Intuitionistic Euler-Venn Diagrams

Linker, Sven ORCID: 0000-0003-2913-7943 (2020) Intuitionistic Euler-Venn Diagrams. In: 11th International Conference on the Theory and Application of Diagrams.

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Official URL: http://dx.doi.org/10.1007/978-3-030-54249-8_21

Abstract

We present an intuitionistic interpretation of Euler-Venn diagrams with respect to Heyting algebras. In contrast to classical Euler-Venn diagrams, we treat shaded and missing zones differently, to have diagrammatic representations of conjunction, disjunction and intuitionistic implication. Furthermore, we need to add new syntactic elements to express these concepts. We present a cut-free sequent calculus for this language, and prove it to be sound and complete. Furthermore, we show that the rules of cut, weakening and contraction are admissible.

Item Type:	Conference or Workshop Item (Unspecified)
Uncontrolled Keywords:	Intuitionistic logic, Euler-Venn diagrams, Proof theory
Depositing User:	Symplectic Admin
Date Deposited:	12 May 2020 09:42
Last Modified:	18 Jan 2023 23:52
DOI:	10.1007/978-3-030-54249-8_21
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3086920