Related papers: Syntax and Consequence Relations -- A Categorical …

While argument mining has achieved significant success in classifying argumentative relations between statements (support, attack, and neutral), we have a limited computational understanding of logical mechanisms that constitute those…

In this paper, firstly, we determine the number of sublogics of variable inclusion of an arbitrary finitary logic L with partition function. Then, we investigate their position into the lattice of consequence relations over the language of…

We bring forward a logical system of transition algebras that enhances many-sorted first-order logic using features from dynamic logics. The sentences we consider include compositions, unions, and transitive closures of transition…

Constructor-Based Conditional Rewriting Logic is a general framework for integrating first-order functional and logic programming which gives an algebraic semantics for non-deterministic functional-logic programs. In the context of this…

This paper introduces and studies the sequential composition and decomposition of propositional logic programs. We show that acyclic programs can be decomposed into single-rule programs and provide a general decomposition result for…

Relational properties arise in many settings: relating two versions of a program that use different data representations, noninterference properties for security, etc. The main ingredient of relational verification, relating aligned pairs…

We extend the framework of abstract algebraic logic to weak logics, namely logical systems which are not necessarily closed under uniform substitution. We interpret weak logics by algebras expanded with an additional predicate and we…

Stepwise refinement of algebraic specifications is a well known formal methodology for program development. However, traditional notions of refinement based on signature morphisms are often too rigid to capture a number of relevant…

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…

In the philosophical tradition of `analytic pragmatism', which attempts to account for linguistic meanings in terms of their practices of use, logical expressivism is a theory which offers a distinct perspective on logic. We shed light on…

This article provides an algebraic study of intermediate inquisitive and dependence logics. While these logics are usually investigated using team semantics, here we introduce an alternative algebraic semantics and we prove it is complete…

We prove a theorem stating that any semantics can be encoded as a compositional semantics, which means that, essentially, the standard definition of compositionality is formally vacuous. We then show that when compositional semantics is…

We have previously introduced role logic as a notation for describing properties of relational structures in shape analysis, databases and knowledge bases. A natural fragment of role logic corresponds to two-variable logic with counting and…

An attempt at unifying logic and functional programming is reported. As a starting point, we take the view that "logic programs" are not about logic but constitute inductive definitions of sets and relations. A skeletal language design…

The aim of these notes is to provide a succinct, accessible introduction to some of the basic ideas of category theory and categorical logic. The notes are based on a lecture course given at Oxford over the past few years. They contain…

There have been a huge number of benchmarks proposed to evaluate how large language models (LLMs) behave for logic inference tasks. However, it remains an open question how to properly evaluate this ability. In this paper, we provide a…

Logic programming is a flexible programming paradigm due to the use of predicates without a fixed data flow. To extend logic languages with the compact notation of functional programming, there are various proposals to map evaluable…

Inferential relations govern our concept use. In order to understand a concept it has to be located in a space of implications. There are different kinds of conditions for statements, i.e. that the conditions represent different kinds of…

I introduce a formalism for representing the syntax of recursively structured graph-like patterns. It does not use production rules, like a conventional graph grammar, but represents the syntactic structure in a more direct and declarative…

This paper shows connections between command injection attacks, continuations, and the Lambek calculus: certain command injections, such as the tautology attack on SQL, are shown to be a form of control effect that can be typed using the…