Functional dependencies, supervenience, and consequence relations

I. L. Humberstone

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7 Citations (Scopus)

Abstract

An analogy between functional dependencies and implicational formulas of sentential logic has been discussed in the literature. We feel that a somewhat different connexion between dependency theory and sentential logic is suggested by the similarity between 'Armstrong's axioms' for functional dependencies and Tarski's defining conditions for consequence relations, and we pursue aspects of this other analogy here for their theoretical interest. The analogy suggests, for example, a different semantic interpretation of consequence relations: instead of thinking of B as a consequence of a set of formulas {A1,..., An} when B is true on every assignment of truth-values on which each Ai is true, we can think of this relation as obtaining when every pair of truth-value assignments which give the same truth-values to A1, the same truth-values to A2,..., and the same truth-values to An, also make the same assignment in respect of B. We describe the former as the consequence relation 'inference-determined' by the class of truth-value assignments (valuations) under consideration, and the latter as the consequence relation 'supervenience-determined' by that class of assignments. Some comparisons will be made between these two notions.

Original languageEnglish
Pages (from-to)309-336
Number of pages28
JournalJournal of Logic, Language and Information
Volume2
Issue number4
DOIs
Publication statusPublished - 1 Oct 1993

Keywords

  • consequence relation
  • Functional dependency
  • supervenience

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