31,731 research outputs found
Answer Set Programming for Qualitative Spatio-Temporal Reasoning: Methods and Experiments
We study the translation of reasoning problems involving qualitative spatio-temporal calculi into answer set programming (ASP). We present various alternative transformations and provide a qualitative comparison among them. An implementation of these transformations is provided by a tool that transforms problem instances specified in the language of the Generic Qualitative Reasoner (GQR) into ASP problems. Finally, we report on an experimental analysis of solving consistency problems for Allen\u27s Interval Algebra and the Region Connection Calculus with eight base relations (RCC-8)
Answer Set Programming for Qualitative Spatio-temporal Reasoning: Methods and Experiments
We study the translation of reasoning problems involving qualitative spatio-temporal calculi into answer set programming (ASP). We present various alternative transformations and provide a qualitative comparison among them. An implementation of these transformations is provided by a tool that transforms problem instances specified in the language of the Generic Qualitative Reasoner (GQR) into ASP problems.
Finally, we report on an experimental analysis of solving consistency problems for Allen’s Interval
Algebra and the Region Connection Calculus with eight base relations (RCC-8)
The Inverse Variational Problem for Autoparallels
We study the problem of the existence of a local quantum scalar field theory
in a general affine metric space that in the semiclassical approximation would
lead to the autoparallel motion of wave packets, thus providing a deviation of
the spinless particle trajectory from the geodesics in the presence of torsion.
The problem is shown to be equivalent to the inverse problem of the calculus of
variations for the autoparallel motion with additional conditions that the
action (if it exists) has to be invariant under time reparametrizations and
general coordinate transformations, while depending analytically on the torsion
tensor. The problem is proved to have no solution for a generic torsion in
four-dimensional spacetime. A solution exists only if the contracted torsion
tensor is a gradient of a scalar field. The corresponding field theory
describes coupling of matter to the dilaton field.Comment: 13 pages, plain Latex, no figure
Shapely monads and analytic functors
In this paper, we give precise mathematical form to the idea of a structure
whose data and axioms are faithfully represented by a graphical calculus; some
prominent examples are operads, polycategories, properads, and PROPs. Building
on the established presentation of such structures as algebras for monads on
presheaf categories, we describe a characteristic property of the associated
monads---the shapeliness of the title---which says that "any two operations of
the same shape agree". An important part of this work is the study of analytic
functors between presheaf categories, which are a common generalisation of
Joyal's analytic endofunctors on sets and of the parametric right adjoint
functors on presheaf categories introduced by Diers and studied by
Carboni--Johnstone, Leinster and Weber. Our shapely monads will be found among
the analytic endofunctors, and may be characterised as the submonads of a
universal analytic monad with "exactly one operation of each shape". In fact,
shapeliness also gives a way to define the data and axioms of a structure
directly from its graphical calculus, by generating a free shapely monad on the
basic operations of the calculus. In this paper we do this for some of the
examples listed above; in future work, we intend to do so for graphical calculi
such as Milner's bigraphs, Lafont's interaction nets, or Girard's
multiplicative proof nets, thereby obtaining canonical notions of denotational
model
Gravity on Finite Groups
Gravity theories are constructed on finite groups G. A self-consistent review
of the differential calculi on finite G is given, with some new developments.
The example of a bicovariant differential calculus on the nonabelian finite
group S_3 is treated in detail, and used to build a gravity-like field theory
on S_3.Comment: LaTeX, 26 pages, 1 figure. Corrected misprints and formula giving
exterior product of n 1-forms. Added note on topological actio
Variable types for meaning assembly: a logical syntax for generic noun phrases introduced by most
This paper proposes a way to compute the meanings associated with sentences
with generic noun phrases corresponding to the generalized quantifier most. We
call these generics specimens and they resemble stereotypes or prototypes in
lexical semantics. The meanings are viewed as logical formulae that can
thereafter be interpreted in your favourite models. To do so, we depart
significantly from the dominant Fregean view with a single untyped universe.
Indeed, our proposal adopts type theory with some hints from Hilbert
\epsilon-calculus (Hilbert, 1922; Avigad and Zach, 2008) and from medieval
philosophy, see e.g. de Libera (1993, 1996). Our type theoretic analysis bears
some resemblance with ongoing work in lexical semantics (Asher 2011; Bassac et
al. 2010; Moot, Pr\'evot and Retor\'e 2011). Our model also applies to
classical examples involving a class, or a generic element of this class, which
is not uttered but provided by the context. An outcome of this study is that,
in the minimalism-contextualism debate, see Conrad (2011), if one adopts a type
theoretical view, terms encode the purely semantic meaning component while
their typing is pragmatically determined
Noncommutative Differential Calculus for D-brane in Non-Constant B Field Background
In this paper we try to construct noncommutative Yang-Mills theory for
generic Poisson manifolds. It turns out that the noncommutative differential
calculus defined in an old work is exactly what we need. Using this calculus,
we generalize results about the Seiberg-Witten map, the Dirac-Born-Infeld
action, the matrix model and the open string quantization for constant B field
to non-constant background with H=0.Comment: 21 pages, Latex file, references added, minor modificatio
Tensor calculus on noncommutative spaces
It is well known that for a given Poisson structure one has infinitely many
star products related through the Kontsevich gauge transformations. These gauge
transformations have an infinite functional dimension (i.e., correspond to an
infinite number of degrees of freedom per point of the base manifold). We show
that on a symplectic manifold this freedom may be almost completely eliminated
if one extends the star product to all tensor fields in a covariant way and
impose some natural conditions on the tensor algebra. The remaining ambiguity
either correspond to constant renormalizations to the symplectic structure, or
to maps between classically equivalent field theory actions. We also discuss
how one can introduce the Riemannian metric in this approach and the
consequences of our results for noncommutative gravity theories.Comment: 17p; v2: extended version, to appear in CQ
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