GReTA seminar: "An Outline of the Theory of Generalized Sketches"
Channel: GReTA Seminar
Date: 2023-04-21

Speaker:

Uwe Wolter (Department of Informatics, University of Bergen, Norway)

Note: This is a joint event with the working group "Catégories supérieures, polygraphes et homotopie" at IRIF, Université Paris Cité (https://www.irif.fr/seminaires/cat/index)

Abstract:

Based on a new concept of first-order generalized sketches we coined lately “Logics of Statements in Context” to provide a unified view on formalisms like Algebraic Specifications, Prolog, First-Order Logic, Ehresmann Sketches, Description Logics, Generalized Sketches à la Makkai/Diskin, Diagram Predicate Framework, Graph Conditions, and others.
 
In the talk we present Generalized Sketches à la Makkai/Diskin as a quite natural generalization of traditional Ehresmann sketches. Generalized Sketches à la Makkai/Diskin can be defined in arbitrary categories. They built upon “atomic statements in context” and utilize sketch implications for axiomatization purposes. Going beyond atomic statements, we outline the definition of arbitrary first-order statements in arbitrary categories enabling us to enhance the expressiveness of Generalized Sketches. In analogy to first-order statements, we can also define arbitrary first-order sketch conditions generalizing thereby different kinds of “nested graph constraints and conditions”.
 
We intend to discuss, on the way, two essential constructions Makkai’s work on Generalized Sketches relies on: “Syntactic representation of models” and “internalization of atomic statements”.


About the GReTA seminars:

The GReTA – Graph TRansformation Theory and Applications virtual seminar series aims to serve as a platform for the international graph rewriting community, to promote recent developments and trends in the field, and to permit a regular networking and interaction between members of this community. Seminars are held twice a month in the form of Zoom sessions (some of which will be live-streamed to YouTube). Please refer to http://www.irif.fr/~greta for further details (including information on how to register for participating in the Zoom meetings).