In this paper we define and investigate basic logical closure properties of propositional proof systems such as closure of arbitrary proof systems under modus ponens or substitutions. As our main result we obtain a purely logical characterization of the degrees of schematic extensions of EF in terms of a simple combination of these properties. This result underlines the empirical evidence that ...

By considering the supreme-utilities among fuzzy sets and the weights among participants simultaneously, we introduce the supreme-weighted value on fuzzy transferable-utility games. Further, we provide some equivalent relations to characterize the family of all solutions that admit a potential on weights. We also propose the dividend approach to provide alternative viewpoint for the potential a...

The usual heat equation is not suitable to preserve the topology of divergence-free vector fields, because it destroys their integral line structure. On the contrary, in the fluid mechanics literature, on can find examples of topology-preserving diffusion equations for divergence-free vector fields. They are very degenerate since they admit all stationary solutions to the Euler equations of inc...

We determine the detailed qualitative behavior of radially symmetric equilibrium states with two or more phases for general classes of nonlinear thermoelastic materials. We treat the cases of structured and non-structured interface. Methods are based on a combination of geometric constructions with phase-plane analyses of the governing equations. A special feature of the solutions is that they ...

According to logical positivism, so the story goes, metaphysical questions are meaningless, since they do not admit of empirical confirmation or refutation. However, the logical positivists did not in fact reject as meaningless all questions about for example, the structure of space and time. Rather, key figures such as Reichenbach and Schlick believed that scientific theories often presupposed...

We consider the diffusive continuous coagulation-fragmentation equations with and without scattering and show that they admit unique strong solutions for a large class of initial values. If the latter values are small with respect to a suitable norm, we provide sufficient conditions for global-in-time existence in the absence of fragmentation.

Heaps models are powerful models for concurrent timed discrete event systems. They admit linear description using dioid algebras. Inspired by supervisory control of logical discrete event systems we introduce parallel composition of heap models, called synchronous product, to formally describe the action of supervisor (represented by another heap model) on the system. This additional explicit c...