We introduce the branching transitive closure operator on weighted monadic second-order logic formulas where the branching corresponds in a natural way to the branching inherent in trees. For arbitrary commutative semirings, we prove that weighted monadic second order logics on trees is equivalent to the definability by formulas which start with one of the following operators: (i) a branching t...

We consider n-dimensional semi-algebraic spatial databases. We compute in first-order logic extended with a transitive closure operator, a linear spatial database which characterizes the semi-algebraic spatial database up to a homeomorphism. In this way, we generalize our earlier results to semi-algebraic spatial databases in arbitrary dimensions, our earlier results being true for only two dim...

A sufficient condition is obtained for two isometries to be unitarily equivalent. Also, a new class of M-hyponormal operator is constructed

The original definition of a topological space given by Hausdorff used neighborhood systems. Lattice-valued maps appear in this context when you identify a topology with a monoid in the Kleisli category of the filter monad on SET. H?hle’s notion of a lattice-valued topology [2] uses the same idea and it’s inspired in the classical lattice-valued topologies. Ltopological spaces are motivated by ...

Abstract The family ${\mathcal{R}} X^*$ of regular subsets the free monoid $X^*$ generated by a finite set X is standard example ${}^*$ -continuous Kleene algebra. Likewise, ${\mathcal{C}} context-free $\mu$ Chomsky algebra, i.e. an idempotent semiring that closed under well-behaved least fixed-point operator . For arbitrary monoids M , M$ closure ${\mathcal{R}}M$ as more briefly, We provide al...

In that paper, the fuzzy nonlinear programming problem is discussed. In order to obtain more accurate solution, the properties of fuzzy set and fuzzy number with linear membership function and fuzzy maximum decision maker is utilized to fuzzifying the crisp problem. In the illustration, we have given a refinement to obtain this solution.

For a symmetric monoidal-closed category X and any object K, the category of K-Chu spaces is small-topological over X and small cotopological over X . Its full subcategory of M-extensive K-Chu spaces is topological over X when X is Mcomplete, for any morphism class M. Often this subcategory may be presented as a full coreflective subcategory of Diers’ category of affine K-spaces. Hence, in addi...

In this paper, we present a new vision for studying ${F}$-open, ${F}$-continuous, and ${F}$-irresolute function in $(L,M)$-fuzzy topological spaces based on the implication operation and $(L,M)$-fuzzy ${F}$-open operator cite{2}. These kinds of functions are generalized with their elementary properties to $(L,M)$-fuzzy topological spaces setting based on graded concepts. Moreover, a systematic ...

In accordance with Tarski point of view, in this chapter the theory of closure operators is proposed as a unifying tool for fuzzy logics. Indeed, let F be the set of formulas of a given language. Then an abstract fuzzy logic is defined by a fuzzy semantics (i.e. a class of valuations of the formulas in F) and by a closure operator in the lattice of the fuzzy subsets of F (we call deduction oper...