Related papers: A Categorical Semantics for Linear Logical Framewo…
We discuss what it means for a symmetric monoidal category to be a module over a commutative semiring category. Each of the categories of (1) cartesian monoidal categories, (2) semiadditive categories, and (3) connective spectra can be…
We present a complete logic for reasoning with functional dependencies (FDs) with semantics defined over classes of commutative integral partially ordered monoids and complete residuated lattices. The dependencies allow us to express…
This paper presents a construction which transforms categorical models of additive-free propositional linear logic, closely based on de Paiva's dialectica categories and Oliva's functional interpretations of classical linear logic. The…
We introduce the notion of a logical model category which is a Quillen model category satisfying some additional conditions. Those conditions provide enough expressive power that one can soundly interpret dependent products and sums in it.…
A symmetric monoidal category naturally arises as the mathematical structure that organizes physical systems, processes, and composition thereof, both sequentially and in parallel. This structure admits a purely graphical calculus. This…
Layered monoidal theories provide a categorical framework for studying scientific theories at different levels of abstraction, via string diagrammatic algebra. We introduce models for three closely related classes of layered monoidal…
We give a natural-deduction-style type theory for symmetric monoidal categories whose judgmental structure directly represents morphisms with tensor products in their codomain as well as their domain. The syntax is inspired by Sweedler…
Intensional computation derives concrete outputs from abstract function definitions; extensional computation defines functions through explicit input-output pairs. In formal semantics: intensional computation interprets expressions as…
Many formal languages of contemporary mathematical music theory -- particularly those employing category theory -- are powerful but cumbersome: ideas that are conceptually simple frequently require expression through elaborate categorical…
We give an exposition of the semantics of the simply-typed lambda-calculus, and its linear and ordered variants, using multi-ary structures. We define universal properties for multicategories, and use these to derive familiar rules for…
Matching logic is a general formal framework for reasoning about a wide range of theories, with particular emphasis on programming language semantics. Notably, the intermediate language of the K semantics framework is an extension of…
We present a categorical model for intuitionistic linear logic where objects are polynomial diagrams and morphisms are simulation diagrams. The multiplicative structure (tensor product and its adjoint) can be defined in any locally…
Languages may encode similar meanings using different sentence structures. This makes it a challenge to provide a single set of formal rules that can derive meanings from sentences in many languages at once. To overcome the challenge, we…
It is well known that dependence logic captures the complexity class NP, and it has recently been shown that inclusion logic captures P on ordered models. These results demonstrate that team semantics offers interesting new possibilities…
At the heart of intuitionistic type theory lies an intuitive semantics called the "meaning explanations"; crucially, when meaning explanations are taken as definitive for type theory, the core notion is no longer "proof" but "verification".…
Linear Logic refines Intuitionnistic Logic by taking into account the resources used during the proof and program computation. In the past decades, it has been extended to various frameworks. The most famous are indexed linear logics which…
A prototypical example of categorial grammars are those based on Lambek calculus, i.e. noncommutative intuitionistic linear logic. However, it has been noted that purely noncommutative operations are often not sufficient for modeling even…
We study categorical models for the unitless fragment of multiplicative linear logic. We find that the appropriate notion of model is a special kind of promonoidal category. Since the theory of promonoidal categories has not been developed…
This paper proposes a way to compute the meanings associated with sentences with generic noun phrases corresponding to the generalized quantifier most. We call these generics specimens and they resemble stereotypes or prototypes in lexical…
In this work we define formal grammars in terms of free monoidal categories, along with a functor from the category of formal grammars to the category of automata. Generalising from the Booleans to arbitrary semirings, we extend our…