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

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Abstract

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.

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REFERENCES

  1. van Benthem, J. F. A. K.: Two simple incomplete modal logics, Theoria 44 (1978), 25-37.

    Google Scholar 

  2. van Benthem, J. F. A. K.: Canonical modal logics and ultrafilter extensions, J. Symbolic Logic 44 (1979), 1-8.

    Google Scholar 

  3. Benton, R. A.: General modal incompleteness and finite axiomatizability, Ph.D. dissertation, University of Michigan, 1985, University Microfilms, Ann Arbor, 1985.

    Google Scholar 

  4. Boolos, G. and Sambin, G.: An incomplete system of modal logic, J. Philos. Logic 14 (1985), 351-358.

    Google Scholar 

  5. Chellas, B.: Modal Logic: An Introduction, Cambridge University Press, Cambridge, 1980.

    Google Scholar 

  6. Cresswell, M. J.: Magari's theorem via the recession frame, J. Philos. Logic 16 (1987), 13-15.

    Google Scholar 

  7. Fine, K.: Normal forms in modal logic, Notre Dame J. Formal Logic 16 (1975), 229-234.

    Google Scholar 

  8. Fine, K.: Some connections between elementary and modal logic, in S. Kanger (ed.), Proceedings of the Third Scandinavian Logic Symposium, North-Holland, Amsterdam, 1975, pp. 15-31.

  9. Lewis, D.: Intensional logics without iterative axioms, J. Philos. Logic 3 (1974), 457-466.

    Google Scholar 

  10. Magari, R.: Primi resultati sulla varieta di Boolos, Boll. Un. Mat. Ital. (6) 1-B (1982), 359-367.

    Google Scholar 

  11. Makinson, D. C.: A normal modal calculus between T and S4 without the finite model property, J. Symbolic Logic 34 (1969), 35-38.

    Google Scholar 

  12. Thomason, S. K.: An incompleteness theorem in modal logic, Theoria 60 (1974), 30-34.

    Google Scholar 

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  1. Departments of Mathematics & Philosophy, Columbia Union College, Takoma Park, MD, 20912, USA

    Roy A. Benton

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  1. Roy A. Benton
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Benton, R.A. A Simple Incomplete Extension of T which is the Union of Two Complete Modal Logics with f.m.p.. Journal of Philosophical Logic 31, 527–541 (2002). https://doi.org/10.1023/A:1021223721102

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