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Journal of Logic and Computation Advance Access originally published online on April 23, 2008
Journal of Logic and Computation 2008 18(6):885-911; doi:10.1093/logcom/exn014
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© The Author, 2008. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Original Articles

Complete Axiomatization of Discrete-Measure Almost-Everywhere Quantification

Luís Cruz-Filipe

Lasige and Dep. Informática, FC, U Lisbon, Portugal.
E-mail: lcf{at}di.fc.ul.pt

João Rasga, Amílcar Sernadas and Cristina Sernadas

SQIG - Instituto de Telecomunicações and Dep. Matemática, IST, TU Lisbon, Portugal.
E-mail: jfr{at}math.ist.utl.pt; acs{at}math.ist.utl.pt; css{at}math.ist.utl.pt

Received 9 June 2006.


  Abstract

Following recent developments in the topic of generalized quantifiers, and also having in mind applications in the areas of security and artificial intelligence, a conservative enrichment of (two-sorted) first-order logic (FOL) with almost-everywhere quantification is proposed. The completeness of the axiomatization against the measure-heoretic semantics is carried out using a variant of the Lindenbaum–Henkin technique. The independence of the axioms is analysed, and the almost-everywhere quantifier is compared with related notions of generalized quantification. A suitable fragment of the logic is translated to FOL and validity is shown to be preserved.

Keywords: Generalized quantification; almost-everywhere logic; probabilistic logic; measure-theoretic semantics; complete axiomatization


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