1,736 research outputs found
Deriving Inverse Operators for Modal Logic
International audienceSpatial constraint systems are algebraic structures from concurrent constraint programming to specify spatial and epistemic behavior in multi-agent systems. We shall use spatial constraint systems to give an abstract characterization of the notion of normality in modal logic and to derive right inverse/reverse operators for modal languages. In particular, we shall identify the weakest condition for the existence of right inverses and show that the abstract notion of normality corresponds to the preservation of finite suprema. We shall apply our results to existing modal languages such as the weakest normal modal logic, Hennessy-Milner logic, and linear-time temporal logic. We shall discuss our results in the context of modal concepts such as bisimilarity and inconsistency invariance
On P-transitive graphs and applications
We introduce a new class of graphs which we call P-transitive graphs, lying
between transitive and 3-transitive graphs. First we show that the analogue of
de Jongh-Sambin Theorem is false for wellfounded P-transitive graphs; then we
show that the mu-calculus fixpoint hierarchy is infinite for P-transitive
graphs. Both results contrast with the case of transitive graphs. We give also
an undecidability result for an enriched mu-calculus on P-transitive graphs.
Finally, we consider a polynomial time reduction from the model checking
problem on arbitrary graphs to the model checking problem on P-transitive
graphs. All these results carry over to 3-transitive graphs.Comment: In Proceedings GandALF 2011, arXiv:1106.081
Well-orders in the transfinite Japaridze algebra
This paper studies the transfinite propositional provability logics
\glp_\Lambda and their corresponding algebras. These logics have for each
ordinal a modality \la \alpha \ra. We will focus on the closed
fragment of \glp_\Lambda (i.e., where no propositional variables occur) and
\emph{worms} therein. Worms are iterated consistency expressions of the form
\la \xi_n\ra \ldots \la \xi_1 \ra \top. Beklemishev has defined
well-orderings on worms whose modalities are all at least and
presented a calculus to compute the respective order-types.
In the current paper we present a generalization of the original
orderings and provide a calculus for the corresponding generalized order-types
. Our calculus is based on so-called {\em hyperations} which are
transfinite iterations of normal functions.
Finally, we give two different characterizations of those sequences of
ordinals which are of the form \la {\formerOmega}_\xi (A) \ra_{\xi \in \ord}
for some worm . One of these characterizations is in terms of a second kind
of transfinite iteration called {\em cohyperation.}Comment: Corrected a minor but confusing omission in the relation between
Veblen progressions and hyperation
Modal Approach to Casimir Forces in Periodic Structures
We present a modal approach to calculate finite temperature Casimir
interactions between two periodically modulated surfaces. The scattering
formula is used and the reflection matrices of the patterned surfaces are
calculated decomposing the electromagnetic field into the natural modes of the
structures. The Casimir force gradient from a deeply etched silicon grating is
evaluated using the modal approach and compared to experiment for validation.
The Casimir force from a two dimensional periodic structure is computed and
deviations from the proximity force approximation examined.Comment: 13 pages, 7 figure
On the Expressiveness of Spatial Constraint Systems
In this paper we shall report on our progress using spatial constraint system as an abstract representation of modal and epistemic behaviour. First we shall give an introduction as well as the background to our work. Then, we present our preliminary results on the representation of modal behaviour by using spatial constraint systems. Then, we present our ongoing work on the characterization of the epistemic notion of knowledge. Finally, we discuss about the future work of our research
Fredkin Gates for Finite-valued Reversible and Conservative Logics
The basic principles and results of Conservative Logic introduced by Fredkin
and Toffoli on the basis of a seminal paper of Landauer are extended to
d-valued logics, with a special attention to three-valued logics. Different
approaches to d-valued logics are examined in order to determine some possible
universal sets of logic primitives. In particular, we consider the typical
connectives of Lukasiewicz and Godel logics, as well as Chang's MV-algebras. As
a result, some possible three-valued and d-valued universal gates are described
which realize a functionally complete set of fundamental connectives.Comment: 57 pages, 10 figures, 16 tables, 2 diagram
Mixed variational formulations of finite element analysis of elastoacoustic/slosh fluid-structure interaction
A general three-field variational principle is obtained for the motion of an acoustic fluid enclosed in a rigid or flexible container by the method of canonical decomposition applied to a modified form of the wave equation in the displacement potential. The general principle is specialized to a mixed two-field principle that contains the fluid displacement potential and pressure as independent fields. This principle contains a free parameter alpha. Semidiscrete finite-element equations of motion based on this principle are displayed and applied to the transient response and free-vibrations of the coupled fluid-structure problem. It is shown that a particular setting of alpha yields a rich set of formulations that can be customized to fit physical and computational requirements. The variational principle is then extended to handle slosh motions in a uniform gravity field, and used to derive semidiscrete equations of motion that account for such effects
- …