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Program-substitution and admissibility of rules in algorithmic logic

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Summary

The purpose of this work is to show a point of view upon the notions of program-substitution and admissibility of rules which are the tools for proving properties of programs of algorithmic logic and the so-called extended algorithmic logic with quantifiers and with non-deterministic programs. We prove that the set of theses of algorithmic logic is closed under each program-substitution. This substitution rule allows us to formulate a problem of algorithmic structural completeness as a question about derivability of all structural, finitary and admissible rules. We prove the incompleteness of algorithmic logic strengthened by the substitution rule and its algorithmically structural completeness.

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Authors and Affiliations

  1. Department of Mathematics, University of Silesia, PL-40-007, Katowice, Poland

    Andrzej Biela

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  1. Andrzej Biela
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This work was supported by the Polish Academy of Sciences CPBP 08–15.

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Biela, A. Program-substitution and admissibility of rules in algorithmic logic. Acta Informatica 25, 439–473 (1988). https://doi.org/10.1007/BF02737110

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