Generalization of Einstein-Lovelock theory to higher order dilaton gravity

A higher order theory of dilaton gravity is constructed as a generalization of the Einstein-Lovelock theory of pure gravity. Its Lagrangian contains terms with higher powers of the Riemann tensor and of the first two derivatives of the dilaton. Nevertheless, the resulting equations of motion are quasi-linear in the second derivatives of the metric and of the dilaton. This property is crucial for the existence of brane solutions in the thin wall limit. At each order in derivatives the contribution to the Lagrangian is unique up to an overall normalization. Relations between symmetries of this theory and the O(d,d) symmetry of the string-inspired models are discussed.Comment: 18 pages, references added, version to be publishe

Towards a Proof Theory of G\"odel Modal Logics

Analytic proof calculi are introduced for box and diamond fragments of basic modal fuzzy logics that combine the Kripke semantics of modal logic K with the many-valued semantics of G\"odel logic. The calculi are used to establish completeness and complexity results for these fragments

Casimir dark energy, stabilization of the extra dimensions and Gauss–Bonnet term

A Casimir dark energy model in a five-dimensional and a six-dimensional spacetime including non-relativistic matter and a Gauss–Bonnet term is investigated. The Casimir energy can play the role of dark energy to drive the late-time acceleration of the universe while the radius of the extra dimensions can be stabilized. The qualitative analysis in four-dimensional spacetime shows that the contribution from the Gauss–Bonnet term will effectively slow down the radion field at the matter-dominated or radiation-dominated epochs so that it does not pass the point at which the minimum of the potential will arise before the minimum has formed. The field then is trapped at the minimum of the potential after the formation leading to the stabilization of the extra dimensions

Processing Information

Abstract. We introduce a general framework for solving the problem of a computer collecting and combining information from various sources. Unlike previous approaches to this problem, in our framework the sources are allowed to provide information about complex formulae too. This is enabled by the use of a new tool — non-deterministic logical matrices. We also consider several alternative plausible assumptions concerning the framework. These assumptions lead to various logics. We provide strongly sound and complete proof systems for all the basic logics induced in this way

On Designated Values in Multi-Valued CTL* Model Checking

A multi-valued version of CTL* (mv-CTL*), where both the propositions and the accessibility relation are multi-valued, taking values in a complete lattice with a complement, is considered. Contrary to all the existing model checking results for multi-valued modal logics, our lattices are not required to be finite. A set of restrictions is provided under which there is a direct translation from mv-CTL* to CTL* model checking problem for designated values. Bisimulation induced by mvCTL* is characterized