Control of multiscale systems with constraints. 1. Basic principles of the concept of evolution of systems with varying constraints

Physical fundamentals of the self-organizing theory for the system with varying constraints are considered. A variation principle, specifically the principle of dynamic harmonization as a generalization of the Gauss-Hertz principle for the systems with varying internal structure is formulated. In compliance with this principle the system evolves through dynamics of the processes leading to harmonization of the internal multiscale structure of the system and its connections with external actions as a result of minimizing the dynamic harmonization function. Main principles of the shell model of self-organization under the action of the dominating entropic disturbance are formulated.Comment: First par

Tackling Incomplete System Specifcations Using Natural Deduction in the Paracomplete Setting

In many modern computer applications the significanceofspecificationbasedverificationiswellaccepted.However, when we deal with such complex processes as the integration of heterogeneous systems, parts of specification may be not known. Therefore it is important to have techniques that are able to cope with such incomplete information. An adequate formal set up is given by so called paracomplete logics, where, contrary to the classical framework, for some statements we do not have evidence to conclude if they are true or false. As a consequence, for example, the law of excluded middle is not valid. In this paper we justify how the automated proof search technique for paracomplete logic PComp can be efficiently applied to the reasoning about systems with incomplete information. Note that for many researchers, one of the core features of natural deduction, the opportunity to introduce arbitrary formulae as assumptions, has been a point of great scepticism regarding the very possibility of the automation of the proof search. Here, not only we show the contrary, but we also turned the assumptions management into an advantage showing the applicability of the proposed technique to assume-guarantee reasoning. Keywords - incomplete information, automated natural deduction, paracomplete logic, requirements engineering, assumeguarantee reasoning, component based system assembly

Towards Generalised Proof Search for Natural Deduction Systems for logics I⟨a;b⟩

We continue our investigation of the proof searching procedures developed for natural deduction calculus for classical and a variety of non-classical logics. In particular, we deal with natural deduction systems for propositional logics I⟨alpha;beta⟩, where alpha, beta are elements of 0, 1, 2, 3,..., w such that I⟨0;0⟩ is classical logic, proposed by Vladimir Popov. We aim at generalising the concept of an inference for these systems that is fundamental to proof searching technique for these logics

Natural Deduction in a Paracomplete Setting

In this paper we present the automated proof search technique in natural deduction paracomplete logic. Here, for some statements we do not have evidence to conclude if they are true or false, as it happens in the classical framework. As a consequence, for example, formulae of the type p_:p, are not valid. In this paper we formulate the natural deduction system for paracompletelogic PComp, explain its main concepts, define proof searching techniques and the searching algorithm providing examples proofs

Natural deduction system in paraconsistent setting: proof search for PCont

This paper continues a systematic approach to build natural deduction calculi and corresponding proof procedures for non-classical logics. Our attention is now paid to the framework of paraconsistent logics. These logics are used, in particular, for reasoning about systems where paradoxes do not lead to the `deductive explosion', i.e., where formulae of the type `A follows from false', for any A, are not valid. We formulate the natural deduction system for the logic PCont, explain its main concepts, define a proof searching technique and illustrate it by examples. The presentation is accompanied by demonstrating the correctness of these developments

Influence of the temperature of electrode material on its disintegration under the action of an arc discharge in hydrogen

An analysis is made of the electrophysical processes occurring at the end surface of rod electrodes during constant and alternating arc discharge in hydrogen. Experiments are reported on the effect of surface temperature of tungsten electrodes on their erosion. The influence of activating additions of thorium oxide, the structure of the tungsten, and the gas surrounding the electrode on the specific thermal loading and the erosion of the electrodes is discussed

Foliations of bounded mean curvature on closed three-dimensional Riemannian manifolds

It is proved that only a finite number of cohomological classes of a closed orientable irreducible three-dimensional Riemannian manifold can be represented by the Euler class of a tangent distribution to a smooth foliation of codimension one whose leaves have the modulus of the mean curvature bounded from above by a fixed constant

On the Complexity of the Natural Deduction Proof Search Algorithm

We present our first account of the complexity of natural deduction proof search algorithms. Though we target the complexity for natural deduction for temporal logic, here we only tackle classical case, comparing the classical part of the proof search for temporal logic with the classical analytical tableau