Notre Dame Journal of Formal Logic

Reasoning with Sentences and Diagrams

Eric Hammer

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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.

Article information

Source
Notre Dame J. Formal Logic, Volume 35, Number 1 (1994), 73-87.

Dates
First available in Project Euclid: 22 December 2002

Permanent link to this document
https://projecteuclid.org/euclid.ndjfl/1040609295

Digital Object Identifier
doi:10.1305/ndjfl/1040609295

Mathematical Reviews number (MathSciNet)
MR1271699

Zentralblatt MATH identifier
0801.03004

Subjects
Primary: 03B99: None of the above, but in this section

Citation

Hammer, Eric. Reasoning with Sentences and Diagrams. Notre Dame J. Formal Logic 35 (1994), no. 1, 73--87. doi:10.1305/ndjfl/1040609295. https://projecteuclid.org/euclid.ndjfl/1040609295


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References

  • Boolos, George., “A Curious Inference,” The Journal of Philosophical Logic, vol. 16 (1987), pp. 1-12.
  • Hammer, Eric., and Norman Danner, “Towards a Model Theory of Venn Diagrams,” Unpublished Paper.
  • Shin, Sun-Joo., The Logical Status of Diagrams, Cambridge University Press, Cambridge, forthcoming.
  • Shin, Sun-Joo., “A Situation-Theoretic Account of Valid Reasoning with Venn Diagrams,” pp. 581–605 in Situation Theory and its Applications II, CSLI, 1991.