Kleene Algebra of Partial Predicates

We show that the set of all partial predicates over a set D together with the disjunction, conjunction, and negation operations, defined in accordance with the truth tables of S.C. Kleene’s strong logic of indeterminacy [17], forms a Kleene algebra. A Kleene algebra is a De Morgan algebra [3] (also...

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Main Authors:	Korniłowicz Artur, Ivanov Ievgen, Nikitchenko Mykola
Format:	Article
Language:	English
Published:	Sciendo 2018-04-01
Series:	Formalized Mathematics
Subjects:	partial predicate kleene algebra 03b70 03g25 03b35
Online Access:	https://doi.org/10.2478/forma-2018-0002

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spelling	doaj-a82acf2410c84470be38e9f0629c50852021-09-05T21:01:04ZengSciendoFormalized Mathematics1426-26301898-99342018-04-01261112010.2478/forma-2018-0002forma-2018-0002Kleene Algebra of Partial PredicatesKorniłowicz Artur0Ivanov Ievgen1Nikitchenko Mykola2Institute of Informatics, University of Białystok, PolandTaras Shevchenko National University, Kyiv, UkraineTaras Shevchenko National University, Kyiv, UkraineWe show that the set of all partial predicates over a set D together with the disjunction, conjunction, and negation operations, defined in accordance with the truth tables of S.C. Kleene’s strong logic of indeterminacy [17], forms a Kleene algebra. A Kleene algebra is a De Morgan algebra [3] (also called quasi-Boolean algebra) which satisfies the condition x ∧¬:x ⩽ y ∨¬ :y (sometimes called the normality axiom). We use the formalization of De Morgan algebras from [8].https://doi.org/10.2478/forma-2018-0002partial predicatekleene algebra03b7003g2503b35
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Korniłowicz Artur Ivanov Ievgen Nikitchenko Mykola
spellingShingle	Korniłowicz Artur Ivanov Ievgen Nikitchenko Mykola Kleene Algebra of Partial Predicates Formalized Mathematics partial predicate kleene algebra 03b70 03g25 03b35
author_facet	Korniłowicz Artur Ivanov Ievgen Nikitchenko Mykola
author_sort	Korniłowicz Artur
title	Kleene Algebra of Partial Predicates
title_short	Kleene Algebra of Partial Predicates
title_full	Kleene Algebra of Partial Predicates
title_fullStr	Kleene Algebra of Partial Predicates
title_full_unstemmed	Kleene Algebra of Partial Predicates
title_sort	kleene algebra of partial predicates
publisher	Sciendo
series	Formalized Mathematics
issn	1426-2630 1898-9934
publishDate	2018-04-01
description	We show that the set of all partial predicates over a set D together with the disjunction, conjunction, and negation operations, defined in accordance with the truth tables of S.C. Kleene’s strong logic of indeterminacy [17], forms a Kleene algebra. A Kleene algebra is a De Morgan algebra [3] (also called quasi-Boolean algebra) which satisfies the condition x ∧¬:x ⩽ y ∨¬ :y (sometimes called the normality axiom). We use the formalization of De Morgan algebras from [8].
topic	partial predicate kleene algebra 03b70 03g25 03b35
url	https://doi.org/10.2478/forma-2018-0002
work_keys_str_mv	AT korniłowiczartur kleenealgebraofpartialpredicates AT ivanovievgen kleenealgebraofpartialpredicates AT nikitchenkomykola kleenealgebraofpartialpredicates
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Kleene Algebra of Partial Predicates

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