Given a hypergraph G, we introduce a Grassmann algebra over the vertex set, and show that a class of Grassmann integrals permits an expansion in terms of spanning hyperforests. Special cases provide the generating functions for rooted and unrooted spanning (hyper)forests and spanning (hyper)trees. All these results are generalizations of Kirchhoff’s matrix-tree theorem. Furthermore, we show tha...

In this paper we prove algebraic equivalents of the conservative extension theorems of Lukasiewicz propositional logic to rational Pavelka propositional logic. The results concerns the conservative extension and the very conservative extension of MV-algebras to Pavelka algebras.

By studying two unsharp quantum structures, namely extended lattice ordered effect algebras and lattice ordered QMV algebras, we obtain some characteristic theorems of MV algebras. We go on to discuss automata theory based on these two unsharp quantum structures. In particular, we prove that an extended lattice ordered effect algebra (or a lattice ordered QMV algebra) is an MV algebra if and on...

We show that the theory of MV-algebras is Morita-equivalent to that of abelian `-groups with strong unit. This generalizes the well-known equivalence between the categories of set-based models of the two theories established by D. Mundici in 1986, and allows to transfer properties and results across them by using the methods of topos theory. We discuss several applications, including a sheaf-th...

This material is studying MV-algebras and BL-algebras in terms of applicability in Boole algebra. Boole algebras are expanded use in fuzzy logic.

In this paper we enlarge the language of MV-algebras by a unary operation r equationally described so as to preserve the basic properties of a state in its original meaning. The resulting class of algebras will be called MV-algebras with internal state (or SMV-algebras for short). After discussing some basic algebraic properties of SMV-algebras, we apply them to the study of the coherence probl...

Motivated by the concept of quantifier (in the sense of P. Halmos) on different algebraic structures (Boolean algebras, Heyting algebras, MV-algebras, orthomodular lattices, bounded distributive lattices) and the resulting notion of monadic algebra, the paper introduces the concept of a monadic quantale algebra, considers its properties and provides several representation theorems for the new s...

This paper reviews the coverage of formal Relational Algebra as it applies to distributed, federated databases in varying network topologies. The review shows that a number of Relational Algebra extensions allow distributed relations and federation of heterogeneous database schema. More concrete physical Relational Algebra extensions support access plans for multi-database query processing but ...

This paper reviews the coverage of formal Relational Algebra as it applies to distributed, federated databases in varying network topologies. The review shows that a number of Relational Algebra extensions allow distributed relations and federation of heterogeneous database schema. More concrete physical Relational Algebra extensions support access plans for multi-database query processing but ...

Effect algebras have been introduced by Foulis and Bennett [2] (see also [3, 4] for equivalent definitions) for modeling unsharp measurements in quantum mechanical systems [5]. They are a generalization of many structures which arise in the axiomatization of quantum mechanics (Hilbert space effects [7]), noncommutative measure theory and probability (orthomodular lattices and posets, [6]), fuzz...