Computer-supported Exploration of a Categorical Axiomatization of Modeloids

A modeloid, a certain set of partial bijections, emerges from the idea to abstract from a structure to the set of its partial automorphisms. It comes with an operation, called the derivative, which is inspired by Ehrenfeucht-Fra\"iss\'e games. In this paper we develop a generalization of a modeloid first to an inverse semigroup and then to an inverse category using an axiomatic approach to category theory. We then show that this formulation enables a purely algebraic view on Ehrenfeucht-Fra\"iss\'e games.Comment: 24 pages; accepted for conference: Relational and Algebraic Methods in Computer Science (RAMICS 2020

Category Theory in Isabelle/HOL as a Basis for Meta-logical Investigation

This paper presents meta-logical investigations based on category theory using the proof assistant Isabelle/HOL. We demonstrate the potential of a free logic based shallow semantic embedding of category theory by providing a formalization of the notion of elementary topoi. Additionally, we formalize symmetrical monoidal closed categories expressing the denotational semantic model of intuitionistic multiplicative linear logic. Next to these meta-logical-investigations, we contribute to building an Isabelle category theory library, with a focus on ease of use in the formalization beyond category theory itself. This work paves the way for future formalizations based on category theory and demonstrates the power of automated reasoning in investigating meta-logical questions.Comment: 15 pages. Preprint of paper accepted for CICM 2023 conferenc

Proceedings of the Deduktionstreffen 2019

The annual meeting Deduktionstreffen is the prime activity of the Special Interest Group on Deduction Systems (FG DedSys) of the AI Section of the German Society for Informatics (GI-FBKI). It is a meeting with a familiar, friendly atmosphere, where everyone interested in deduction can report on their work in an informal setting

Free Higher-Order Logic - Notion, Definition and Embedding in HOL

Free logics are a family of logics that are free of any existential assumptions. This family can roughly be divided into positive, negative, neutral and supervaluational free logic whose semantics differ in the way how nondenoting terms are treated. While there has been remarkable work done concerning the definition of free first-order logic, free higher-order logic has not been addressed thoroughly so far. The purpose of this thesis is, firstly, to give a notion and definition of free higher-order logic based on simple type theory and, secondly, to propose faithful shallow semantical embeddings of free higher-order logic into classical higher order logic found on this definition. Such embeddings can then effectively be utilized to enable the application of powerful state-of-the-art higher-order interactive and automated theorem provers for the formalization and verification and also the further development of increasingly important free logical theories