ISSN:
1572-9273
Keywords:
06B05
;
06A15
;
Context
;
arrow relation
;
concept lattice
;
context pattern
;
strictly realizable context pattern
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract In this paper, we consider the following reconstruction problem: Given two ordered sets (G, ≤) and (M, ≤) representing join- and meet-irreducible elements, respectively together with three relationsJ, , $${\hbox{\ \hbox{$\mid$}\kern -1em\lower .5em \hbox{$\leftarrow$}}} $$ onG×M modelling comparability (g≤m) and maximal noncomparability with respect tog (g≰m, butg≤m*) and with respect tom (g≰m, butg≤m*). We determine necessary and sufficient conditions for the existence of a finite latticeL and injections α:G→J(L) and β:M→M(L) such that the given order relations and the abstract relations coincide with the one induced by the latticeL.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01108830
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