caa a22 4500 60547009X CHVBK 20210128100326.0 cr unu---uuuuu 210128e20150401xx s 000 0 eng 10.1007/s00500-014-1494-3 doi (NATIONALLICENCE)springer-10.1007/s00500-014-1494-3 Ciungu Lavinia Department of Mathematics, University of Iowa, 14 MacLean Hall, 52242-1419, Iowa City, Iowa, USA aut Internal states on equality algebras [Elektronische Daten] [Lavinia Ciungu] This paper investigates properties of equality algebras introduced by Jenei as a possible algebraic semantic for fuzzy type theory. We define and study the pointed equality algebras and its subclass of compatible pointed equality algebras. We introduce and investigate the internal states and the state-morphism operators on equality algebras and on their corresponding BCK-meet-semilattices. We prove that any internal state (state-morphism) on an equality algebra is also an internal state (state-morphism) on its corresponding BCK-meet-semilattice, and we prove the converse for the case of linearly ordered equality algebras. Another main result consists of proving that any state-morphism on a linearly ordered equality algebra is an internal state on it. We show that any internal state on a linearly ordered BCK-meet-semilattice satisfying the distributivity condition is also an internal state on its corresponding equality algebra and a state-morphism on a BCK-meet-semilattice satisfying the distributivity condition is also a state-morphism on its corresponding equality algebra. Springer-Verlag Berlin Heidelberg, 2014 Equality algebra nationallicence BCK-algebra nationallicence Meet-semilattice nationallicence Pointed equality algebra nationallicence Compatible equality algebra nationallicence Internal state nationallicence State-morphism operator nationallicence Soft Computing Springer Berlin Heidelberg 19/4(2015-04-01), 939-953 1432-7643 19:4<939 2015 19 500 https://doi.org/10.1007/s00500-014-1494-3 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00500-014-1494-3 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Ciungu Lavinia Department of Mathematics, University of Iowa, 14 MacLean Hall, 52242-1419, Iowa City, Iowa, USA aut NATIONALLICENCE 773 0- Soft Computing Springer Berlin Heidelberg 19/4(2015-04-01), 939-953 1432-7643 19:4<939 2015 19 500