In this paper we define and examine frame constructions for the family of many-valued modal logics introduced by M. Fitting in the ’90s. Every language of this family is built on an underlying space of truth values, a Heyting algebra H. We generalize Fitting’s original work by considering complete Heyting algebras as truth spaces and proceed to define a suitable notion of H-indexed families of ...

Let (M,F) be a foliated m + n-dimensional manifold M with n-dimensional foliation F . Let V be a finite dimensional vector space over R. We describe all canonical (Folm,n-invariant) V -valued 1-forms Θ: TP r(M,F) → V on the r-th order adapted frame bundle P r(M,F) of (M,F). All manifolds and maps are assumed to be of class C∞. A definition of foliations can be found in [2]. Let Folm,n be the ca...

Let L2(R,H) denote the space of all square integrable quaternionic-valued functions. In this article, let Φ∈L2(R,H). We consider perturbation problems wavelet frame {Φm,n,a0,b0,m,n∈Z} about translation parameter b0 and dilation a0. particular, we also research stability irregular {SmΦ(Smx−nb),m,n∈Z} for sampling.

We give a program describing the pervasiveness of the short-time Fourier transform (STFT) in a host of topics including the following: waveform design and optimal ambiguity function behavior for radar and communications applications; vector-valued ambiguity function theory for multi-sensor environments; finite Gabor frames for deterministic compressive sensing and as a background for the HRT co...

in this paper, we study the existence of generalized solutions for the infinite dimensional nonlinear stochastic differential inclusions $dx(t) in f(t,x(t))dt +g(t,x(t))dw_t$ in which the multifunction $f$ is semimonotone and hemicontinuous and the operator-valued multifunction $g$ satisfies a lipschitz condition. we define the it^{o} stochastic integral of operator set-valued stochastic pr...

Informationally complete measurements on a quantum system allow to estimate the expectation value of any arbitrary operator by just averaging functions of the experimental outcomes. We show that such kind of measurements can be achieved through positive-operator valued measures (POVM’s) related to unitary irreducible representations of a group on the Hilbert space of the system. With the help o...

A many-valued modal logic is introduced that combines the standard (crisp) Kripke frame semantics of the modal logic K with connectives interpreted locally as abelian group operations over the real numbers. A labelled tableau system and a sequent calculus admitting cut elimination are then defined for this logic and used to establish completeness of an axiomatic extension of the multiplicative ...

Closed classes of three-valued logic generated by periodic symmetric funtions that equal 1 in tuples from {1, 2} and equal 0 on the rest tuples are considered. Criteria for bases existence and finite bases existence for these classes is obtained. The problem of the bases existence for some families of closed classes of the three-valued logic functions is considered in the paper. E. Post [1] (se...

Partial functions are abundant in mathematics and program specifications. Unfortunately, their importance has been mostly ignored in automated theorem proving. In this paper, we develop a theorem proving strategy for Partial Classical Logic (PCL). Proof search takes place in Kleene Logic. We show that PCL theories can be translated into equivalent sets of formulas in Kleene logic. For proof sea...

Łukasiewicz three-valued logic Ł3 is often understood as the set of 3-valued valid formulas according to Łukasiewicz’s 3-valued matrices. Following Wojcicki, in addition, we shall consider two alternative interpretations of Ł3: “well-determined” Ł3a and “truth-preserving” Ł3b defined by two different consequence relations on the 3-valued matrices. The aim of this paper is to provide (by using D...