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Negation and BCK‐algebras
Author(s) -
García Olmedo Francisco M.,
Rodríguez Salas Antonio J.
Publication year - 2003
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.200310035
Subject(s) - negation , mathematics , negation as failure , commutative property , pure mathematics , context (archaeology) , algebra over a field , semantics (computer science) , computer science , stable model semantics , programming language , paleontology , biology , operational semantics
In this paper we consider twelve classical laws of negation and study their relations in the context of BCK‐algebras. A classification of the laws of negation is established and some characterizations are obtained. For example, using the concept of translation we obtain some characterizations of Hilbert algebras and commutative BCK‐algebras with minimum. As a consequence we obtain a theorem relating those algebras to Boolean algebras.