Galois lattice as a framework to specify building class hierarchies algorithms
Galois Lattice as a Framework to Specify Building Class Hierarchies Algorithms
In the context of object-oriented systems, algorithms for building class hierarchies are currently receiving much attention. We present here a characterization of several global algorithms. A global algorithm is one which starts with only the set of classes (provided with all their properties) and directly builds the hierarchy. The algorithms scrutinized were developped each in a different framework. In this survey, they are explained in a single framework, which takes advantage of a substructure...
Galois theory for groups
Galois triangle theory for direct summands of modules
Galois-type connections and closure operations on preordered sets.
Game properties of Boolean algebras
Gaps and dualities in Heyting categories
We present an algebraic treatment of the correspondence of gaps and dualities in partial ordered classes induced by the morphism structures of certain categories which we call Heyting (such are for instance all cartesian closed categories, but there are other important examples). This allows to extend the results of [14] to a wide range of more general structures. Also, we introduce a notion of combined dualities and discuss the relation of their structure to that of the plain ones.
Gate circuits in the algebra of transients
We study simulation of gate circuits in the infinite algebra of transients recently introduced by Brzozowski and Ésik. A transient is a word consisting of alternating s and s; it represents a changing signal. In the algebra of transients, gates process transients instead of s and s. Simulation in this algebra is capable of counting signal changes and detecting hazards. We study two simulation algorithms: a general one that works with any initial state, and a special one that applies only if...
Gate circuits in the algebra of transients
We study simulation of gate circuits in the infinite algebra of transients recently introduced by Brzozowski and Ésik. A transient is a word consisting of alternating 0s and 1s; it represents a changing signal. In the algebra of transients, gates process transients instead of 0s and 1s. Simulation in this algebra is capable of counting signal changes and detecting hazards. We study two simulation algorithms: a general one that works with any initial state, and a special one that applies only if...
Gelfand theorem implies Stone representation theorem of Boolean rings.
General algebraic geometry and formal concept analysis.
General comparability of pseudo MV-algebras
Generalization of ideal topology in chains
Generalizations of Boolean algebras. An attribute exploration
Generalizations of pseudo MV-algebras and generalized pseudo effect algebras
We deal with unbounded dually residuated lattices that generalize pseudo -algebras in such a way that every principal order-ideal is a pseudo -algebra. We describe the connections of these generalized pseudo -algebras to generalized pseudo effect algebras, which allows us to represent every generalized pseudo -algebra by means of the positive cone of a suitable -group . We prove that the lattice of all (normal) ideals of and the lattice of all (normal) convex -subgroups of are isomorphic....
Generalized cardinal properties of lattices and lattice ordered groups
We denote by the class of all cardinals; put . Let be a class of algebraic systems. A generalized cardinal property on is defined to be a rule which assings to each an element of such that, whenever and , then . In this paper we are interested mainly in the cases when (i) is the class of all bounded lattices having more than one element, or (ii) is a class of lattice ordered groups.
Generalized Dedekind completion of a lattice ordered group
Generalized difference posets and orthoalgebras.
Generalized -semigroups
A semigroup is called a generalized -semigroup if there exists a group congruence on such that the identity class contains a greatest element with respect to the natural partial order of . Using the concept of an anticone, all partially ordered groups which are epimorphic images of a semigroup are determined. It is shown that a semigroup is a generalized -semigroup if and only if contains an anticone, which is a principal order ideal of . Also a characterization by means of the structure...
Generalized free products
A subalgebra B of the direct product of Boolean algebras is finitely closed if it contains along with any element f any other member of the product differing at most at finitely many places from f. Given such a B, let B* be the set of all members of B which are nonzero at each coordinate. The generalized free product corresponding to B is the subalgebra of the regular open algebra with the poset topology on B* generated by the natural basic open sets. Properties of this product are developed....