On the Completeness of Spider Diagrams Augmented with Constants

Stapleton, Gem and Howse, John and Thompson, Simon and Taylor, John and Chapman, Peter (2013) On the Completeness of Spider Diagrams Augmented with Constants. In: Moktefi, Amirouche and Shin, Sun-Joo, eds. Visual Reasoning with Diagrams. Studies in Universal Logic . Birkhauser, pp. 101-133. ISBN 978-3-0348-0599-5. E-ISBN 978-3-0348-0600-8. (doi:10.1007/978-3-0348-0600-8_7)

Abstract

Diagrammatic reasoning can be described formally by a number of diagrammatic logics; spider diagrams are one of these, and are used for expressing logical statements about set membership and containment. Here, existing work on spider diagrams is extended to include constant spiders that represent specific individuals. We give a formal syntax and semantics for the extended diagram language before introducing a collection of reasoning rules encapsulating logical equivalence and logical consequence. We prove that the resulting logic is sound, complete and decidable.

Item Type:	Book section
DOI/Identification number:	10.1007/978-3-0348-0600-8_7
Uncontrolled keywords:	Spider diagrams ; Constants ; Soundness ; Completeness ; Monadic first-order logic ; Diagrammatic reasoning
Subjects:	Q Science > QA Mathematics (inc Computing science) > QA 9 Formal systems, logics
Divisions:	Faculties > Sciences > School of Computing Faculties > Sciences > School of Computing > Programming Languages and Systems Group
Depositing User:	Simon Thompson
Date Deposited:	14 Aug 2014 14:19 UTC
Last Modified:	29 May 2019 12:55 UTC
Resource URI:	https://kar.kent.ac.uk/id/eprint/42317 (The current URI for this page, for reference purposes)