775 research outputs found
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
Broken triangles: From value merging to a tractable class of general-arity constraint satisfaction problems
International audienceA binary CSP instance satisfying the broken-triangle property (BTP) can be solved in polynomial time. Unfortunately, in practice, few instances satisfy the BTP. We show that a local version of the BTP allows the merging of domain values in arbitrary instances of binary CSP, thus providing a novel polynomial-time reduction operation. Extensive experimental trials on benchmark instances demonstrate a significant decrease in instance size for certain classes of problems. We show that BTP-merging can be generalised to instances with constraints of arbitrary arity and we investigate the theoretical relationship with resolution in SAT. A directional version of general-arity BTP-merging then allows us to extend the BTP tractable class previously defined only for binary CSP. We investigate the complexity of several related problems including the recognition problem for the general-arity BTP class when the variable order is unknown, finding an optimal order in which to apply BTP merges and detecting BTP-merges in the presence of global constraints such as AllDifferent
Characterising Fixed Parameter Tractability for Query Evaluation over Guarded TGDs
We consider the parameterized complexity of evaluating Ontology Mediated Queries (OMQ) based on Guarded TGDs (GTGD) and Unions of Conjunctive Queries, in the case where relational symbols have unrestricted arity and where the parameter is the size of the OMQ. We establish exact criteria for fixed-parameter tractable (fpt) evaluation of recursively enumerable (r.e.) classes of such OMQs (under the widely held Exponential Time Hypothesis). One of the main technical tools introduced in the paper is an fpt-reduction from deciding parameterized uniform CSPs to parameterized OMQ evaluation. The reduction preserves measures known to be essential for classifying r.e. classes of parameterized uniform CSPs: submodular width (according to the well known result of Marx for unrestricted-arity schemas) and treewidth (according to the well known result of Grohe for bounded-arity schemas). As such, it can be employed to obtain hardness results for evaluation of r.e. classes of parameterized OMQs based on GTGD both in the unrestricted and in the bounded arity case. Previously, for bounded arity schemas, this has been tackled using a technique requiring full introspection into the construction employed by Grohe
Relational Neural Machines
Deep learning has been shown to achieve impressive results in several tasks
where a large amount of training data is available. However, deep learning
solely focuses on the accuracy of the predictions, neglecting the reasoning
process leading to a decision, which is a major issue in life-critical
applications. Probabilistic logic reasoning allows to exploit both statistical
regularities and specific domain expertise to perform reasoning under
uncertainty, but its scalability and brittle integration with the layers
processing the sensory data have greatly limited its applications. For these
reasons, combining deep architectures and probabilistic logic reasoning is a
fundamental goal towards the development of intelligent agents operating in
complex environments. This paper presents Relational Neural Machines, a novel
framework allowing to jointly train the parameters of the learners and of a
First--Order Logic based reasoner. A Relational Neural Machine is able to
recover both classical learning from supervised data in case of pure
sub-symbolic learning, and Markov Logic Networks in case of pure symbolic
reasoning, while allowing to jointly train and perform inference in hybrid
learning tasks. Proper algorithmic solutions are devised to make learning and
inference tractable in large-scale problems. The experiments show promising
results in different relational tasks
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