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Elementary Definability and Completeness in General and Positive Modal Logic

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Abstract

The paper generalises Goldblatt's completeness proof for Lemmon–Scott formulas to various modal propositional logics without classical negation and without ex falso, up to positive modal logic, where conjunction and disjunction, andwhere necessity and possibility are respectively independent.Further the paper proves definability theorems for Lemmon–Scottformulas, which hold even in modal propositional languages without negation and without falsum. Both, the completeness theorem and the definability theoremmake use only of special constructions of relations,like relation products. No second order logic, no general frames are involved.

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Authors and Affiliations

  1. Elzacher Strasse 3, D-71034, Boeblingen, Germany

    Ernst Zimmermann

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  1. Ernst Zimmermann
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Zimmermann, E. Elementary Definability and Completeness in General and Positive Modal Logic. Journal of Logic, Language and Information 12, 99–117 (2003). https://doi.org/10.1023/A:1021189103204

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  • DOI: https://doi.org/10.1023/A:1021189103204

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