54,347 research outputs found
Graphene: Semantically-Linked Propositions in Open Information Extraction
We present an Open Information Extraction (IE) approach that uses a
two-layered transformation stage consisting of a clausal disembedding layer and
a phrasal disembedding layer, together with rhetorical relation identification.
In that way, we convert sentences that present a complex linguistic structure
into simplified, syntactically sound sentences, from which we can extract
propositions that are represented in a two-layered hierarchy in the form of
core relational tuples and accompanying contextual information which are
semantically linked via rhetorical relations. In a comparative evaluation, we
demonstrate that our reference implementation Graphene outperforms
state-of-the-art Open IE systems in the construction of correct n-ary
predicate-argument structures. Moreover, we show that existing Open IE
approaches can benefit from the transformation process of our framework.Comment: 27th International Conference on Computational Linguistics (COLING
2018
Dyck algebras, interval temporal logic and posets of intervals
We investigate a natural Heyting algebra structure on the set of Dyck paths
of the same length. We provide a geometrical description of the operations of
pseudocomplement and relative pseudocomplement, as well as of regular elements.
We also find a logic-theoretic interpretation of such Heyting algebras, which
we call Dyck algebras, by showing that they are the algebraic counterpart of a
certain fragment of a classical interval temporal logic (also known as
Halpern-Shoham logic). Finally, we propose a generalization of our approach,
suggesting a similar study of the Heyting algebra arising from the poset of
intervals of a finite poset using Birkh\"off duality. In order to illustrate
this, we show how several combinatorial parameters of Dyck paths can be
expressed in terms of the Heyting algebra structure of Dyck algebras together
with a certain total order on the set of atoms of each Dyck algebra.Comment: 17 pages, 3 figure
Linear and Branching System Metrics
We extend the classical system relations of trace\ud
inclusion, trace equivalence, simulation, and bisimulation to a quantitative setting in which propositions are interpreted not as boolean values, but as elements of arbitrary metric spaces.\ud
\ud
Trace inclusion and equivalence give rise to asymmetrical and symmetrical linear distances, while simulation and bisimulation give rise to asymmetrical and symmetrical branching distances. We study the relationships among these distances, and we provide a full logical characterization of the distances in terms of quantitative versions of LTL and μ-calculus. We show that, while trace inclusion (resp. equivalence) coincides with simulation (resp. bisimulation) for deterministic boolean transition systems, linear\ud
and branching distances do not coincide for deterministic metric transition systems. Finally, we provide algorithms for computing the distances over finite systems, together with a matching lower complexity bound
Uniform Strategies
We consider turn-based game arenas for which we investigate uniformity
properties of strategies. These properties involve bundles of plays, that arise
from some semantical motive. Typically, we can represent constraints on allowed
strategies, such as being observation-based. We propose a formal language to
specify uniformity properties and demonstrate its relevance by rephrasing
various known problems from the literature. Note that the ability to correlate
different plays cannot be achieved by any branching-time logic if not equipped
with an additional modality, so-called R in this contribution. We also study an
automated procedure to synthesize strategies subject to a uniformity property,
which strictly extends existing results based on, say standard temporal logics.
We exhibit a generic solution for the synthesis problem provided the bundles of
plays rely on any binary relation definable by a finite state transducer. This
solution yields a non-elementary procedure.Comment: (2012
Gravitational Energy in Spherical Symmetry
Various properties of the Misner-Sharp spherically symmetric gravitational
energy E are established or reviewed. In the Newtonian limit of a perfect
fluid, E yields the Newtonian mass to leading order and the Newtonian kinetic
and potential energy to the next order. For test particles, the corresponding
Hajicek energy is conserved and has the behaviour appropriate to energy in the
Newtonian and special-relativistic limits. In the small-sphere limit, the
leading term in E is the product of volume and the energy density of the
matter. In vacuo, E reduces to the Schwarzschild energy. At null and spatial
infinity, E reduces to the Bondi-Sachs and Arnowitt-Deser-Misner energies
respectively. The conserved Kodama current has charge E. A sphere is trapped if
E>r/2, marginal if E=r/2 and untrapped if E<r/2, where r is the areal radius. A
central singularity is spatial and trapped if E>0, and temporal and untrapped
if E<0. On an untrapped sphere, E is non-decreasing in any outgoing spatial or
null direction, assuming the dominant energy condition. It follows that E>=0 on
an untrapped spatial hypersurface with regular centre, and E>=r_0/2 on an
untrapped spatial hypersurface bounded at the inward end by a marginal sphere
of radius r_0. All these inequalities extend to the asymptotic energies,
recovering the Bondi-Sachs energy loss and the positivity of the asymptotic
energies, as well as proving the conjectured Penrose inequality for black or
white holes. Implications for the cosmic censorship hypothesis and for general
definitions of gravitational energy are discussed.Comment: 23 pages. Belatedly replaced with substantially extended published
versio
Quantified CTL: Expressiveness and Complexity
While it was defined long ago, the extension of CTL with quantification over
atomic propositions has never been studied extensively. Considering two
different semantics (depending whether propositional quantification refers to
the Kripke structure or to its unwinding tree), we study its expressiveness
(showing in particular that QCTL coincides with Monadic Second-Order Logic for
both semantics) and characterise the complexity of its model-checking and
satisfiability problems, depending on the number of nested propositional
quantifiers (showing that the structure semantics populates the polynomial
hierarchy while the tree semantics populates the exponential hierarchy)
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