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Syllogistic logic with “Most”

Published online by Cambridge University Press:  13 March 2019

Jörg Endrullis  and
Lawrence S. Moss
Jörg Endrullis
Affiliation:
Department of Computer Science, Vrije Universiteit Amsterdam, 1081 HV Amsterdam, The Netherlands Department of Mathematics, Indiana University, Bloomington, IU 47405, USA
Lawrence S. Moss*
Affiliation:
Department of Mathematics, Indiana University, Bloomington, IU 47405, USA
*
*Corresponding author. Email: lmoss@indiana.edu
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Abstract

We add Most X are Y to the syllogistic logic of All X are Y and Some X are Y. We prove soundness, completeness, and decidability in polynomial time. Our logic has infinitely many rules, and we prove that this is unavoidable.

Keywords

syllogistic logicmajority quantifiercompleteness theorem
Type
Paper
Information
Mathematical Structures in Computer Science , Volume 29 , Issue 6 , June 2019 , pp. 763 - 782
Copyright
© Cambridge University Press 2019 

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References

Lai, T., Endrullis, J. and Moss, L. S. (2016). Majority digraphs. Proceedings of the American Mathematical Society 144(9): 3701–3715.CrossRefGoogle Scholar
Moss, L. S. (2008). Completeness theorems for syllogistic fragments. In: Hamm, F. and Kepser, S. (eds.) Logics for Linguistic Structures, Mouton de Gruyter, Berlin, 143–173.Google Scholar
Pratt-Hartmann, I. (2009). No syllogisms for the numerical syllogistic. In: Languages: from Formal to Natural, vol. 5533, LNCS, Springer, Berlin 192–203.Google Scholar
Pratt-Hartmann, I. and Moss, L. S. (2009). Logics for the relational syllogistic. Review of Symbolic Logic 2(4):647–683.Google Scholar