29,491 research outputs found
Constraint Programming viewed as Rule-based Programming
We study here a natural situation when constraint programming can be entirely
reduced to rule-based programming. To this end we explain first how one can
compute on constraint satisfaction problems using rules represented by simple
first-order formulas. Then we consider constraint satisfaction problems that
are based on predefined, explicitly given constraints. To solve them we first
derive rules from these explicitly given constraints and limit the computation
process to a repeated application of these rules, combined with labeling.We
consider here two types of rules. The first type, that we call equality rules,
leads to a new notion of local consistency, called {\em rule consistency} that
turns out to be weaker than arc consistency for constraints of arbitrary arity
(called hyper-arc consistency in \cite{MS98b}). For Boolean constraints rule
consistency coincides with the closure under the well-known propagation rules
for Boolean constraints. The second type of rules, that we call membership
rules, yields a rule-based characterization of arc consistency. To show
feasibility of this rule-based approach to constraint programming we show how
both types of rules can be automatically generated, as {\tt CHR} rules of
\cite{fruhwirth-constraint-95}. This yields an implementation of this approach
to programming by means of constraint logic programming. We illustrate the
usefulness of this approach to constraint programming by discussing various
examples, including Boolean constraints, two typical examples of many valued
logics, constraints dealing with Waltz's language for describing polyhedral
scenes, and Allen's qualitative approach to temporal logic.Comment: 39 pages. To appear in Theory and Practice of Logic Programming
Journa
Relating Weight Constraint and Aggregate Programs: Semantics and Representation
Weight constraint and aggregate programs are among the most widely used logic
programs with constraints. In this paper, we relate the semantics of these two
classes of programs, namely the stable model semantics for weight constraint
programs and the answer set semantics based on conditional satisfaction for
aggregate programs. Both classes of programs are instances of logic programs
with constraints, and in particular, the answer set semantics for aggregate
programs can be applied to weight constraint programs. We show that the two
semantics are closely related. First, we show that for a broad class of weight
constraint programs, called strongly satisfiable programs, the two semantics
coincide. When they disagree, a stable model admitted by the stable model
semantics may be circularly justified. We show that the gap between the two
semantics can be closed by transforming a weight constraint program to a
strongly satisfiable one, so that no circular models may be generated under the
current implementation of the stable model semantics. We further demonstrate
the close relationship between the two semantics by formulating a
transformation from weight constraint programs to logic programs with nested
expressions which preserves the answer set semantics. Our study on the
semantics leads to an investigation of a methodological issue, namely the
possibility of compact representation of aggregate programs by weight
constraint programs. We show that almost all standard aggregates can be encoded
by weight constraints compactly. This makes it possible to compute the answer
sets of aggregate programs using the ASP solvers for weight constraint
programs. This approach is compared experimentally with the ones where
aggregates are handled more explicitly, which show that the weight constraint
encoding of aggregates enables a competitive approach to answer set computation
for aggregate programs.Comment: To appear in Theory and Practice of Logic Programming (TPLP), 2011.
30 page
A CHR-based Implementation of Known Arc-Consistency
In classical CLP(FD) systems, domains of variables are completely known at
the beginning of the constraint propagation process. However, in systems
interacting with an external environment, acquiring the whole domains of
variables before the beginning of constraint propagation may cause waste of
computation time, or even obsolescence of the acquired data at the time of use.
For such cases, the Interactive Constraint Satisfaction Problem (ICSP) model
has been proposed as an extension of the CSP model, to make it possible to
start constraint propagation even when domains are not fully known, performing
acquisition of domain elements only when necessary, and without the need for
restarting the propagation after every acquisition.
In this paper, we show how a solver for the two sorted CLP language, defined
in previous work, to express ICSPs, has been implemented in the Constraint
Handling Rules (CHR) language, a declarative language particularly suitable for
high level implementation of constraint solvers.Comment: 22 pages, 2 figures, 1 table To appear in Theory and Practice of
Logic Programming (TPLP
Distributed Abductive Reasoning: Theory, Implementation and Application
Abductive reasoning is a powerful logic inference mechanism that allows assumptions to be
made during answer computation for a query, and thus is suitable for reasoning over incomplete
knowledge. Multi-agent hypothetical reasoning is the application of abduction in a distributed
setting, where each computational agent has its local knowledge representing partial world and
the union of all agents' knowledge is still incomplete. It is different from simple distributed
query processing because the assumptions made by the agents must also be consistent with
global constraints.
Multi-agent hypothetical reasoning has many potential applications, such as collaborative planning
and scheduling, distributed diagnosis and cognitive perception. Many of these applications
require the representation of arithmetic constraints in their problem specifications as well as
constraint satisfaction support during the computation. In addition, some applications may
have confidentiality concerns as restrictions on the information that can be exchanged between
the agents during their collaboration. Although a limited number of distributed abductive systems
have been developed, none of them is generic enough to support the above requirements.
In this thesis we develop, in the spirit of Logic Programming, a generic and extensible distributed
abductive system that has the potential to target a wide range of distributed problem
solving applications. The underlying distributed inference algorithm incorporates constraint
satisfaction and allows non-ground conditional answers to be computed. Its soundness and
completeness have been proved. The algorithm is customisable in that different inference and
coordination strategies (such as goal selection and agent selection strategies) can be adopted
while maintaining correctness. A customisation that supports confidentiality during problem
solving has been developed, and is used in application domains such as distributed security
policy analysis. Finally, for evaluation purposes, a
flexible experimental environment has been
built for automatically generating different classes of distributed abductive constraint logic programs.
This environment has been used to conduct empirical investigation of the performance
of the customised system
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
- …