Abstract Categorical Logic / Isabelle Bloch / LUW February 22

[jean-yves beziau]

The next session of the Logica Universalis Webinar will be Wednesday
February 22 at 4pm CET (Paris-Geneva-Rome)

Speaker:  Isabelle Bloch, Sorbonne, Paris, France
Title of the talk: Abstract Categorical Logic
Abstract: We present in this talk  an abstract categorical logic based on
an abstraction of quantifier. More precisely, the proposed logic is
abstract because no structural constraints are imposed on models (semantics
free). By contrast, formulas are inductively defined from an abstraction
both of atomic formulas and of quantifiers. In this sense, the proposed
approach differs from other works interested in formalizing the notion of
abstract logic and of which the closest to our approach are the
institutions, which in addition to be semantics free do not also impose any
syntactic contingencies on the structure of formulas. To define the
semantical framework in which formulas will be interpreted, we propose to
follow the idea from categorical logic which defines the semantical
interpretation of formulas from context and as subobjects of an object of a
given category. In the spirit of Lawvere’s hyperdoctrines, we use a more
abstract notion which generalizes the notion of subobject, standard in
category theory: Pitt’s prop-categories. Always in the spirit of
categorical logic, we propose a sequent calculus of which we show
correctness and completeness for all semantical frameworks defined over any
prop-categories. We then study some conditions which allow us to get this
completeness result for particular classes of prop-categories.
https://link.springer.com/article/10.1007/s11787-022-00320-w

Associate Organization: GDR IA,  CNRS, presented by  Meghyn Bienvenu

Chair: Andrei Rodin, Editorial Board LU

Everybody is welcome to join, register here:
https://www.springer.com/journal/11787/updates/23910922
Jean-Yves Beziau
Organizer of LUW and Editor-in-Chief of Logica Universalis
http://www.jyb-logic.org/
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