Completeness and super-valuations

Journal of Philosophical Logic 34 (1):81 - 95 (2005)
Abstract
This paper uses the notion of Galois-connection to examine the relation between valuation-spaces and logics. Every valuation-space gives rise to a logic, and every logic gives rise to a valuation space, where the resulting pair of functions form a Galoisconnection, and the composite functions are closure-operators. A valuation-space is said to be complete precisely if it is Galois-closed. Two theorems are proven. A logic is complete if and only if it is reflexive and transitive. A valuation-space is complete if and only if it is closed under formation of super-valuations.
Keywords completeness  Galois-connection  logic  super-valuation  valuation-space
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DOI 10.1007/s10992-004-6302-6
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What is a Non-Truth-Functional Logic?João Marcos - 2009 - Studia Logica 92 (2):215-240.
Inferentializing Semantics.Jaroslav Peregrin - 2010 - Journal of Philosophical Logic 39 (3):255 - 274.
Duality and Inferential Semantics.James Trafford - 2015 - Axiomathes 25 (4):495-513.

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