2023/08/03 by Yuta Yamamoto, Yamamoto, Yuta
Computer Science · #Advanced Algebra and Logic #Logic, Reasoning, and Knowledge #Bayesian Modeling and Causal Inference
paper · pdf · doi:10.48550/arxiv.2308.01662
Führmann and Pym constructed models of classical propositional logic in an order-enriched categorical setting, whose typical example is the category Rel of sets and relations. It is remarkable in that they are both non-degenerate and symmetric, i.e., free from the choices of the reduction strategy. As a furter categorification of this direction, we give bicategorical models of classical propositional logic that is also symmetric and non-degenerate. Primal examples of our models include Rel, Span, and Prof, which shows that we can construct models that are non-degenerate not only for 1-cells but also for 2-cells and the logical negations.