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Generalized existential completions and their regular and exact completions
Maria Emilia Maietti, Davide Trotta
This paper aims to apply the tool of generalized existential completions of conjunctive doctrines, concerning a class of morphisms of their base category, to deepen the study o…
A Presheaf Semantics for Quantified Temporal Logics
Fabio Gadducci, Davide Trotta
Temporal logics stands for a widely adopted family of formalisms for the verification of computational devices, enriching propositional logics by operators predicating on the step-…
Dialectica Logical Principles
Davide Trotta, Matteo Spadetto, Valeria de Paiva
Gödel's Dialectica interpretation was designed to obtain a relative consistency proof for Heyting arithmetic, to be used in conjunction with the double negation interpretation to o…
The existential completion
Davide Trotta
We determine the existential completion of a primary doctrine, and we prove that the 2-monad obtained from it is lax-idempotent, and that the 2-category of existential doctrines is…
An algebraic approach to the completions of elementary doctrines
Davide Trotta
We provide a thorough algebraic analysis of three known completions having a central role in the exact completions of Lawvere's doctrines: the one adding comprehensive diagonals (i…