New probabilistic model for pseudo-BCK algebras and pseudo-hoops. (English) Zbl 1393.06021

Ciungu, Lavinia Corina; Kuhr, Jan

J. Mult.-Val. Log. Soft Comput. 20, No. 3-4, 373-400 (2013).

Summary: The notion of state is an analogue to probability measure and its basic idea is an averaging of events of a given algebraic structure. States on multiple-valued logic algebras proved to be the most suitable models for averaging the truth-value in their corresponding logics. They have been introduced on commutative and non-commutative algebras of fuzzy logics as functions defined on these algebras with values in \([0, 1]\). For the case of bounded residuated lattices, the states were generalized as functions with values in a bounded residuated lattice. In this paper we extend the generalized states for the cases of bounded pseudo-BCK algebras, involutive pseudo-BCK algebras and bounded pseudo-hoops.

MSC:

06F35	BCK-algebras, BCI-algebras (aspects of ordered structures)
03G25	Other algebras related to logic

Keywords:

pseudo-BCK algebra; pseudo-hoop; Wajsberg pseudo-hoop; generalized Bosbach state; generalized state-morphism; generalized Riečan state; Glivenko property; state operator