Categorical semiotics

TL;DR

This paper extends algebraic specification methods using graphic structures inspired by category theory to better integrate and reason about diverse data models and knowledge representations.

Contribution

It introduces a novel framework combining algebraic specifications with fuzzy sketches for improved data and model integration.

Findings

Framework effectively combines deterministic and nondeterministic data structures

Uses graphic languages for reasoning and task decomposition

Enhances integration of models from different sources

Abstract

The integration of knowledge extracted from different models described by domain experts or from models generated by machine learning algorithms is strongly conditioned by the lack of an appropriated framework to specify and integrate structures, learning processes, data transformations and data models or data rules. In this work we extended algebraic specification methods to be used in this type of framework. This methodology uses graphic structures similar to Ehresmann's sketches interpreted on a fuzzy set universe. This approach takes advantages of the sketches ability to integrate data deterministic and nondeterministic structures. Selecting this strategy we also try to take advantage on how the graphic languages, used in Category theory in general and used for sketch definition in particular, are suited to reasoning about problems, to structural description and to task specification and task decomposition.