Crawley Completions of Residuated Lattices and Algebraic Completeness of Substructural Predicate Logics

Studia Logica 100 (1-2):339-359 (2012)
Abstract
This paper discusses Crawley completions of residuated lattices. While MacNeille completions have been studied recently in relation to logic, Crawley completions (i.e. complete ideal completions), which are another kind of regular completions, have not been discussed much in this relation while many important algebraic works on Crawley completions had been done until the end of the 70’s. In this paper, basic algebraic properties of ideal completions and Crawley completions of residuated lattices are studied first in their conncetion with the join infinite distributivity and Heyting implication. Then some results on algebraic completeness and conservativity of Heyting implication in substructural predicate logics are obtained as their consequences
Keywords regular completions  Crawley completions  infinite distributivities  residuated lattices  algebraic completeness  substructural predicate logics
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DOI 10.1007/s11225-012-9381-3
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The Mathematics of Metamathematics.Helena Rasiowa - 1963 - Warszawa, Państwowe Wydawn. Naukowe.
Logics Without the Contraction Rule.Hiroakira Ono & Yuichi Komori - 1985 - Journal of Symbolic Logic 50 (1):169-201.

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