Reasoning with Sentences and Diagrams


Abstract
A formal system is studied having both sentences and diagrams as well-formed representations. Proofs in the system allow inference back and forth between sentences and diagrams, as well as between diagrams and diagrams, and between sentences and sentences. This sort of heterogeneous system is of interest because external representations other than linguistic ones occur commonly in actual reasoning in conjunction with language. Syntax, semantics, and rules of inference for the system are given and it is shown to be sound and complete
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DOI 10.1305/ndjfl/1040609295
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A Diagrammatic Calculus of Syllogisms.Ruggero Pagnan - 2012 - Journal of Logic, Language and Information 21 (3):347-364.
Syllogisms in Rudimentary Linear Logic, Diagrammatically.Ruggero Pagnan - 2013 - Journal of Logic, Language and Information 22 (1):71-113.
Euler’s Visual Logic.Eric Hammer & Sun-Joo Shin - 1998 - History and Philosophy of Logic 19 (1):1-29.
On the Insufficiency of Linear Diagrams for Syllogisms.Oliver Lemon & Ian Pratt - 1998 - Notre Dame Journal of Formal Logic 39 (4):573-580.

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