Journal of Philosophical Logic

, Volume 31, Issue 6, pp 527-541

First online:

A Simple Incomplete Extension of T which is the Union of Two Complete Modal Logics with f.m.p.

  • Roy A. BentonAffiliated withDepartments of Mathematics & Philosophy, Columbia Union College

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I present here a modal extension of T called KTLM which is, by several measures, the simplest modal extension of T yet presented. Its axiom uses only one sentence letter and has a modal depth of 2. Furthermore, KTLM can be realized as the logical union of two logics KM and KTL which each have the finite model property (f.m.p.), and so themselves are complete. Each of these two component logics has independent interest as well.

complete model property incomplete modal logic union