NDLI: Lattice pseudoeffect algebras as double residuated structures

Content Provider	Springer Nature Link
Author	Foulis, David J. Vinceková, Elena Pulmanvá, Sylvia
Copyright Year	2011
Abstract	Pseudoeffect algebras are partial algebraic structures which are non-commutative generalizations of effect algebras. The main result of the paper is a characterization of lattice pseudoeffect algebras in terms of so-called pseudo Sasaki algebras. In contrast to pseudoeffect algebras, pseudo Sasaki algebras are total algebras. They are obtained as a generalization of Sasaki algebras, which in turn characterize lattice effect algebras. Moreover, it is shown that lattice pseudoeffect algebras are a special case of double CI-posets, which are algebraic structures with two pairs of residuated operations, and which can be considered as generalizations of residuated posets. For instance, a lattice ordered pseudoeffect algebra, regarded as a double CI-poset, becomes a residuated poset if and only if it is a pseudo MV-algebra. It is also shown that an arbitrary pseudoeffect algebra can be described as a special case of conditional double CI-poset, in which case the two pairs of residuated operations are only partially defined.
Ending Page	2488
Page Count	10
Starting Page	2479
File Format	PDF
ISSN	14327643
e-ISSN	14337479
Journal	Soft Computing
Issue Number	12
Volume Number	15
Language	English
Publisher	Springer-Verlag
Publisher Date	2011-05-03
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Pseudoeffect algebra Negation Quantum logic Residuation Implication Logical foundations of quantum mechanics; quantum logic Computational Intelligence Control, Robotics, Mechatronics Partial algebras Conjunction Artificial Intelligence (incl. Robotics) Double CI-poset Mathematical Logic and Foundations Pseudo Sasaki algebra Conditional double CI-poset
Content Type	Text
Resource Type	Article
Subject	Theoretical Computer Science Software Geometry and Topology

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