Related papers: Category-theoretical Semantics of the Description …

We define LE-ALC, a generalization of the description logic ALC based on the propositional logic of general (i.e. not necessarily distributive) lattices, and semantically interpreted on relational structures based on formal contexts from…

Various topological concepts are often involved in the research of mathematical logic, and almost all of these concepts can be regarded as developing from the Stone representation theorem. In the Stone representation theorem, a Boolean…

A term calculus for the proofs in multiplicative-additive linear logic is introduced and motivated as a programming language for channel based concurrency. The term calculus is proved complete for a semantics in linearly distributive…

Non-normal modal logics, interpreted on neighbourhood models which generalise the usual relational semantics, have found application in several areas, such as epistemic, deontic, and coalitional reasoning. We present here preliminary…

We will investigate proof-theoretic and linguistic aspects of first-order linear logic. We will show that adding partial order constraints in such a way that each sequent defines a unique linear order on the antecedent formulas of a sequent…

The primary goal of this paper is to present a unified way to transform the syntax of a logic system into certain initial algebraic structure so that it can be studied algebraically. The algebraic structures which one may choose for this…

Category theory provides a powerful tool to organize mathematics. A sample of this descriptive power is given by the categorical analysis of the practice of "classes as shorthands" in ZF set theory. In this case category theory provides a…

Canonical extension has proven to be a powerful tool in algebraic study of propositional logics. In this paper we describe a generalization of the theory of canonical extension to the setting of first order logic. We define a notion of…

We provide a denotational semantics for first-order logic that captures the two-level view of the computation process typical for constraint programming. At one level we have the usual program execution. At the other level an automatic…

We introduce a variation on Barthe et al.'s higher-order logic in which formulas are interpreted as predicates over open rather than closed objects. This way, concepts which have an intrinsically functional nature, like continuity,…

We propose a categorial grammar based on classical multiplicative linear logic. This can be seen as an extension of abstract categorial grammars (ACG) and is at least as expressive. However, constituents of {\it linear logic grammars (LLG)}…

Categorization systems are widely studied in psychology, sociology, and organization theory as information-structuring devices which are critical to decision-making processes. In the present paper, we introduce a sound and complete…

Logic has proved essential for formally modeling software based systems. Such formal descriptions, frequently called specifications, have served not only as requirements documentation and formalisation, but also for providing the…

Semiring semantics for first-order logic provides a way to trace how facts represented by a model are used to deduce satisfaction of a formula. Team semantics is a framework for studying logics of dependence and independence in diverse…

We present a domain-specific type theory for constructions and proofs in category theory. The type theory axiomatizes notions of category, functor, profunctor and a generalized form of natural transformations. The type theory imposes an…

Algebraic theories with dependency between sorts form the structural core of Martin-L\"of type theory and similar systems. Their denotational semantics are typically studied using categorical techniques; many different categorical…

There is a growing need for abstractions in logic specification languages such as FO(.) and ASP. One technique to achieve these abstractions are templates (sometimes called macros). While the semantics of templates are virtually always…

In this paper, we study whether transformer-based language models can extract predicate argument structure from simple sentences. We firstly show that language models sometimes confuse which predicates apply to which objects. To mitigate…

In these lecture notes, we give a brief introduction to some elements of category theory. The choice of topics is guided by applications to functional programming. Firstly, we study initial algebras, which provide a mathematical…

We show that the proof-theoretic notion of logical preorder coincides with the process-theoretic notion of contextual preorder for a CCS-like calculus obtained from the formula-as-process interpretation of a fragment of linear logic. The…