On algebras of relations
On connections between information systems, rough sets and algebraic logic
In this note we remark upon some relationships between the ideas of an approximation space and rough sets due to Pawlak ([9] and [10]) and algebras related to the study of algebraic logic - namely, cylindric algebras, relation algebras, and Stone algebras. The paper consists of three separate observations. The first deals with the family of approximation spaces induced by the indiscernability relation for different sets of attributes of an information system. In [3] the family of closure operators...
On Equational Classes of Algebraic Versions of Logic I.
On the weak representability of -complete dimension complemented cylindric algebras
One-generated clones of operations on binary relations
Polyadic algebras over nonclassical logics
The polyadic algebras that arise from the algebraization of the first-order extensions of a SIC are characterized and a representation theorem is proved. Standard implicational calculi (SIC)'s were considered by H. Rasiowa [19] and include classical and intuitionistic logic and their various weakenings and fragments, the many-valued logics of Post and Łukasiewicz, modal logics that admit the rule of necessitation, BCK logic, etc.
Relational specifications
Relativization of cylindric algebras
Statistical estimation of deducibility in polyadic algebras
Strong completeness of the Lambek Calculus with respect to Relational Semantics
In [vB88], Johan van Benthem introduces Relational Semantics (RelSem for short), and states Soundness Theorem for Lambek Calculus (LC) w.r.t. RelSem. After doing this, he writes: "it would be very interesting to have the converse too", i.e., to have Completeness Theorem. The same question is in [vB91, p. 235]. In the following, we state Strong Completeness Theorems for different versions of LC.
Substitution algebras in their relation to cylindric algebras.
The class of 2-dimensional neat reducts is not elementary
SC, CA, QA and QEA stand for the classes of Pinter's substitution algebras, Tarski's cylindric algebras, Halmos' quasipolyadic algebras and Halmos' quasipolyadic algebras with equality, respectively. Generalizing a result of Andréka and Németi on cylindric algebras, we show that for K ∈ SC,QA,CA,QEA and any β > 2 the class of 2-dimensional neat reducts of β-dimensional algebras in K is not closed under forming elementary subalgebras, hence is not elementary. Whether this result extends to higher...
The theory of boolean algebras with a distinguished subalgebra is undecidable
Two notes on locally finite cylindric algebras
Une généralisation du théorème d'omission des types dans les algèbres polyadiques
Weak cylindric probability algebras.
Weak products of universal algebras
Weak direct products of arbitrary universal algebras are introduced. The usual notion for groups and rings is a special case. Some universal algebraic properties are proved and applications to cylindric and polyadic algebras are considered.
What the finitization problem is not
О регулярности элементов релятива