Multiple Conclusion Rules in Logics with the Disjunction Property

We prove that for the intermediate logics with the disjunction property any basis of admissible rules can be reduced to a basis of admissible m-rules (multiple-conclusion rules), and every basis of admissible m-rules can be reduced to a basis of admissible rules. These results can be generalized to a broad class of logics including positive logic and its extensions, Johansson logic, normal extensions of S4, n-transitive logics and intuitionistic modal logics

Admissibility of logical inference rules

The aim of this book is to present the fundamental theoretical results concerning inference rules in deductive formal systems. Primary attention is focused on: admissible or permissible inference rules the derivability of the admissible inference rules the structural completeness of logics the bases for admissible and valid inference rules. There is particular emphasis on propositional non-standard logics (primary, superintuitionistic and modal logics) but general logical consequence relations and classical first-order theories are also considered. The book is basically self-contained an

Construction of an explicit basis for rules admissible in modal system S4

We find an explicit basis for all admissible rules of the modal logic S4. Our basis consists of an infinite sequence of rules which have compact and simple, readable form and depend on increasing set of variables. This gives a basis for all quasi-identities valid in the free modal algebra F-S4(omega) of countable rank

On finite model property for admissible rules

WOS: 000083646500008Our investigation is concerned with the finite model property (fmp) with respect to admissible rules. We establish general sufficient conditions for absence of fmp w.r.t. admissibility which are applicable to modal logics containing K4: Theorem 3.1 says that no logic lambda containing K4 with the co-cover property and of width > 2 has fmp w.r.t. admissibility. Surprisingly many, if not to say all, important modal logics of width > 2 are within the scope of this theorem - K4 itself, S4, GL, K4.1, K4.2, S4.1, S4.2, GL.2, etc. Thus the situation is completely opposite to the case of the ordinary fmp - the absolute majority of important logics have fmp, but not with respect to admissibility. As regards logics of width I 2, there exists a Bone for fmp w.r.t. admissibility. It is shown (Theorem 4.3) that all modal logics lambda of width I 2 extending S4 which are not sub-logics of three special tabular logics (which is equipotent to all these lambda extend a certain subframe logic defined over S4 by omission of four special frames) have fmp w.r.t. admissibility

Additive Manufacturing of Ceramic Products Based on Millimeter-Wave Heating

Abstract Additive manufacturing of ceramic articles making use of concentrated energy flows attracts the research interest worldwide. While the application of laser beams faces serious problems associated with high temperature of sintering and low thermal conductivity of ceramics, layer-by-layer sintering by focused millimeter-wave radiation appears to be a promising method of additive manufacturing. This paper describes the studies of fast millimeter-wave sintering of yttria-stabilized zirconia and hydroxyapatite ceramics. Coefficients of the millimeter-wave absorption have been determined in broad frequency and temperature ranges. Rapid sintering of compacted ceramics samples was accomplished using volumetric microwave heating in a work chamber of a 24 GHz / 5 kW gyrotron system. In addition, using a 263 GHz / 1 kW cwgyrotron millimeter-wave source and a purposely designed electrodynamic focusing structure, radiation intensities of up to 20 kW/cm2could be achieved, which was sufficient for fast localized heating of ceramic layers to the solidification temperature. The results of a study of the microstructure and mechanical properties of the sintered ceramics are presented.</jats:p