منابع مشابه
Stone Algebras
A range of algebras between lattices and Boolean algebras generalise the notion of a complement. We develop a hierarchy of these pseudo-complemented algebras that includes Stone algebras. Independently of this theory we study filters based on partial orders. Both theories are combined to prove Chen and Grätzer’s construction theorem for Stone algebras. The latter involves extensive reasoning ab...
متن کاملStone-Kleene Relation Algebras
We develop Stone-Kleene relation algebras, which expand Stone relation algebras with a Kleene star operation to describe reachability in graphs. We show that finite matrices over extended real numbers form an instance. These theories are being prepared for the Archive of Formal Proofs. Further documentation will be added.
متن کاملKleene and Stone Algebras
Boolean algebras are affine complete by a well-known result of G. Grätzer. Various generalizations of this result have been obtained. Among them, a characterization of affine complete Stone algebras having a smallest dense element was given by R. Beazer. In this paper, generalizations of Beazer’s result are presented for algebras abstracting simultaneously Kleene and Stone algebras.
متن کاملStone Relation Algebras
We develop Stone relation algebras, which generalise relation algebras by replacing the underlying Boolean algebra structure with a Stone algebra. We show that finite matrices over bounded linear orders form an instance. As a consequence, relation-algebraic concepts and methods can be used for reasoning about weighted graphs. We also develop a fixpoint calculus and apply it to compare different...
متن کاملSTONE DUALITY FOR R0-ALGEBRAS WITH INTERNAL STATES
$Rsb{0}$-algebras, which were proved to be equivalent to Esteva and Godo's NM-algebras modelled by Fodor's nilpotent minimum t-norm, are the equivalent algebraic semantics of the left-continuous t-norm based fuzzy logic firstly introduced by Guo-jun Wang in the mid 1990s.In this paper, we first establish a Stone duality for the category of MV-skeletons of $Rsb{0}$-algebras and the category of t...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2000
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(00)00053-4