A Diagrammatic Inference System with Euler Circles

Journal of Logic, Language and Information 21 (3):365-391 (2012)
  Copy   BIBTEX

Abstract

Proof-theory has traditionally been developed based on linguistic (symbolic) representations of logical proofs. Recently, however, logical reasoning based on diagrammatic or graphical representations has been investigated by logicians. Euler diagrams were introduced in the eighteenth century. But it is quite recent (more precisely, in the 1990s) that logicians started to study them from a formal logical viewpoint. We propose a novel approach to the formalization of Euler diagrammatic reasoning, in which diagrams are defined not in terms of regions as in the standard approach, but in terms of topological relations between diagrammatic objects. We formalize the unification rule, which plays a central role in Euler diagrammatic reasoning, in a style of natural deduction. We prove the soundness and completeness theorems with respect to a formal set-theoretical semantics. We also investigate structure of diagrammatic proofs and prove a normal form theorem.

Other Versions

No versions found

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 101,505

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

How Diagrams Can Support Syllogistic Reasoning: An Experimental Study.Yuri Sato & Koji Mineshima - 2015 - Journal of Logic, Language and Information 24 (4):409-455.
On automating diagrammatic proofs of arithmetic arguments.Mateja Jamnik, Alan Bundy & Ian Green - 1999 - Journal of Logic, Language and Information 8 (3):297-321.
Speedith: A Reasoner for Spider Diagrams.Matej Urbas, Mateja Jamnik & Gem Stapleton - 2015 - Journal of Logic, Language and Information 24 (4):487-540.
Calculus CL as a Formal System.Jens Lemanski & Ludger Jansen - 2020 - In Ahti Veikko Pietarinen, Peter Chapman, Leonie Bosveld-de Smet, Valeria Giardino, James Corter & Sven Linker (eds.), Diagrammatic Representation and Inference. Diagrams 2020. Lecture Notes in Computer Science, vol 12169. 2020. pp. 445-460.
Prolegomena to a cognitive investigation of Euclidean diagrammatic reasoning.Yacin Hamami & John Mumma - 2013 - Journal of Logic, Language and Information 22 (4):421-448.

Analytics

Added to PP
2012-03-28

Downloads
116 (#185,946)

6 months
19 (#155,223)

Historical graph of downloads
How can I increase my downloads?

Author Profiles

Citations of this work

A Bitstring Semantics for Calculus CL.Fabien Schang & Jens Lemanski - 2022 - In Jean-Yves Beziau & Ioannis Vandoulakis (eds.), The Exoteric Square of Opposition. Birkhauser. pp. 171–193.
Syllogisms in Rudimentary Linear Logic, Diagrammatically.Ruggero Pagnan - 2013 - Journal of Logic, Language and Information 22 (1):71-113.
How Diagrams Can Support Syllogistic Reasoning: An Experimental Study.Yuri Sato & Koji Mineshima - 2015 - Journal of Logic, Language and Information 24 (4):409-455.

View all 7 citations / Add more citations

References found in this work

Symbolic logic.John Venn - 1894 - New York,: B. Franklin.
Symbolic Logic.John Venn - 1881 - Mind 6 (24):574-581.
Logic and Visual Information.Eric Hammer - 1995 - CSLI Publications.
[Introduction].O. H. Mitchell & J. Venn - 1884 - Mind 9 (34):321-322.
Euler’s visual logic.Eric Hammer & Sun-Joo Shin - 1998 - History and Philosophy of Logic 19 (1):1-29.

View all 6 references / Add more references