Complete Axiomatization of Discrete-Measure Almost-Everywhere Quantification

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 t...

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Bibliographic Details
Published in:Journal of logic and computation 2008-12, Vol.18 (6), p.885-911
Main Authors: Cruz-Filipe, Luís, Rasga, João, Sernadas, Amílcar, Sernadas, Cristina
Format: Article
Language:English
Subjects:
almost-everywhere logic
complete axiomatization
Generalized quantification
measure-theoretic semantics
probabilistic logic
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Summary: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.
ISSN:0955-792X
1465-363X
DOI:10.1093/logcom/exn014