Related papers: Categorical Models for a Semantically Linear Lambd…
We describe a notion of categorical model for unitless fragments of (multiplicative) linear logic. The basic definition uses promonoidal categories, and we also give an equivalent elementary axiomatisation.
In this paper, we study a functional programming approach to natural language semantics, allowing us to increase the expressiveness of a more traditional denotation style. We will formalize a category based type and effect system to…
It is known that different categorial grammars have surface representation in a fragment of first order multiplicative linear logic (MLL1). We show that the fragment of interest is equivalent to the recently introduced extended tensor type…
In this survey article, we review some conceptual approaches to the cyclic category $\Lambda$, as well as its description as a crossed simplicial group. We then give a new proof of the model structure on cyclic sets, work through the…
We give a simple order-theoretic construction of a Cartesian closed category of sequential functions. It is based on bistable biorders, which are sets with a partial order -- the extensional order -- and a bistable coherence, which captures…
For every functor $\mathcal{F} : \mathcal{K} \to \mathbf{C}$, where $\mathcal{K}$ is a small category and $\mathbf{C}$ is a model category which satisfies some mild hypotheses, we define a model category $\mathbf{C}^m$ of…
We present a linearity theorem for a proof language of intuitionistic multiplicative additive linear logic, incorporating addition and scalar multiplication. The proofs in this language are linear in the algebraic sense. This work is part…
This paper discusses a Domain Specific Language (DSL) that has been developed to enable implementation of concepts of discrete mathematics. A library of data types and functions provides functionality which is frequently required by users.…
Classification is an important goal in many branches of mathematics. The idea is to describe the members of some class of mathematical objects, up to isomorphism or other important equivalence in terms of relatively simple invariants. Where…
Modern programming frequently requires generalised notions of program equivalence based on a metric or a similar structure. Previous work addressed this challenge by introducing the notion of a V-equation, i.e. an equation labelled by an…
Large Language Models (LLMs) are increasingly integrated into the software engineering ecosystem. Their test-time compute (TTC) reasoning capabilities show significant potential for understanding program logic and semantics beyond mere…
Message passing is a key ingredient of concurrent programming. The purpose of this paper is to describe the equivalence between the proof theory, the categorical semantics, and term calculus of message passing. In order to achieve this we…
We investigate the possibility of a semantic account of the execution time (i.e. the number of beta-steps leading to the normal form, if any) for the shuffling calculus, an extension of Plotkin's call-by-value lambda-calculus. For this…
The growing complexity of modern practical problems puts high demands on the mathematical modelling. Given that various models can be used for modelling one physical phenomenon, the role of model comparison and model choice becomes…
Cirquent calculus is a novel proof theory permitting component-sharing between logical expressions. Using it, the predecessor article "Elementary-base cirquent calculus I: Parallel and choice connectives" built the sound and complete…
We develop a general theory of semantic dynamics for large language models by formalizing them as Continuous State Machines (CSMs): smooth dynamical systems whose latent manifolds evolve under probabilistic transition operators. The…
Large language models (LLMs) are increasingly used for semantic query processing over large corpora. A set of semantic operators derived from relational algebra has been proposed to provide a unified interface for expressing such queries,…
Linear dependent types allow to precisely capture both the extensional behaviour and the time complexity of lambda terms, when the latter are evaluated by Krivine's abstract machine. In this work, we show that the same paradigm can be…
Completeness proofs in categorical semantics usually proceed by building a syntactic category whose composition is given by substitution. For untyped effectful Call-by-Value languages, this runs into a basic obstacle: there is no canonical…
This thesis deals with two main topics: virtual double categories as semantics environments for predicate logic, and a syntactic presentation of virtual double categories as a type theory. One significant principle of categorical logic is…