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A b s t r a c t. The purpose of this note is to expose a new way of viewing the canonical extension of posets and bounded lattices. Specifically, we seek to expose categorical features of this completion and to reveal its relationship to other completion processes. The theory of canonical extensions is introduced by Jónsson and Tarski [15, 16] for Boolean(More)
This paper presents a unified account of a number of dual category equivalences of relevance to the theory of canonical extensions of distributive lattices. Each of the categories involved is generated by an object having a 2-element underlying set; additional structure may be algebraic (lattice or complete lattice operations) or relational (order) and, in(More)
Partition-induced natural dl alit& for varieties of pseudo-compicmented distrrbutivc lattices, Discrete Malhematics 113 (1993) 41-58. A natural dl:sitty is obtained for each finitely generated variety B,, (n < CG) of distributive p-algebras. 7 he duality for B,, is based on a schizophrenic object: E:, in B,, is the algebra 2 " @ 1 which gencrates the(More)
This paper studies algebras arising as algebraic semantics for logics used to model reasoning with incomplete or inconsistent information. In particular we study, in a uniform way, varieties of bilattices equipped with additional logic-related operations and their product representations. Our principal result is a very general product representation(More)