The Number of Clones Determined by Disjunctions of Unary Relationsстатья
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Дата последнего поиска статьи во внешних источниках: 15 августа 2019 г.
Аннотация:We consider finitary relations (also known as crosses) that are definable via finite disjunctions of unary relations, i.e. subsets, taken from a fixed finite parameter set Γ. We prove that whenever Γ contains at least one non-empty relation distinct from the full carrier set, there is a countably infinite number of polymorphism clones determined by relations that are disjunctively definable from Γ. Finally, we extend our result to finitely related polymorphism clones and countably infinite sets Γ. These results address an open problem raised in Creignou, N., et al. Theory Comput. Syst. 42(2), 239–255 (2008), which is connected to the complexity analysis of the satisfiability problem of certain multiple-valued logics studied in Hähnle, R. Proc. 31st ISMVL 2001, 137–146 (2001).