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...

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 ...

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.

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...

We consider the Fokker–Planck operator with a strong external magnetic field. show maximal type estimate on this using nilpotent approach vector field polynomial operators and including notion of representation Lie algebra. This makes it possible to give an optimal characterization domain closure considered operator.

In this paper, the local function, weak semi-local function and closure are compared with each other according to inclusion relation. We define a new operator by using investigate its properties. Thanks operator, we obtain two topologies which finer than some previously defined topologies.

First introduced in the study of the Sturmian words, the iterated palindromic closure was generalized to pseudopalindromes. This operator allows one to construct words with infinitely many pseudopalindromic prefixes, called pseudostandard words. We provide here several combinatorial properties of the fixed points under the iterated pseudopalindromic closure.

The Abiteboul and Beeri algebra for complex objects can express a query whose meaning is transitive closure, but the algorithm naturally associated to this query needs exponential space. We show that any other query in the algebra which expresses transitive closure needs exponential space. This proves that in general the powerset is an intractable operator for implementing xpoint queries.

We define the notion of weak relative pseudo-complement on meet semi-lattices, and we show that it is strictly weaker than relative pseudo-complementation, but stronger than pseudo-complementation. Our main result is that if a complete lattice L is meet-continuous, then every closure operator on L admits weak relative pseudo-complements with respect to continuous closure operators on L.

A constructively valid counterpart to Bourbaki’s Fixpoint Lemma for chaincomplete partially ordered sets is presented to obtain a condition for one closure system in a complete lattice L to be stable under another closure operator of L. This is then used to deal with coproducts and other aspects of frames.