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)
Download (629kB)
Preview
|
|
|
Official URL http://dx.doi.org/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) |
- Export to:
- RefWorks
- EPrints3 XML
- BibTeX
- CSV
- Depositors only (login required):