Logical systems with classical negation and means for sentential or propositional self-reference involve, in some way, paradoxical statements such as the liar. However, the paradox disappears if one replaces classical by an appropriate non-classical negation such as a paraconsistent one (no paradox arises if the liar is both true and false). We consider a non-Fregean logic which is a revised an...

A formalism is proposed for representing uncertain information on set-valued variables using the formalism of belief functions. A set-valued variableX on a domain Ω is a variable taking zero, one or several values in Ω. While defining mass functions on the frame 22 Ω is usually not feasible because of the double-exponential complexity involved, we propose an approach based on a definition of a ...

Grassmann-valued Dirac fields together with the electromagnetic field (the pseudoclassical basis of QED) are reformulated on spacelike hypersurfaces in Minkowski spacetime and then restricted to Wigner hyperplanes to get their description in the rest-frame Wigner-covariant instant form of dynamics. The canonical reduction to the Wigner-covariant Coulomb gauge is done in the rest frame. It is sh...

Let 1 p 1 and = (1 ; : : : ; r) T be a vector-valued compactly supported L p function on R d. Deene V p (() = n P r i=1 P j2Z d d i (j) i (? j) : (d i (j)) j2Z d 2 ` p ; 1 i r o : In this paper, we consider the p-frame property of the space V p (() with being compactly supported function in L p \ L p=(p?1). Moreover, for the one-dimensional case, we show that if f i (? j) : 1 i r; j 2 Zg is a p...

Description Logics (DLs, for short) provide a logical reconstruction of the so-called frame-based knowledge representation languages. Originally, four-valued DLs have been proposed in order to develop expressively powerful DLs with tractable subsumption algorithms. Recently, four-valued DLs have been proposed as a model for (multimedia) document retrieval. In this context, the main reasoning ta...

We look at extensions (i.e., stronger logics in the same language) of the Belnap-Dunn four-valued logic. We prove the existence of a countable chain of logics that extend the Belnap-Dunn and do not coincide with any of the known extensions (Kleene’s logics, Priest’s logic of paradox). We characterize the reduced algebraic models of these new logics and prove a completeness result for the first ...

this paper is a continuation of [uniformities and covering properties for partial frames (i)], in which we make use of the notion of a partial frame, which is a meet-semilattice in which certain designated subsets are required to have joins, and finite meets distribute over these. after presenting there our axiomatization of partial frames, which we call $sels$-frames, we added structure, in th...

Abstract The similarity measures are essential concepts to discuss the closeness between sets. Fuzzy and intuitionistic fuzzy dealt with incomplete inconsistent data more efficiently. With time in decision-making theory, a complex frame of environment that occurs cannot be specified entirely by these A generalization like Pythagorean set can handle such situation applicability this attracted re...

partial frames provide a rich context in which to do pointfree structured and unstructured topology. a small collection of axioms of an elementary nature allows one to do much traditional pointfree topology, both on the level of frames or locales, and that of uniform or metric frames. these axioms are sufficiently general to include as examples bounded distributive lattices, $sigma$-frames, $ka...

The phase retrieval problem in the classical setting is to reconstruct real/complex functions from magnitudes of their Fourier/frame measurements. In this paper, we consider a new paradigm vector-valued setting, which motivated by complex conjugate vectors range space real matrix and Paley-Wiener space, also determination vector field defined on graph relative between neighboring vertices. prov...