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of 55
pro vyhledávání: '"Trotta, Davide"'
Grothendieck fibrations are fundamental in capturing the concept of dependency, notably in categorical semantics of type theory and programming languages. A relevant instance are Dialectica fibrations which generalise G\"odel's Dialectica proof inter
Externí odkaz:
http://arxiv.org/abs/2407.15765
Fo-bicategories are a categorification of Peirce's calculus of relations. Notably, their laws provide a proof system for first-order logic that is both purely equational and complete. This paper illustrates a correspondence between fo-bicategories an
Externí odkaz:
http://arxiv.org/abs/2404.18795
Autor:
Maietti, Maria Emilia, Trotta, Davide
We provide a new description of Joyal's arithmetic universes through a characterization of the exact and regular completions of pure existential completions. We show that the regular and exact completions of the pure existential completion of an elem
Externí odkaz:
http://arxiv.org/abs/2306.13610
Autor:
Maschio, Samuele, Trotta, Davide
Publikováno v:
Annals of Pure and Applied Logic, Vol. 3, 2023, No. 3, p 103390
Implicative algebras have been recently introduced by Miquel in order to provide a unifying notion of model, encompassing the most relevant and used ones, such as realizability (both classical and intuitionistic), and forcing. In this work, we initia
Externí odkaz:
http://arxiv.org/abs/2306.04534
We present a first-order linear-time temporal logic for reasoning about the evolution of directed graphs. Its semantics is based on the counterpart paradigm, thus allowing our logic to represent the creation, duplication, merging, and deletion of ele
Externí odkaz:
http://arxiv.org/abs/2305.03832
Publikováno v:
10th Conference on Algebra and Coalgebra in Computer Science (CALCO 2023), 16:1--16:17
Introduced in the 1990s in the context of the algebraic approach to graph rewriting, gs-monoidal categories are symmetric monoidal categories where each object is equipped with the structure of a commutative comonoid. They arise for example as Kleisl
Externí odkaz:
http://arxiv.org/abs/2303.14049
This paper presents categorical formulations of Turing, Medvedev, Muchnik, and Weihrauch reducibilities in Computability Theory, utilizing Lawvere doctrines. While the first notions lend themselves to a smooth categorical presentation, essentially du
Externí odkaz:
http://arxiv.org/abs/2208.08656
Publikováno v:
Theoretical Computer Science, vol. 947, 2023
G\"odel's Dialectica interpretation was conceived as a tool to obtain the consistency of Peano arithmetic via a proof of consistency of Heyting arithmetic in the 40s. In recent years, several proof-theoretic transformations, based on G\"odel's Dialec
Externí odkaz:
http://arxiv.org/abs/2205.07093
Publikováno v:
Appl. Categ. Structures 31, 42 (2023)
Originally introduced in the context of the algebraic approach to term graph rewriting, the notion of gs-monoidal category has surfaced a few times under different monikers in the last decades. They can be thought of as symmetric monoidal categories
Externí odkaz:
http://arxiv.org/abs/2205.06892
Publikováno v:
In Nuclear Inst. and Methods in Physics Research, A October 2024 1067