Henkin and Tarski proved that an atomic cylindric algebra in which every atom is a rectangle must be representable (as a cylindric set algebra). This theorem and its analogues for quasi-polyadic algebras with and without equality are formulated in Henkin-Monk-Tarski 1985]. We introduce a natural and more general notion of rectangular density that can be applied to arbitrary cylindric and quasi-...

This is a summary of our paper \Process algebras with alternative quantii-cation over data" (Groote and Luttik (1998)). In this paper, we deene a class of process algebras with a generalised operation P that allows explicit treatment of alternative quantiication over data, and investigate the speciic subclass formed by the algebras of nite processes modulo strong bisimulation. We have shown tha...

We introduce algorithmic logic – an algebraic approach according to [25]. It is done in three stages: propositional calculus, quantifier calculus with equality, and finally proper algorithmic logic. For each stage appropriate signature and theory are defined. Propositional calculus and quantifier calculus with equality are explored according to [24]. A language is introduced with language signa...

EQ-algebras introduced by Novák are algebras of truth values for a higher-order fuzzy logic (fuzzy type theory). In this paper, the compatibility of multiplication w.r.t. the fuzzy equality in an arbitrary EQ-algebra is examined. Particularly, an example indicates that the compatibility axiom does not always hold, and then a class of EQ-algebras satisfying the compatibility axiom is characteriz...

There are currently no fewer than four dedicated logics for equality reasoning over nominal sets: nominal algebra, nominal equational logic, nominal equational logic with equality only, and permissive-nominal algebra. In this survey and research paper we present these logics side-by-side in a common notation, survey their similarities and differences, discuss their proofand model-theories, and ...

Given a simple atomic relation algebra A and a finite n ≥ 3, we construct effectively an atomic n-dimensional polyadic equality-type algebra P such that for any subsignature L of the signature of P that contains the boolean operations and cylindrifications, the L-reduct of P is completely representable if and only if A is completely representable. If A is finite then so is P. It follows that th...

We consider the relationship between the Haagerup constants for a C-algebra and its crossed product by an amenable group. We prove equality when the group is discrete, and deduce equality when the group is compact and abelian.

We prove a necessary and sufficient condition for the states which satisfy strong subadditivity of von Neumann entropy with equality on CAR algebra and we show an example when the equality holds but the state is not separable.

It is proved that every involutive equivalential equality algebra (E, ∧, ∼, 1), an residualted lattice EQ-algebra, which operation ⊗ defined by x y = (x → 0 ) . Moreover, it showen EQ-algebra we have

We consider algebraic speciications with observational features. Axioms as well as observations are formulae of full (Many-Sorted) First Order Logic with Equality. The associated semantics is based on a non standard interpretation of equality called observational equality. We study the adequacy of this semantics for software specii-cation and the relationship with behavioural equivalence of alg...