804 research outputs found
Temporal Landscapes: A Graphical Temporal Logic for Reasoning
We present an elementary introduction to a new logic for reasoning about
behaviors that occur over time. This logic is based on temporal type theory.
The syntax of the logic is similar to the usual first-order logic; what differs
is the notion of truth value. Instead of reasoning about whether formulas are
true or false, our logic reasons about temporal landscapes. A temporal
landscape may be thought of as representing the set of durations over which a
statement is true. To help understand the practical implications of this
approach, we give a wide variety of examples where this logic is used to reason
about autonomous systems.Comment: 20 pages, lots of figure
Levelable Sets and the Algebraic Structure of Parameterizations
Asking which sets are fixed-parameter tractable for a given parameterization
constitutes much of the current research in parameterized complexity theory.
This approach faces some of the core difficulties in complexity theory. By
focussing instead on the parameterizations that make a given set
fixed-parameter tractable, we circumvent these difficulties. We isolate
parameterizations as independent measures of complexity and study their
underlying algebraic structure. Thus we are able to compare parameterizations,
which establishes a hierarchy of complexity that is much stronger than that
present in typical parameterized algorithms races. Among other results, we find
that no practically fixed-parameter tractable sets have optimal
parameterizations
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
Lifted Relax, Compensate and then Recover: From Approximate to Exact Lifted Probabilistic Inference
We propose an approach to lifted approximate inference for first-order
probabilistic models, such as Markov logic networks. It is based on performing
exact lifted inference in a simplified first-order model, which is found by
relaxing first-order constraints, and then compensating for the relaxation.
These simplified models can be incrementally improved by carefully recovering
constraints that have been relaxed, also at the first-order level. This leads
to a spectrum of approximations, with lifted belief propagation on one end, and
exact lifted inference on the other. We discuss how relaxation, compensation,
and recovery can be performed, all at the firstorder level, and show
empirically that our approach substantially improves on the approximations of
both propositional solvers and lifted belief propagation.Comment: Appears in Proceedings of the Twenty-Eighth Conference on Uncertainty
in Artificial Intelligence (UAI2012
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