We introduce a natural class of quantifiers Th containing all monadic type quantifiers, all quantifiers for linear orders, quantifiers for isomorphism, Ramsey type quantifiers, and plenty more, showing that no sublogic of Lo~o,(Th) or countably compact regular sublogic of L~o,(Th), properly extending L,o,o, satisfies the uniform reduction property for quotients. As a consequence, none of these ...

We prove that if u1, u2 : (0,∞)× Rd → (0,∞) are sufficiently well-behaved solutions to certain heat inequalities on Rd then the function u : (0,∞) × Rd → (0,∞) given by u1/p = u 1/p1 1 ∗ u 1/p2 2 also satisfies a heat inequality of a similar type provided 1 p1 + 1 p2 = 1 + 1 p . On iterating, this result leads to an analogous statement concerning n-fold convolutions. As a corollary, we give a d...

Locally finite ω-languages, defined via second order quantifications followed by a first order locally finite sentence, were introduced by Ressayre in [Res88]. They enjoy very nice properties and extend ω-languages accepted by finite automata or defined by monadic second order sentences. We study here closure properties of the family LOCω of locally finite omega languages. In particular we show...

Among the various proposals for defeasible reasoning for description logics, Rational Closure, a procedure originally defined for propositional logic, turns out to have a number of desirable properties. Not only it is computationally feasible, but it can also be implemented using existing classical reasoners. One of its drawbacks is that it can be seen as too weak from the inferential point of ...

The purpose of this paper is to introduce and study regular bopen sets (briefly rb-open sets) in topological spaces and obtain some of their properties. We introduce the rb-closure and discuss some basic properties of the rb-closure. Also we study the new concepts of rb-closed spaces by means of filter bases. Mathematics Subject Classification: 54A05, 54A20

In this paper, the notions of anti-reflexive kernel, symmetric kernel, reflexive closure, and symmetric closure of a soft set relation are first introduced, respectively. Then, their accurate calculation formulae and some properties are obtained. Finally, soft set relation mappings and inverse soft set relationmappings are proposed, and some related properties are discussed. © 2010 Elsevier Ltd...

This paper deals with closure properties of models of fuzzy attribute implications. Fuzzy attribute implications are particular IF-THEN rules which can be interpreted in data tables with fuzzy attributes and/or ranked data tables over domains with similarity relations. We show that models of any set of fuzzy attribute implications form a fuzzy closure system with hedge. Conversely, we show that...

The main goal of this paper is to introduce and study a new class of function via the notions of $e$-$theta$-open sets and $e$-$theta$-closure operator which are defined by Özkoç and Aslım [10] called weakly $eR$-open functions and $e$-$theta$-open functions. Moreover, we investigate not only some of their basic properties but also their relationships with other types of already existing topolo...

We study closure properties with respect to products for hypergroupoids, semihypergroups and hypergroups associated to binary relations. Using some basic category theory tools, from a certain point, the investigation turns into studying closure properties with respect to direct products for some classes of monounary multialgebras.