Related papers: Logical relations for call-by-push-value models, v…
We exhibit a computational type theory which combines the higher-dimensional structure of cartesian cubical type theory with the internal parametricity primitives of parametric type theory, drawing out the similarities and distinctions…
Representation theorems for formal systems often take the form of an inductive translation that satisfies certain invariants, which are proved inductively. Theory morphisms and logical relations are common patterns of such inductive…
Natural language definitions possess a recursive, self-explanatory semantic structure that can support representation learning methods able to preserve explicit conceptual relations and constraints in the latent space. This paper presents a…
We give a categorical semantics for a call-by-value linear lambda calculus. Such a lambda calculus was used by Selinger and Valiron as the backbone of a functional programming language for quantum computation. One feature of this lambda…
We consider the 3-category $2\mathfrak{C}at$ whose objects are 2-categories, 1-morphisms are lax functors, 2-morphisms are lax transformations and 3-morphisms are modifications. The aim is to show that it carries interesting…
Cubical type theory provides a constructive justification to certain aspects of homotopy type theory such as Voevodsky's univalence axiom. This makes many extensionality principles, like function and propositional extensionality, directly…
Concept Bottleneck Models (CBMs) first map raw input(s) to a vector of human-defined concepts, before using this vector to predict a final classification. We might therefore expect CBMs capable of predicting concepts based on distinct…
Following Herranz and Santander [Herranz F.J., Santander M., Mem. Real Acad. Cienc. Exact. Fis. Natur. Madrid 32 (1998), 59-84, physics/9702030] we will construct homogeneous spaces based on possible kinematical algebras and groups [Bacry…
In each variant of the lambda-calculus, factorization and normalization are two key-properties that show how results are computed. Instead of proving factorization/normalization for the call-by-name (CbN) and call-by-value (CbV) variants…
We reconcile the two different category-theoretic semantics of regular theories in predicate logic. A 2-category of `regular fibrations' is constructed, as well as a 2-category of `regular proarrow equipments', and it is shown that the two…
The study of polarity in computation has revealed that an "ideal" programming language combines both call-by-value and call-by-name evaluation; the two calling conventions are each ideal for half the types in a programming language. But…
This paper is a sequel to "Logical systems I: Lambda calculi through discreteness". It provides a general 2-categorical setting for extensional calculi and shows how intensional and extensional calculi can be related in logical systems. We…
This article presents a reformulation of the Theory of Functional Connections: a general methodology for functional interpolation that can embed a set of user-specified linear constraints. The reformulation presented in this paper exploits…
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…
A kind of unstable homotopy theory on the category of associative rings (without unit) is developed. There are the notions of fibrations, homotopy (in the sense of Karoubi), path spaces, Puppe sequences, etc. One introduces the notion of a…
In an impressive series of papers, Krivine showed at the edge of the last decade how classical realizability provides a surprising technique to build models for classical theories. In particular, he proved that classical realizability…
The program of internal type theory seeks to develop the categorical model theory of dependent type theory using the language of dependent type theory itself. In the present work we study internal homotopical type theory by relaxing the…
Process theories combine a graphical language for compositional reasoning with an underlying categorical semantics. They have been successfully applied to fields such as quantum computation, natural language processing, linear dynamical…
We use the theory of Tambara modules to extend and generalize the reconstruction theorem for module categories over a rigid monoidal category to the non-rigid case. We show a biequivalence between the $2$-category of cyclic module…
Human beings possess the most sophisticated computational machinery in the known universe. We can understand language of rich descriptive power, and communicate in the same environment with astonishing clarity. Two of the many contributors…