6,612 research outputs found
A logic for reasoning about knowledge of unawareness
In the most popular logics combining knowledge and awareness, it is not possible to express statements about knowledge of unawareness such as “Ann knows that Bill is aware of something Ann is not aware of” – without using a stronger statement such as “Ann knows that Bill is aware of p and Ann is not aware of p”, for some particular p. In Halpern and Rêgo (2006, 2009b) (revisited in Halpern and Rêgo (2009a, 2013)) Halpern and Rêgo introduced a logic in which such statements about knowledge of unawareness can be expressed. The logic extends the traditional framework with quantification over formulae, and is thus very expressive. As a consequence, it is not decidable. In this paper we introduce a decidable logic which can be used to reason about certain types of unawareness. Our logic extends the traditional framework with an operator expressing full awareness, i.e., the fact that an agent is aware of everything, and another operator expressing relative awareness, the fact that one agent is aware of everything another agent is aware of. The logic is less expressive than Halpern’s and Rêgo’s logic. It is, however, expressive enough to express all of the motivating examples in Halpern and Rêgo (2006, 2009b). In addition to proving that the logic is decidable and that its satisfiability problem is PSPACE-complete, we present an axiomatisation which we show is sound and complete
Modal Logics with Hard Diamond-free Fragments
We investigate the complexity of modal satisfiability for certain
combinations of modal logics. In particular we examine four examples of
multimodal logics with dependencies and demonstrate that even if we restrict
our inputs to diamond-free formulas (in negation normal form), these logics
still have a high complexity. This result illustrates that having D as one or
more of the combined logics, as well as the interdependencies among logics can
be important sources of complexity even in the absence of diamonds and even
when at the same time in our formulas we allow only one propositional variable.
We then further investigate and characterize the complexity of the
diamond-free, 1-variable fragments of multimodal logics in a general setting.Comment: New version: improvements and corrections according to reviewers'
comments. Accepted at LFCS 201
Hamiltonian Formulation of Open WZW Strings
Using a Hamiltonian approach, we construct the classical and quantum theory
of open WZW strings on a strip. (These are the strings which end on WZW
branes.) The development involves non-abelian generalized Dirichlet images in
an essential way. At the classical level, we find a new non-commutative
geometry in which the equal-time coordinate brackets are non-zero at the
world-sheet boundary, and the result is an intrinsically non-abelian effect
which vanishes in the abelian limit. Using the classical theory as a guide to
the quantum theory, we also find the operator algebra and the analogue of the
Knizhnik-Zamolodchikov equations for the the conformal field theory of open WZW
strings.Comment: 34 pages. Added an equation in Appendix C; some typos corrected.
Footnote b changed. Version to appear on IJMP
Memristive excitable cellular automata
The memristor is a device whose resistance changes depending on the polarity
and magnitude of a voltage applied to the device's terminals. We design a
minimalistic model of a regular network of memristors using
structurally-dynamic cellular automata. Each cell gets info about states of its
closest neighbours via incoming links. A link can be one 'conductive' or
'non-conductive' states. States of every link are updated depending on states
of cells the link connects. Every cell of a memristive automaton takes three
states: resting, excited (analog of positive polarity) and refractory (analog
of negative polarity). A cell updates its state depending on states of its
closest neighbours which are connected to the cell via 'conductive' links. We
study behaviour of memristive automata in response to point-wise and spatially
extended perturbations, structure of localised excitations coupled with
topological defects, interfacial mobile excitations and growth of information
pathways.Comment: Accepted to Int J Bifurcation and Chaos (2011
Controllability and observabiliy of an artificial advection-diffusion problem
In this paper we study the controllability of an artificial
advection-diffusion system through the boundary. Suitable Carleman estimates
give us the observability on the adjoint system in the one dimensional case. We
also study some basic properties of our problem such as backward uniqueness and
we get an intuitive result on the control cost for vanishing viscosity.Comment: 20 pages, accepted for publication in MCSS. DOI:
10.1007/s00498-012-0076-
Probabilistic Algorithmic Knowledge
The framework of algorithmic knowledge assumes that agents use deterministic
knowledge algorithms to compute the facts they explicitly know. We extend the
framework to allow for randomized knowledge algorithms. We then characterize
the information provided by a randomized knowledge algorithm when its answers
have some probability of being incorrect. We formalize this information in
terms of evidence; a randomized knowledge algorithm returning ``Yes'' to a
query about a fact \phi provides evidence for \phi being true. Finally, we
discuss the extent to which this evidence can be used as a basis for decisions.Comment: 26 pages. A preliminary version appeared in Proc. 9th Conference on
Theoretical Aspects of Rationality and Knowledge (TARK'03
General Solution of the non-abelian Gauss law and non-abelian analogs of the Hodge decomposition
General solution of the non-abelian Gauss law in terms of covariant curls and
gradients is presented. Also two non-abelian analogs of the Hodge decomposition
in three dimensions are addressed. i) Decomposition of an isotriplet vector
field as sum of covariant curl and gradient with respect to an
arbitrary background Yang-Mills potential is obtained. ii) A decomposition of
the form which involves non-abelian
magnetic field of a new Yang-Mills potential C is also presented. These results
are relevant for duality transformation for non-abelian gauge fields.Comment: 6 pages, no figures, revte
Performance of Driven Piles in Gravelly Sands With Cobbles
Steel piles are known for their high resistance to driving and handling, as well as their large lateral stiffness. Difficulty of driving depends on the subsurface conditions, pile type, and type of impact hammer used to drive piles. This case history presents observations of pile construction for a bridge widening retrofit in the city of Irwindale. The proposed foundations consisted of twenty seven 14-inch-diameter Caltrans Standard Plan B2-5 Alternative V closed-end pipe piles with quarter-inch thick steel sections. Piles were 35 feet in length and were designed to be driven piles. Subsurface investigations indicated the soils consisted of silty gravels with sand and silty sands with gravel in a medium dense condition. Excavations for the pile cap revealed a large amount of cobbles and boulders unknown during design. Difficult driving conditions resulted in failure of several closed-end steel pipe piles. Attempts at driving open-ended steel pipe piles also failed. Mushrooming of pile tops as well as buckling and shearing of piles was observed during pile driving. Failed piles were extracted for further examination. An alternative method of installation was developed to minimize the impact to the original scope of work and utilize materials already furnished for the job. The alternative method of installation consisted of pre-drilling 20-inch-diameter holes to pile tip elevation, and placing the steel shells in open excavations without driving. High-strength grout was used to fill in the annular space between the steel pipe pile and the surrounding soils. Analysis was performed to ensure the alternative installation method did not adversely affect the required load capacity of the piles
Self-Interaction and Gauge Invariance
A simple unified closed form derivation of the non-linearities of the
Einstein, Yang-Mills and spinless (e.g., chiral) meson systems is given. For
the first two, the non-linearities are required by locality and consistency; in
all cases, they are determined by the conserved currents associated with the
initial (linear) gauge invariance of the first kind. Use of first-order
formalism leads uniformly to a simple cubic self-interaction.Comment: Missing last reference added. 9 pages, This article, the first paper
in Gen. Rel. Grav. [1 (1970) 9], is now somewhat inaccessible; the present
posting is the original version, with a few subsequent references included.
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