In this paper X denotes a set. Let L be a lattice. Note that Poset(L) has l.u.b.’s and g.l.b.’s. Let L be an upper-bounded lattice. One can verify that Poset(L) is upper-bounded. Let L be a lower-bounded lattice. One can verify that Poset(L) is lower-bounded. Let L be a complete lattice. Note that Poset(L) is complete. Let X be a set. Then X is an order in X . Let X be a set. The functor 〈X ,⊆〉...

Let Q-L be the least predicate extension of a normal extension L of S4 and BF be the Barcan formula ∀x2A(x) ⊃ 2∀xA(x). Ghilardi [3] showed that it is rare that Q-L is complete with respect to Kripke semantics. On the other hand, if L is a subframe logic with the finite embedding property, we can show the completeness of Q-L + BF by the method of canonical models (cf. Lemma 3 [2], Theorem 3.9 [5...

Closure (interior) operators and closure systems are important tools in many mathematical environments. Considering the logical sense of a complete residuated lattice L, this paper aims to present concepts L-closure (L-interior) by means infimums (supremums) L-families L-subsets show their equivalence categorical sense. Also, two types fuzzy relations between corresponding L-interior proposed, ...

We study the properties of a system biorthogonal to complete and minimal exponentials in $$L^2(E)$$ , where E is finite union intervals, show that case when two or three intervals also complete.

Let E be a set of real restricted quasi-analytic functions ; we describe a language L definable from E , +, × and <, and a L-theory T , universal and “explicit”, such that T is equivalent to the complete theory of R in L and T is model-complete. As a consequence, we give a description of the prime model of this theory.

An orthomodular lattice L is said to be interval homogeneous (resp. centrally interval homogeneous) if it is σ-complete and satisfies the following property: Whenever L is isomorphic to an interval, [a, b], in L then L is isomorphic to each interval [c, d] with c ≤ a and d ≥ b (resp. the same condition as above only under the assumption that all elements a, b, c, d are central in L). Let us den...

form a complete lattice, the D e d e k i n d M a c N e i l l e c o m p l e t i o n (or short comp l e t i o n ) of (P, <). It is the smallest complete lattice containing a subset orderisomorphic with (P, <). The size of the completion may be exponential in [PI. The completion can be computed in steps: first complete a small part of (P, <), then add another element, complete again, et cetera. Ea...

We consider a bi-criteria generalization of the pathwidth problem, where, for given integers k, l and a graph G, we ask whether there exists a path decomposition P of G such that the width of P is at most k and the number of bags in P, i.e., the length of P, is at most l. We provide a complete complexity classification of the problem in terms of k and l for general graphs. Contrary to the origi...

As an application of the dual equivalence between the category of L-spatialC-objects and the category of L-sober C-M-L-spaces, it is shown in this paper that for a fixed augmented partially ordered set A, there exists a dual equivalence between the category of A-spatial augmented partially ordered sets and the category of A-sober A-valued spaces. Then, with regard to this duality, for a fixed (...