Acta Informatica

, Volume 25, Issue 4, pp 439–473

# Program-substitution and admissibility of rules in algorithmic logic

• Andrzej Biela
Article

## 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.

## Keywords

Inductive Hypothesis Generalize Formula Ordinal Number Classical Formula Elementary Formula
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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