Glivenko like theorems in natural expansions of BCK-logic
The classical Glivenko theorem asserts that a prepositional formula admits a classical proof if and only if its double negation admits an intuitionistic proof. By a natural expansion of the BCK-logic with negation we understand an algebraizable logic whose language is an expansion of the language of...
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todo:paper_09425616_v50_n2_p111_Cignoli2023-10-03T15:49:00Z Glivenko like theorems in natural expansions of BCK-logic Cignoli, R. Torrell, A.T. Algebraic semantics Bounded BCK-algebra Bounded BCK-logic Bounded pocrim Glivenko's theorem Involutive BCK-algebra Natural expansion of a logic Natural expansion of a quasivariety Regular element The classical Glivenko theorem asserts that a prepositional formula admits a classical proof if and only if its double negation admits an intuitionistic proof. By a natural expansion of the BCK-logic with negation we understand an algebraizable logic whose language is an expansion of the language of BCK-logic with negation by a family of connectives implicitly defined by equations and compatible with BCK-congruences. Many of the logics in the current literature are natural expansions of BCK-logic with negation. The validity of the analogous of Glivenko theorem in these logics is equivalent to the validity of a simple one-variable formula in the language of BCK-logic with negation. © 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_09425616_v50_n2_p111_Cignoli |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
Algebraic semantics Bounded BCK-algebra Bounded BCK-logic Bounded pocrim Glivenko's theorem Involutive BCK-algebra Natural expansion of a logic Natural expansion of a quasivariety Regular element |
| spellingShingle |
Algebraic semantics Bounded BCK-algebra Bounded BCK-logic Bounded pocrim Glivenko's theorem Involutive BCK-algebra Natural expansion of a logic Natural expansion of a quasivariety Regular element Cignoli, R. Torrell, A.T. Glivenko like theorems in natural expansions of BCK-logic |
| topic_facet |
Algebraic semantics Bounded BCK-algebra Bounded BCK-logic Bounded pocrim Glivenko's theorem Involutive BCK-algebra Natural expansion of a logic Natural expansion of a quasivariety Regular element |
| description |
The classical Glivenko theorem asserts that a prepositional formula admits a classical proof if and only if its double negation admits an intuitionistic proof. By a natural expansion of the BCK-logic with negation we understand an algebraizable logic whose language is an expansion of the language of BCK-logic with negation by a family of connectives implicitly defined by equations and compatible with BCK-congruences. Many of the logics in the current literature are natural expansions of BCK-logic with negation. The validity of the analogous of Glivenko theorem in these logics is equivalent to the validity of a simple one-variable formula in the language of BCK-logic with negation. © 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim. |
| format |
JOUR |
| author |
Cignoli, R. Torrell, A.T. |
| author_facet |
Cignoli, R. Torrell, A.T. |
| author_sort |
Cignoli, R. |
| title |
Glivenko like theorems in natural expansions of BCK-logic |
| title_short |
Glivenko like theorems in natural expansions of BCK-logic |
| title_full |
Glivenko like theorems in natural expansions of BCK-logic |
| title_fullStr |
Glivenko like theorems in natural expansions of BCK-logic |
| title_full_unstemmed |
Glivenko like theorems in natural expansions of BCK-logic |
| title_sort |
glivenko like theorems in natural expansions of bck-logic |
| url |
http://hdl.handle.net/20.500.12110/paper_09425616_v50_n2_p111_Cignoli |
| work_keys_str_mv |
AT cignolir glivenkoliketheoremsinnaturalexpansionsofbcklogic AT torrellat glivenkoliketheoremsinnaturalexpansionsofbcklogic |
| _version_ |
1807314383778349056 |