A note on categories enriched in quantaloids and modal and temporal logic
0. Introduction. Besides being of intrinsic interest, cylindric (semi-) lattices arise naturally from the study of dependencies in relational databases; the polynomials on a cylindric semilattice are closely related to the queries obtainable from project-join mappings on a relational database (cf. [D] for references). This note is intended to initiate the study of these structures, and only a few, rather basic results will be given. Some problems at the end will hopefully stimulate further research....
Pseudo BL-algebras are a noncommutative extention of BL-algebras. In this paper we study good pseudo BL-algebras and consider some classes of these algebras.
In [4] Blok and Pigozzi prove syntactically that RM, the propositional calculus also called R-Mingle, is algebraizable, and as a consequence there is a unique quasivariety (the so-called equivalent quasivariety semantics) associated to it. In [3] it is stated that this quasivariety is the variety of Sugihara algebras. Starting from this fact, in this paper we present an equational base for this variety obtained as a subvariety of the variety of R-algebras, found in [7] to be associated in the same...
This paper aims to propose a complete relational semantics for the so-called logic of bounded lattices, and prove a completeness theorem with regard to a class of two-sorted frames that is dually equivalent (categorically) to the variety of bounded lattices.
A finite orthomodular lattice in which every maximal Boolean subalgebra (block) has the same cardinality is called -regular, if each atom is a member of just blocks. We estimate the minimal number of blocks of -regular orthomodular lattices to be lower than of equal to regardless of .