Algebras of imperative programming languages have been successful in reasoning about programs. In general an algebra of programs is an algebraic structure with programs as elements and with program compositions (sequential composition, choice, skip) as algebra operations. Various versions of these algebras were introduced to model partial correctness, total correctness, refinement, demonic choi...

In this paper Boolean games are introduced as a class of two-player zero-sum games along with a number of operations on them. We argue that Boolean games can be interpreted as modelling the information structures of two-person zero-sum games. As such they comprise games of imperfect information. The algebra of Boolean games modulo strategic equivalence is then proven to be isomorphic to the Lin...

We establish a connection between skew Boolean algebras and Church algebras. We prove that the set of all semicentral elements in a right Church algebra forms a right-handed skew Boolean algebra for the properly defined operations. The main result of this paper states that the variety of all semicentral right Church algebras of type τ is term equivalent to the variety of right-handed skew Boole...

Reasoning with Boolean Algebras is just propositional reasoning. This is well investigated and a lot of good algorithms have been developed. Other formal systems, for example mathematical programming for reasoning about arithmetical equation systems, are equally well developed. Combining such a system with a Boolean component where the Boolean expressions are interpreted as sets, would allow on...

The Boolean Differential Calculus is a powerful theory that extends the Boolean algebra significantly. Based on a small number of definitions a lot of theorems were proven. The available operations have been efficiently implemented in several software packages. There is a very wide field of applications. In this paper we combine a compact introduction into the Boolean Differential Calculus with...

and prove that the study of such structures is equivalent to the study of generalized Boolean algebras. We call such structures Boolean subtractive algebras since they are subtractive algebras in the sense of Crapo and Rota ([1], 3.7). Alternatively, such structures might be called generalized colonies since, as we later prove, every colony is a Boolean subtractive algebra. As an example of a B...

Given a Boolean algebra B and an embedding e : B → P(N)/ fin we consider the possibility of extending each or some automorphism of B to the whole P(N)/ fin. Among other things, we show, assuming CH, that for a wide class of Boolean algebras there are embeddings for which no non-trivial automorphism can be extended.

In this paper we introduce the notion of Boolean filters in a pseudo-complemented distributive lattice and characterize the class of all Boolean filters. Further a set of equivalent conditions are derived for a proper filter to become a prime Boolean filter. Also a set of equivalent conditions is derived for a pseudo-complemented distributive lattice to become a Boolean algebra. Finally, a Bool...

The paper aims at developing an algebraic representation of normative systems by sets of minimal norms, “connections”, within relational structures called condition implication structures. It is shown that, given some general presuppositions, a normative system is completely determined by its set of connections, and that comparisons between normative systems can be made by considering whether c...