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SYLLOGISTIC LOGIC WITH CARDINALITY COMPARISONS, ON INFINITE SETS

  • LAWRENCE S. MOSS (a1) and SELÇUK TOPAL (a2)
Abstract

This article enlarges classical syllogistic logic with assertions having to do with comparisons between the sizes of sets. So it concerns a logical system whose sentences are of the following forms: All x are y and Some x are y, There are at least as many x as y, and There are more x than y. Here x and y range over subsets (not elements) of a given infinite set. Moreover, x and y may appear complemented (i.e., as $\bar{x}$ and $\bar{y}$ ), with the natural meaning. We formulate a logic for our language that is based on the classical syllogistic. The main result is a soundness/completeness theorem. There are efficient algorithms for proof search and model construction.

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Corresponding author
*DEPARTMENT OF MATHEMATICS INDIANA UNIVERSITY BLOOMINGTON, IN, USA E-mail: lmoss@indiana.edu
DEPARTMENT OF MATHEMATICS BITLIS EREN UNIVERSITY BITLIS, TURKEY E-mail: s.topal@beu.edu.tr
References
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Moss, L. S. (2008). Completeness theorems for syllogistic fragments. In Hamm, F. and Kepser, S., editors. Logics for Linguistic Structures. Berlin: Mouton de Gruyter, pp. 143173.
Moss, L. S. (2016). Syllogistic logic with cardinality comparisons. In Bimbo, K., editor. J. Michael Dunn on Information Based Logics. Outstanding Contributions to Logic. Cham, Switzerland: Springer, pp. 391415.
Pratt-Hartmann, I. & Moss, L. S. (2009). Logics for the relational syllogistic. Review of Symbolic Logic, 2(4), 647683.
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The Review of Symbolic Logic
  • ISSN: 1755-0203
  • EISSN: 1755-0211
  • URL: /core/journals/review-of-symbolic-logic
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