In the article presented we deal with one method of stochastic programming – probabilistic programming. It is a programming in which the probabilities of the values of the variables are of interest. Our approach is that solving problem we can construct in logical reasoning over some mathematical theories. In this approach we use category theory for construction of type theory and of the logical...

Interactive theorem proving has grown from toy examples to major projects formalizing mathematics and verifying software, and there is now a critical need for theory engineering techniques to support these efforts. This paper introduces the OpenTheory project, which aims to provide an effective package management system for logical theories. The OpenTheory article format allows higher order log...

We present an algorithm for unification of higher-order patterns modulo simple syntactic equational theories as defined by Kirchner [14]. The algorithm by Miller [17] for pattern unification, refined by Nipkow [18] is first modified in order to behave as a first-order unification algorithm. Then the mutation rule for syntactic theories of Kirchner [13, 14] is adapted to pattern E-unification. I...

This work is a sequel to our 14]. It is shown how Theorem 6 of 14], dealing with the translatability of HA (Heyting's arithmetic) into negationless arithmetic NA, can be extended to the case of intuition-istic arithmetic in higher types.

Higher-order theories of consciousness argue that conscious awareness crucially depends on higher-order mental representations that represent oneself as being in particular mental states. These theories have featured prominently in recent debates on conscious awareness. We provide new leverage on these debates by reviewing the empirical evidence in support of the higher-order view. We focus on ...

We consider models involving the higher (third) derivative extension of the abelian Chern-Simons (CS) topological term in D=2+1 dimensions. The polarisation vectors in these models reveal an identical structure with the corresponding expressions for usual models which contain, at most, quadratic structures. We also investigate the Hamiltonian structure of these models and show how Wigner’s litt...

Bending analyses of isotropic, functionally graded, laminated composite, and sandwich beams are carried out using a quasi-3D polynomial shear and normal deformation theory. The most important feature of the proposed theory is that it considers the effects of transverse shear and transverse normal deformations. It accounts for parabolic variations in the strain/stress produced by transverse shea...

This study presents an analytical solution for free vibration analysis of two-dimensional functionally graded (2D-FG) porous sandwich beams. The equations motion the beam were derived using Hamilton's principle, and then Galerkin method was employed to solve equations. material properties beams vary with thickness length each layer according power-law function. mechanical gradually changed from...

Based on the nonlocal Timoshenko beam theory, the dynamic stability of functionally gradded (FG) nanoeams under axial load is studied in thermal environment, with considering surface effect. It is used power law distribution for FGM and the surface stress effects are considered based on Gurtin-Murdoch continuum theory. Using Von Karman geometric nonlinearity, governing equations are derived bas...

Displacement finite element models of various beam theories have been developed traditionally using conventional finite element basis functions (i.e., cubic Hermite, equi-spaced Lagrange interpolation functions, or spectral/hp Legendre functions). Various finite element models of beams differ from each other in the choice of the interpolation functions used for the transverse deflection w, tota...