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Journal of Philosophical Logic

, Volume 34, Issue 1, pp 81–95 | Cite as

Completeness and super-valuations

  • Gary M. Hardegree
Article

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 Galois-connection, and the composite functions are closure-operators. A valuation-space (resp., logic) 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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Copyright information

© Springer 2005

Authors and Affiliations

  1. 1.Department of PhilosophyUniversity of MassachusettsAmherst

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