4 research outputs found
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