<abstract xmlns="http://www.w3.org/1999/xhtml"><p>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.</p></abstract>

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.

Algebraic Approach to Algorithmic Logic

Association of Mizar Users Białystok, Poland

Formalized Mathematics

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

{"article-title":"Algebraic Approach to Algorithmic Logic"}

We introduce algorithmic logic - an algebraic approach according to [25]. It is done in three stages: propositional calculus, quantifier calculus with...

Algebraic Approach to Algorithmic Logic

Published Online: Mar 31, 2014

Page range: 225 - 255

Received: Sep 15, 2014

DOI: https://doi.org/10.2478/forma-2014-0025

© by Grzegorz Bancerek

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