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Kripke completeness of some intermediate predicate logics with the axiom of constant domain and a variant of canonical formulas

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Abstract

For each intermediate propositional logicJ, J * denotes the least predicate extension ofJ. By the method of canonical models, the strongly Kripke completeness ofJ *+D(=∀x(p(x)∨q)⊃∀xp(x)∨q) is shown in some cases including:

  1. 1.

    J is tabular,

  2. 2.

    J is a subframe logic.

A variant of Zakharyashchev's canonical formulas for intermediate logics is introduced to prove the second case.

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Authors and Affiliations

  1. Department of Mathematics College of Science and Technology, Nihon University, Surugadai, 101, Tokyo, Japan

    Tatsuya Shimura

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  1. Tatsuya Shimura
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Additional information

This research was partially supported by Grant-in-Aid for Scientific Research (No. 01302006), Ministry of Education, Science and Culture.

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Shimura, T. Kripke completeness of some intermediate predicate logics with the axiom of constant domain and a variant of canonical formulas. Stud Logica 52, 23–40 (1993). https://doi.org/10.1007/BF01053062

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  • DOI: https://doi.org/10.1007/BF01053062

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