Logical foundations of quantitative equality
F Dagnino, F Pasquali - Proceedings of the 37th Annual ACM/IEEE …, 2022 - dl.acm.org
In quantitative reasoning one compares objects by distances, instead of equivalence
relations, so that one can measure how much they are similar, rather than just saying …
relations, so that one can measure how much they are similar, rather than just saying …
Adding a constant and an axiom to a doctrine
F Guffanti - Mathematical Logic Quarterly, 2024 - Wiley Online Library
We study the meaning of “adding a constant to a language” for any doctrine, and “adding an
axiom to a theory” for a primary doctrine, by showing how these are actually two instances of …
axiom to a theory” for a primary doctrine, by showing how these are actually two instances of …
Strategies in spatio-temporal logics for multi-agent systems
In distributed agent systems, agents with different abilities work autonomously to reach a
common task, in the face of challenges posed by their environment. Two types of structures …
common task, in the face of challenges posed by their environment. Two types of structures …
A fibrational tale of operational logical relations
Logical relations built on top of an operational semantics are one of the most successful
proof methods in programming language semantics. In recent years, more and more …
proof methods in programming language semantics. In recent years, more and more …
A Fibrational Tale of Operational Logical Relations: Pure, Effectful and Differential
Logical relations built on top of an operational semantics are one of the most successful
proof methods in programming language semantics. In recent years, more and more …
proof methods in programming language semantics. In recent years, more and more …
The Relational Quotient Completion
F Dagnino, F Pasquali - arXiv preprint arXiv:2412.11295, 2024 - arxiv.org
Taking a quotient roughly means changing the notion of equality on a given object, set or
type. In a quantitative setting, equality naturally generalises to a distance, measuring how …
type. In a quantitative setting, equality naturally generalises to a distance, measuring how …
Cauchy-completions and the rule of unique choice in relational doctrines
F Dagnino, F Pasquali - arXiv preprint arXiv:2402.19266, 2024 - arxiv.org
Lawvere's generalised the notion of complete metric space to the field of enriched
categories: an enriched category is said to be Cauchy-complete if every left adjoint bimodule …
categories: an enriched category is said to be Cauchy-complete if every left adjoint bimodule …
Quantitative Equality in Substructural Logic via Lipschitz Doctrines
F Dagnino, F Pasquali - arXiv preprint arXiv:2110.05388, 2021 - arxiv.org
Substructural logics naturally support a quantitative interpretation of formulas, as they are
seen as consumable resources. Distances are the quantitative counterpart of equivalence …
seen as consumable resources. Distances are the quantitative counterpart of equivalence …