Related papers: $\mu\lambda\epsilon\delta$-Calculus: A Self Optimi…
Nondeterminism introduced by race conditions and message reorderings makes parallel and distributed programming hard. Nevertheless, promising approaches such as LVars and CRDTs address this problem by introducing a partial order structure…
Soft linear logic ([Lafont02]) is a subsystem of linear logic characterizing the class PTIME. We introduce Soft lambda-calculus as a calculus typable in the intuitionistic and affine variant of this logic. We prove that the (untyped) terms…
We present a call-by-need $\lambda$-calculus that enables strong reduction (that is, reduction inside the body of abstractions) and guarantees that arguments are only evaluated if needed and at most once. This calculus uses explicit…
LLMs approach logical and mathematical reasoning through natural or symbolic languages. While natural language offers human-accessible flexibility but suffers from ambiguity, symbolic reasoning provides precise, machine-executable…
Logic is the science of correct inferences and a logical system is a tool to prove assertions in a certain logic in a correct way. There are many logical systems, and many ways of formalizing them, e.g., using natural deduction or sequent…
In some contexts, well-formed natural language cannot be expected as input to information or communication systems. In these contexts, the use of grammar-independent input (sequences of uninflected semantic units like e.g.…
Many different systems with explicit substitutions have been proposed to implement a large class of higher-order languages. Motivations and challenges that guided the development of such calculi in functional frameworks are surveyed in the…
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) are increasingly used in situations where human values are at stake, such as decision-making tasks that involve reasoning when performed by humans. We investigate the so-called reasoning capabilities of LLMs…
Mathematical problem solving is a fundamental benchmark for assessing the reasoning capabilities of artificial intelligence and a gateway to applications in education, science, and engineering where reliable symbolic reasoning is essential.…
Chain-of-thought (CoT) reasoning has enabled large language models (LLMs) to utilize additional computation through intermediate tokens to solve complex tasks. However, we posit that typical reasoning traces contain many redundant tokens,…
As a supplement to my talk at the workshop, this extended abstract motivates and summarizes my work with co-authors on problems in two separate areas: first, in the lambda-calculus with letrec, a universal model of computation, and second,…
Large Language Models (LLMs) have achieved remarkable success in tasks requiring complex reasoning, such as code generation, mathematical problem solving, and algorithmic synthesis -- especially when aided by reasoning tokens and…
Prolog's very useful expressive power is not captured by traditional logic programming semantics, due mainly to the cut and goal and clause order. Several alternative semantics have been put forward, exposing operational details of the…
Large language models (LLMs) have demonstrated remarkable capabilities in problem-solving. However, their proficiency in solving mathematical problems remains inadequate. We propose MathScale, a simple and scalable method to create…
We present a comprehensive programme analysing the decomposition of proof systems for non-classical logics into proof systems for other logics, especially classical logic, using an algebra of constraints. That is, one recovers a proof…
Large Language Models (LLMs), excel in natural language understanding, but their capability for complex mathematical reasoning with an amalgamation of structured tables and unstructured text is uncertain. This study explores LLMs'…
The categorical models of the differential lambda-calculus are additive categories because of the Leibniz rule which requires the summation of two expressions. This means that, as far as the differential lambda-calculus and differential…
Convincing someone of the truth value of a premise requires understanding and articulating the core logical structure of the argument which proves or disproves the premise. Understanding the logical structure of an argument refers to…
Large Language Models (LLMs) have shown to be capable of various tasks, yet their capability in interpreting and reasoning over tabular data remains an underexplored area. In this context, this study investigates from three core…