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Formalized Mathematics

(a computer assisted approach)

Editor-in-Chief: Matuszewski, Roman

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Volume 22, Issue 3 (Sep 2014)


Algebraic Approach to Algorithmic Logic

Grzegorz Bancerek
Published Online: 2014-03-31 | DOI: https://doi.org/10.2478/forma-2014-0025


We introduce algorithmic logic - an algebraic approach according to [25]. It is done in three stages: propositional calculus, quantifier calculus with equality, and finally proper algorithmic logic. For each stage appropriate signature and theory are defined. Propositional calculus and quantifier calculus with equality are explored according to [24]. A language is introduced with language signature including free variables, substitution, and equality. Algorithmic logic requires a bialgebra structure which is an extension of language signature and program algebra. While-if algebra of generator set and algebraic signature is bialgebra with appropriate properties and is used as basic type of algebraic logic.

Keywords : propsitional calcus; quantifier calcus; algorithmic logic


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About the article

Received: 2014-09-15

Published Online: 2014-03-31

Published in Print: 2014-09-01

Citation Information: Formalized Mathematics, ISSN (Online) 1898-9934, DOI: https://doi.org/10.2478/forma-2014-0025.

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© by Grzegorz Bancerek. This work is licensed under the Creative Commons Attribution-ShareAlike 3.0 License. (CC BY-SA 3.0) BY-SA 3.0

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