19,395 research outputs found
Temporalized logics and automata for time granularity
Suitable extensions of the monadic second-order theory of k successors have
been proposed in the literature to capture the notion of time granularity. In
this paper, we provide the monadic second-order theories of downward unbounded
layered structures, which are infinitely refinable structures consisting of a
coarsest domain and an infinite number of finer and finer domains, and of
upward unbounded layered structures, which consist of a finest domain and an
infinite number of coarser and coarser domains, with expressively complete and
elementarily decidable temporal logic counterparts.
We obtain such a result in two steps. First, we define a new class of
combined automata, called temporalized automata, which can be proved to be the
automata-theoretic counterpart of temporalized logics, and show that relevant
properties, such as closure under Boolean operations, decidability, and
expressive equivalence with respect to temporal logics, transfer from component
automata to temporalized ones. Then, we exploit the correspondence between
temporalized logics and automata to reduce the task of finding the temporal
logic counterparts of the given theories of time granularity to the easier one
of finding temporalized automata counterparts of them.Comment: Journal: Theory and Practice of Logic Programming Journal Acronym:
TPLP Category: Paper for Special Issue (Verification and Computational Logic)
Submitted: 18 March 2002, revised: 14 Januari 2003, accepted: 5 September
200
Specific-to-General Learning for Temporal Events with Application to Learning Event Definitions from Video
We develop, analyze, and evaluate a novel, supervised, specific-to-general
learner for a simple temporal logic and use the resulting algorithm to learn
visual event definitions from video sequences. First, we introduce a simple,
propositional, temporal, event-description language called AMA that is
sufficiently expressive to represent many events yet sufficiently restrictive
to support learning. We then give algorithms, along with lower and upper
complexity bounds, for the subsumption and generalization problems for AMA
formulas. We present a positive-examples--only specific-to-general learning
method based on these algorithms. We also present a polynomial-time--computable
``syntactic'' subsumption test that implies semantic subsumption without being
equivalent to it. A generalization algorithm based on syntactic subsumption can
be used in place of semantic generalization to improve the asymptotic
complexity of the resulting learning algorithm. Finally, we apply this
algorithm to the task of learning relational event definitions from video and
show that it yields definitions that are competitive with hand-coded ones
Temporal Stream Algebra
Data stream management systems (DSMS) so far focus on
event queries and hardly consider combined queries to both
data from event streams and from a database. However,
applications like emergency management require combined
data stream and database queries. Further requirements are
the simultaneous use of multiple timestamps after different
time lines and semantics, expressive temporal relations between multiple time-stamps and
exible negation, grouping
and aggregation which can be controlled, i. e. started and
stopped, by events and are not limited to fixed-size time
windows. Current DSMS hardly address these requirements.
This article proposes Temporal Stream Algebra (TSA) so
as to meet the afore mentioned requirements. Temporal
streams are a common abstraction of data streams and data-
base relations; the operators of TSA are generalizations of
the usual operators of Relational Algebra. A in-depth 'analysis of temporal relations guarantees that valid TSA expressions are non-blocking, i. e. can be evaluated incrementally.
In this respect TSA differs significantly from previous algebraic approaches which use specialized operators to prevent
blocking expressions on a "syntactical" level
Certainty Closure: Reliable Constraint Reasoning with Incomplete or Erroneous Data
Constraint Programming (CP) has proved an effective paradigm to model and
solve difficult combinatorial satisfaction and optimisation problems from
disparate domains. Many such problems arising from the commercial world are
permeated by data uncertainty. Existing CP approaches that accommodate
uncertainty are less suited to uncertainty arising due to incomplete and
erroneous data, because they do not build reliable models and solutions
guaranteed to address the user's genuine problem as she perceives it. Other
fields such as reliable computation offer combinations of models and associated
methods to handle these types of uncertain data, but lack an expressive
framework characterising the resolution methodology independently of the model.
We present a unifying framework that extends the CP formalism in both model
and solutions, to tackle ill-defined combinatorial problems with incomplete or
erroneous data. The certainty closure framework brings together modelling and
solving methodologies from different fields into the CP paradigm to provide
reliable and efficient approches for uncertain constraint problems. We
demonstrate the applicability of the framework on a case study in network
diagnosis. We define resolution forms that give generic templates, and their
associated operational semantics, to derive practical solution methods for
reliable solutions.Comment: Revised versio
Probabilistic Interval Temporal Logic and Duration Calculus with Infinite Intervals: Complete Proof Systems
The paper presents probabilistic extensions of interval temporal logic (ITL)
and duration calculus (DC) with infinite intervals and complete Hilbert-style
proof systems for them. The completeness results are a strong completeness
theorem for the system of probabilistic ITL with respect to an abstract
semantics and a relative completeness theorem for the system of probabilistic
DC with respect to real-time semantics. The proposed systems subsume
probabilistic real-time DC as known from the literature. A correspondence
between the proposed systems and a system of probabilistic interval temporal
logic with finite intervals and expanding modalities is established too.Comment: 43 page
The Complexity of Datalog on Linear Orders
We study the program complexity of datalog on both finite and infinite linear
orders. Our main result states that on all linear orders with at least two
elements, the nonemptiness problem for datalog is EXPTIME-complete. While
containment of the nonemptiness problem in EXPTIME is known for finite linear
orders and actually for arbitrary finite structures, it is not obvious for
infinite linear orders. It sharply contrasts the situation on other infinite
structures; for example, the datalog nonemptiness problem on an infinite
successor structure is undecidable. We extend our upper bound results to
infinite linear orders with constants.
As an application, we show that the datalog nonemptiness problem on Allen's
interval algebra is EXPTIME-complete.Comment: 21 page
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