Completeness and super-valuations

Journal of Philosophical Logic 34 (1):81 - 95 (2005)
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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 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.

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2009-01-28

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Gary Hardegree
University of Massachusetts, Amherst

Citations of this work

Inferentialism: Why Rules Matter.Jaroslav Peregrin - 2014 - London and New York: Palgrave-Macmillan.
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Valuations: Bi, Tri, and Tetra.Rohan French & David Ripley - 2019 - Studia Logica 107 (6):1313-1346.
Valuations: Bi, Tri, and Tetra.Rohan French & David Ripley - 2019 - Studia Logica 107 (6):1313-1346.
Speech Acts, Categoricity, and the Meanings of Logical Connectives.Ole Thomassen Hjortland - 2014 - Notre Dame Journal of Formal Logic 55 (4):445-467.

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References found in this work

Lattice Theory.Garrett Birkhoff - 1940 - Journal of Symbolic Logic 5 (4):155-157.
Lattice Theory.Garrett Birkhoff - 1950 - Journal of Symbolic Logic 15 (1):59-60.

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