ISSN:
1572-8730
Keywords:
many-valued logic
;
infinitely-valued logic
;
distribution quantifiers
;
distributive lattices
;
semantic tableaux
;
sequent calculi
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
,
Philosophy
Notes:
Abstract We provide tools for a concise axiomatization of a broad class of quantifiers in many-valued logic, so-called distribution quantifiers. Although sound and complete axiomatizations for such quantifiers exist, their size renders them virtually useless for practical purposes. We show that for quantifiers based on finite distributive lattices compact axiomatizations can be obtained schematically. This is achieved by providing a link between skolemized signed formulas and filters/ideals in Boolean set lattices. Then lattice theoretic tools such as Birkhoff's representation theorem for finite distributive lattices are used to derive tableau-style axiomatizations of distribution quantifiers.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1005086415447
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