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Symmetric Propositions and Logical Quantifiers

Authors:	R Gregory Taylor

Institution:	(1) Department of Mathematics and Computer Science, Manhattan College, Riverdale, NY 10471, USA

Abstract:	Symmetric propositions over domain $\mathfrak{D}$ and signature $\Sigma = \langle R^{n_1}_1, \ldots, R^{n_p}_p \rangle$ are characterized following Zermelo, and a correlation of such propositions with logical type- $\langle \vec{n} \rangle$ quantifiers over $\mathfrak{D}$ is described. Boolean algebras of symmetric propositions over $\mathfrak{D}$ and Σ are shown to be isomorphic to algebras of logical type- $\langle \vec{n} \rangle$ quantifiers over $\mathfrak{D}$ . This last result may provide empirical support for Tarski’s claim that logical terms over fixed domain are all and only those invariant under domain permutations.

Keywords:	generalized quantifier logical notion symmetric proposition
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