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Towards a model theory of diagrams

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Abstract

A logical system is studied whose well-formed representations consist of diagrams rather than formulas. The system, due to Shin [2, 3], is shown to be complete by an argument concerning maximally consistent sets of diagrams. The argument is complicated by the lack of a straight forward counterpart of atomic formulas for diagrams, and by the lack of a counterpart of negation for most diagrams.

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References

  1. V. Polythress and H. Sun. A Method to Contruct Convex, Connected Venn Diagrams for Any Finite Number of Sets. Pentagon, 1972.

  2. Sun-Joo Shin. The Logical Status of Diagrams. Cambridge University Press, 1995.

  3. Sun-Joo Shin. A Situation-Theoretic Account of Valid Reasoning with Venn Diagrams. In J. Barwise et al., (eds), Situation Theory and Its Applications, Vol. 2. Stanford: CSLI, 1991.

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  4. More Trenchard. On the Construction of Venn Diagrams, Journal of Symbolic Logic 24 (1959), 303–304.

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Authors and Affiliations

  1. Department of Philosophy, Indiana University, 47405, Bloomington, IN, USA

    Eric Hammer & Norman Danner

  2. Department of Mathematics, Indiana University, 47405, Bloomington, IN, USA

    Eric Hammer & Norman Danner

Authors
  1. Eric Hammer
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  2. Norman Danner
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Additional information

The authors are grateful to Jon Barwise and an anonymous referee for valuable comments and suggestions.

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Hammer, E., Danner, N. Towards a model theory of diagrams. J Philos Logic 25, 463–482 (1996). https://doi.org/10.1007/BF00257381

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  • DOI: https://doi.org/10.1007/BF00257381

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