Algebraic Approach to Algorithmic Logic

• Autorzy: Grzegorz Bancerek
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

propsitional calcus; quantifier calcus; algorithmic logic

• Wydawca: De Gruyter Open
• Czasopismo: Formalized Mathematics
• Rocznik: 2014
• Tom: 22
• Numer: 3
• Strony: 225-255

Daty

wydano

2014-09-01

otrzymano

2014-09-15

online

2015-04-30

Twórcy

autor

Grzegorz Bancerek

• Association of Mizar Users Białystok, Poland

Bibliografia

• [1] Grzegorz Bancerek. Mizar analysis of algorithms: Preliminaries. Formalized Mathematics, 15(3):87-110, 2007. doi:10.2478/v10037-007-0011-x.[Crossref]
• [2] Grzegorz Bancerek. Program algebra over an algebra. Formalized Mathematics, 20(4): 309-341, 2012. doi:10.2478/v10037-012-0037-6.[Crossref]
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• [7] Grzegorz Bancerek. Translations, endomorphisms, and stable equational theories. Formalized Mathematics, 5(4):553-564, 1996.
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• [29] Andrzej Trybulec. Binary operations applied to functions. Formalized Mathematics, 1 (2):329-334, 1990.
• [30] Andrzej Trybulec. Tuples, projections and Cartesian products. Formalized Mathematics, 1(1):97-105, 1990.
• [31] Andrzej Trybulec. Many sorted algebras. Formalized Mathematics, 5(1):37-42, 1996.
• [32] Andrzej Trybulec. Many sorted sets. Formalized Mathematics, 4(1):15-22, 1993.
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• [35] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1 (1):73-83, 1990.

Identyfikatory

DOI

10.2478/forma-2014-0025