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Transformation of propositional calculus statements into integer and mixed integer programs: An approach towards automatic reformulation
A systematic procedure for transforming a set of logical statements or logical conditions imposed on a model into an Integer Linear Progamming (ILP) formulation Mixed Integer Programming (MIP) formulation is presented. An ILP stated as a system of linear constraints involving integer variables and an objective function, provides a powerful representation of decision problems through a tightly interrelated closed system of choices. It supports direct representation of logical (Boolean or prepositional calculus) expressions. Binary variables (hereafter called logical variables) are first introduced and methods of logically connecting these to other variables are then presented. Simple constraints can be combined to construct logical relationships and the methods of formulating these are discussed. A reformulation procedure which uses the extended reverse polish representation of a compound logical form is then described. These reformulation procedures are illustrated by two examples. A scheme of implementation.ithin an LP modelling system is outlined
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
A Survey of Satisfiability Modulo Theory
Satisfiability modulo theory (SMT) consists in testing the satisfiability of
first-order formulas over linear integer or real arithmetic, or other theories.
In this survey, we explain the combination of propositional satisfiability and
decision procedures for conjunctions known as DPLL(T), and the alternative
"natural domain" approaches. We also cover quantifiers, Craig interpolants,
polynomial arithmetic, and how SMT solvers are used in automated software
analysis.Comment: Computer Algebra in Scientific Computing, Sep 2016, Bucharest,
Romania. 201
Developing a labelled object-relational constraint database architecture for the projection operator
Current relational databases have been developed in order to improve the handling of
stored data, however, there are some types of information that have to be analysed for
which no suitable tools are available. These new types of data can be represented and treated
as constraints, allowing a set of data to be represented through equations, inequations
and Boolean combinations of both. To this end, constraint databases were defined and
some prototypes were developed. Since there are aspects that can be improved, we propose
a new architecture called labelled object-relational constraint database (LORCDB). This provides
more expressiveness, since the database is adapted in order to support more types of
data, instead of the data having to be adapted to the database. In this paper, the projection
operator of SQL is extended so that it works with linear and polynomial constraints and
variables of constraints. In order to optimize query evaluation efficiency, some strategies
and algorithms have been used to obtain an efficient query plan.
Most work on constraint databases uses spatiotemporal data as case studies. However,
this paper proposes model-based diagnosis since it is a highly potential research area,
and model-based diagnosis permits more complicated queries than spatiotemporal examples.
Our architecture permits the queries over constraints to be defined over different sets
of variables by using symbolic substitution and elimination of variables.Ministerio de Ciencia y TecnologĆa DPI2006-15476-C02-0
PDDL2.1: An extension of PDDL for expressing temporal planning domains
In recent years research in the planning community has moved increasingly towards application of planners to realistic problems involving both time and many types of resources. For example, interest in planning demonstrated by the space research community has inspired work in observation scheduling, planetary rover ex ploration and spacecraft control domains. Other temporal and resource-intensive domains including logistics planning, plant control and manufacturing have also helped to focus the community on the modelling and reasoning issues that must be confronted to make planning technology meet the challenges of application. The International Planning Competitions have acted as an important motivating force behind the progress that has been made in planning since 1998. The third competition (held in 2002) set the planning community the challenge of handling time and numeric resources. This necessitated the development of a modelling language capable of expressing temporal and numeric properties of planning domains. In this paper we describe the language, PDDL2.1, that was used in the competition. We describe the syntax of the language, its formal semantics and the validation of concurrent plans. We observe that PDDL2.1 has considerable modelling power --- exceeding the capabilities of current planning technology --- and presents a number of important challenges to the research community
Solving Set Constraint Satisfaction Problems using ROBDDs
In this paper we present a new approach to modeling finite set domain
constraint problems using Reduced Ordered Binary Decision Diagrams (ROBDDs). We
show that it is possible to construct an efficient set domain propagator which
compactly represents many set domains and set constraints using ROBDDs. We
demonstrate that the ROBDD-based approach provides unprecedented flexibility in
modeling constraint satisfaction problems, leading to performance improvements.
We also show that the ROBDD-based modeling approach can be extended to the
modeling of integer and multiset constraint problems in a straightforward
manner. Since domain propagation is not always practical, we also show how to
incorporate less strict consistency notions into the ROBDD framework, such as
set bounds, cardinality bounds and lexicographic bounds consistency. Finally,
we present experimental results that demonstrate the ROBDD-based solver
performs better than various more conventional constraint solvers on several
standard set constraint problems
Learning Qualitative Constraint Networks
Temporal and spatial reasoning is a fundamental task in artificial intelligence and its related areas including scheduling, planning and Geographic Information Systems (GIS). In these applications, we often deal with incomplete and qualitative information. In this regard, the symbolic representation of time and space using Qualitative Constraint Networks (QCNs) is therefore substantial.
We propose a new algorithm for learning a QCN from a non expert. The learning process includes different cases where querying the user is an essential task. Here, membership queries are asked in order to elicit temporal or spatial relationships between pairs of temporal or spatial entities. During this acquisition process, constraint propagation through Path Consistency (PC) is performed in order to reduce the number of membership queries needed to reach the target QCN. We use the learning theory machinery to prove some limits on learning path consistent QCNs from queries. The time performances of our algorithm have been experimentally evaluated using different scenarios
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