning requires not only high accuracy but also the ability to justify decisions through verifiable and contestable arguments. However, existing Large Language Model (LLM) approaches, such as Chain-of-Thought (CoT) and…

Applying reinforcement learning (RL) to real-world tasks requires converting informal descriptions into a formal Markov decision process (MDP), implementing an executable environment, and training a policy agent. Automating this process is…

We present a prototype of an integrated reasoning environment for educational purposes. The presented tool is a fragment of a proof assistant and automated theorem prover. We describe the existing and planned functionality of the theorem…

Logic rules are powerful for expressing complex reasoning and analysis problems. At the same time, they are inconvenient or impossible to use for many other aspects of applications. Integrating rules in a language with sets and functions,…

We present Diagrammatica, a symbolic computation extension to the HEPTAPOD agentic framework, which enables LLM agents to plan and execute multi-step theoretical calculations. Symbolic computation poses a distinctive reliability challenge…

\textbf{Background:} Regulatory frameworks for AI in healthcare, including the EU AI Act and FDA guidance on AI/ML-based medical devices, require clinical decision support to demonstrate not only accuracy but auditability. Existing formal…

A major challenge in the deployment of scientific software solutions is the adaptation of research prototypes to production-grade code. While high-level languages like MATLAB are useful for rapid prototyping, they lack the resource…

Agda is a dependently-typed functional programming language, based on an extension of intuitionistic Martin-L\"of type theory. We implement first order natural deduction in Agda. We use Agda's type checker to verify the correctness of…

Recent advancements in large language models have led to significant improvements across various tasks, including mathematical reasoning, which is used to assess models' intelligence in logical reasoning and problem-solving. Models are…

We present a sound and complete focusing calculus for the core of the logic behind the proof assistant Beluga as well as an overview of its implementation as a tactic in Beluga's interactive proof environment Harpoon. The focusing calculus…

Mathematicians and computer scientists are increasingly using proof assistants to formalize and check correctness of complex proofs. This is a non-trivial task in itself, however, with high demands on human expertise. Can we lower the bar…

In this paper, we aim to establish a simple, effective, and theoretically grounded benchmark for rigorously probing abstract reasoning in Large Language Models (LLMs). To achieve this, we first develop a mathematic framework that defines…

Mathematical reasoning is a primary indicator of large language models (LLMs) intelligence. However, existing LLMs exhibit failures of robustness and generalization. This paper attributes these deficiencies to spurious reasoning, i.e.,…

The lambda calculus with constructors is an extension of the lambda calculus with variadic constructors. It decomposes the pattern-matching a la ML into a case analysis on constants and a commutation rule between case and application…

Theorem provers are tools that help users to write machine readable proofs. Some of this tools are also interactive. The need of such softwares is increasing since they provide proofs that are more certified than the hand written ones. Agda…

Machine Learning (ML) has become an integral part of our society, commonly used in critical domains such as finance, healthcare, and transportation. Therefore, it is crucial to evaluate not only whether ML models make correct predictions…

This paper introduces MeLA, a Metacognitive LLM-Driven Architecture that presents a new paradigm for Automatic Heuristic Design (AHD). Traditional evolutionary methods operate directly on heuristic code; in contrast, MeLA evolves the…

The recent rise in popularity of large language models (LLMs) has prompted considerable concerns about their moral capabilities. Although considerable effort has been dedicated to aligning LLMs with human moral values, existing benchmarks…

Deep research agents increasingly automate complex information-seeking tasks, producing evidence-grounded reports via multi-step reasoning, tool use, and synthesis. Their growing role demands scalable, reliable evaluation, positioning…

We describe a type system for the linear-algebraic lambda-calculus. The type system accounts for the part of the language emulating linear operators and vectors, i.e. it is able to statically describe the linear combinations of terms…