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SYLLOGISTIC LOGIC WITH CARDINALITY COMPARISONS, ON INFINITE SETS

Published online by Cambridge University Press:  05 June 2018

LAWRENCE S. MOSS  and
SELÇUK TOPAL
LAWRENCE S. MOSS*
Affiliation:
Department of Mathematics, Indiana University
SELÇUK TOPAL*
Affiliation:
Department of Mathematics, Bitlis Eren University
*
*DEPARTMENT OF MATHEMATICS INDIANA UNIVERSITY BLOOMINGTON, IN, USA E-mail: [email protected]
†DEPARTMENT OF MATHEMATICS BITLIS EREN UNIVERSITY BITLIS, TURKEY E-mail: [email protected]
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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.

Keywords

03B2003B6503C80syllogistic logiccardinalitycompleteness theorem
Type
Research Article
Information
The Review of Symbolic Logic , Volume 13 , Issue 1 , March 2020 , pp. 1 - 22
Copyright
Copyright © Association for Symbolic Logic 2018 

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References

BIBLIOGRAPHY

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. 143–173.Google Scholar
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. 391–415.CrossRefGoogle Scholar
Pratt-Hartmann, I. & Moss, L. S. (2009). Logics for the relational syllogistic. Review of Symbolic Logic, 2(4), 647–683.CrossRefGoogle Scholar