Related papers: A Proof-Theoretic Approach to the Semantics of Cla…
Viewing formal mathematical proofs as logical terms provides a powerful and elegant basis for analyzing how human experts tend to structure proofs and how proofs can be structured by automated methods. We pursue this approach by (1)…
Differentiable logics (DL) have recently been proposed as a method of training neural networks to satisfy logical specifications. A DL consists of a syntax in which specifications are stated and an interpretation function that translates…
We have designed a new logic programming language called LM (Linear Meld) for programming graph-based algorithms in a declarative fashion. Our language is based on linear logic, an expressive logical system where logical facts can be…
Many complex scenarios require the coordination of agents possessing unique points of view and distinct semantic commitments. In response, standpoint logic (SL) was introduced in the context of knowledge integration, allowing one to reason…
This paper explores proof-theoretic semantics, a formal approach to inferential semantics. It derives sentence meaning from formalized proofs, building upon Gentzen and Prawitz's work. The study addresses challenges in understanding how…
Formal logic has often been seen as uniquely placed to analyze mathematical argumentation. While formal logic is certainly necessary for a complete understanding of mathematical practice, it is not sufficient. Important aspects of…
We give a novel approach to proving soundness and completeness for a logic (henceforth: the object-logic) that bypasses truth-in-a-model to work directly with validity. Instead of working with specific worlds in specific models, we reason…
We give a proof-theoretic as well as a semantic characterization of a logic in the signature with conjunction, disjunction, negation, and the universal and existential quantifiers that we suggest has a certain fundamental status. We present…
Classical computation, grounded in formal, logical systems, has been the engine of technological progress for decades, excelling at problems that can be described with unambiguous rules. This paradigm, however, leaves a vast ocean of human…
This paper presents an abstract, mathematical formulation of classical propositional logic. It proceeds layer by layer: (1) abstract, syntax-free propositions; (2) abstract, syntax-free contraction-weakening proofs; (3) distribution; (4)…
Human logic has gradually shifted from intuition-driven inference to rigorous formal systems. Motivated by recent advances in large language models (LLMs), we explore whether LLMs exhibit a similar evolution in the underlying logical…
We develop team semantics for Linear Temporal Logic (LTL) to express hyperproperties, which have recently been identified as a key concept in the verification of information flow properties. Conceptually, we consider an asynchronous and a…
We seize the opportunity of the publication of selected papers from the \emph{Logic, categories, semantics} workshop in the \emph{Journal of Applied Logic} to survey some current trends in logic, namely intuitionistic and linear type…
We apply to logic programming some recently emerging ideas from the field of reduction-based communicating systems, with the aim of giving evidence of the hidden interactions and the coordination mechanisms that rule the operational…
The origins of proof-theoretic semantics lie in the question of what constitutes the meaning of the logical connectives and its response: the rules of inference that govern the use of the connective. However, what if we go a step further…
Although Large Language Models (LLMs) have demonstrated impressive formal reasoning abilities, they often break down when problems require complex proof planning. One promising approach for improving LLM reasoning abilities involves…
This paper represents classical propositional proofs as *combinatorial proofs*, which are more abstract than proof nets: superposition (contraction/weakening) is modelled mathematically, as a lax form of fibration, rather than syntactically…
We present LISA, a proof system and proof assistant for constructing proofs in schematic first-order logic and axiomatic set theory. The logical kernel of the system is a proof checker for first-order logic with equality and schematic…
Linear logic has provided new perspectives on proof-theory, denotational semantics and the study of programming languages. One of its main successes are proof-nets, canonical representations of proofs that lie at the intersection between…
The present paper provides an analysis of the existing proof systems for dynamic epistemic logic from the viewpoint of proof-theoretic semantics. Dynamic epistemic logic is one of the best known members of a family of logical systems which…