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Journal of Logic and Computation, Volume 11, Issue 6, pp. 879-907: Abstract.

Reducing Modal Consequence Relations

Marcus Kracht

II. Mathematisches Institut, Arnimallee 3, 14195 Berlin, Germany. E-mail: kracht@math.fu-berlin.de

In this paper we investigate the possibility of reducing derivability in a modal consequence relation to consistency in unimodal and polymodal K by means of so-called reduction functions. We present new and easy methods to prove standard results on decidability, complexity, finite model property, interpolation and Halldén-completeness using only the reduction functions. Some new results on complexity of modal logics will be established. All proofs are in addition constructive.

Keywords: Modal logic, consequence relations, complexity

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