Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

CHARACTERIZATIONS OF POSETS VIA WEAK STATES

CHARACTERIZATIONS OF POSETS VIA WEAK STATES DEMONSTRATIO MATHEMATICAVol. X L INo 32008I. Chajda, M. Kolarik, H. LängerCHARACTERIZATIONS OF POSETS VIA W E A K STATESA b s t r a c t . Weak states on posets are defined which are in some analogy to stateson orthomodular posets used in axiomatic quantum mechanics. It is shown how certainproperties of the set of weak states characterize certain properties of the underlying poset.Orthomodular posets serve as algebraic models for logics in axiomaticquantum mechanics. States on them are considered which reflect the properties of states of the corresponding physical system. A crucial property ofsuch states is monotonicity. In analogy to these states we define so-calledweak states on an arbitrary poset. These weak states are also monotonousand play some role in the characterization of certain algebraic models ofquantum systems (cf. [2]). We use properties of the set of weak states inorder to characterize certain properties of the underlying poset. In this context semilattices play an important role. For the theory of semilattices werefer the reader to the recent monograph [1],In the following let V = (P, < ) be an arbitrary but fixed non-emptyposet.DEFINITION1. We call V trivialn a n d a\,...,anU(ai,...,an)6 P:=if |P| = 1.p u t L(ai,...,an){x http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Demonstratio Mathematica de Gruyter

CHARACTERIZATIONS OF POSETS VIA WEAK STATES

Demonstratio Mathematica , Volume 41 (3): 6 – Jul 1, 2008

Loading next page...
 
/lp/de-gruyter/characterizations-of-posets-via-weak-states-RPXylXiaLR

References

References for this paper are not available at this time. We will be adding them shortly, thank you for your patience.

Publisher
de Gruyter
Copyright
© by I. Chajda
ISSN
0420-1213
eISSN
2391-4661
DOI
10.1515/dema-2008-0302
Publisher site
See Article on Publisher Site

Abstract

DEMONSTRATIO MATHEMATICAVol. X L INo 32008I. Chajda, M. Kolarik, H. LängerCHARACTERIZATIONS OF POSETS VIA W E A K STATESA b s t r a c t . Weak states on posets are defined which are in some analogy to stateson orthomodular posets used in axiomatic quantum mechanics. It is shown how certainproperties of the set of weak states characterize certain properties of the underlying poset.Orthomodular posets serve as algebraic models for logics in axiomaticquantum mechanics. States on them are considered which reflect the properties of states of the corresponding physical system. A crucial property ofsuch states is monotonicity. In analogy to these states we define so-calledweak states on an arbitrary poset. These weak states are also monotonousand play some role in the characterization of certain algebraic models ofquantum systems (cf. [2]). We use properties of the set of weak states inorder to characterize certain properties of the underlying poset. In this context semilattices play an important role. For the theory of semilattices werefer the reader to the recent monograph [1],In the following let V = (P, < ) be an arbitrary but fixed non-emptyposet.DEFINITION1. We call V trivialn a n d a\,...,anU(ai,...,an)6 P:=if |P| = 1.p u t L(ai,...,an){x

Journal

Demonstratio Mathematicade Gruyter

Published: Jul 1, 2008

There are no references for this article.