The scores can be used in themselv es or serve as the basis for ranking or choice. For the present, only a few scoring pro cedures are endowed with their axiomatic characterizations. At the same time, a large num ber of ingenious procedures are advocated and used in such disciplines as manageme nt science, operations research, psychometrics, applied statistics, processing of spor t tournaments, graph theory, etc. Very few social choice papers deal with them. The aim of this pa per is to take one circumspect step toward an axiomatic framework for comparin g the merits of these elaborate procedures. As a result, we would like to isolate a family of s coring procedures that comprises a majority of'reasonable' procedures (so that th e further axioms could be imposed on this family). Two main approaches are applicable. The first one is to express the desired properties axiomatically, the second is to gather the ex isting procedures and specify their common algebraic form.

Constraint Programming (CP)[21] is a powerful technique for spec ifying Constraint Satisfaction Problems (CSPs) based on allowing a constraintprogrammer to model problems in terms of high-level constraints. Using such global constraints allows easier specification of problems but also allows for faster solve rs that take advantage of the structure in the problem. The classica l approach to CSP solving is to explore the search tree of all possible assignment s to the variables in a depth-first search backtracking manner, guided by v arious heuristics, until a solution is found or proven not to exist. One of the most basic techniques for reducing the number of search tree nodes explore d is to perform domain propagation at each node. In order to get as much domain propagation as possible we wish for each constraint to remove from the variable d omains all values that cannot participate in a solution to that constraint.

INRA Toulouse, France Abstract Weighted Max-SA T is the optimization version of SA T and many important problems can be naturally encoded as such. Solving weighted Max-SA T is an important problem from both a theoretical and a practical point of view. In recent ye ars, there has been considerable interest in finding efficient solving techniques. Most of thi s work focus on the computation of good quality lower bounds to be used within a branch and bou nd DPLL-like algorithm. Most often, these lower bounds are described in a procedural way. Because of that, it is difficult to realize the logic that is behind. In this paper we introduce an original framework for Max-SA T that stresses the parallelism with classical SA T. Then, we extend the two basic SA T s olving techniques: search and inference. We show that many algorithmic tricks used in state-of-the-art Max-SA T solvers are easily expressable in logic terms with our framework in a unified manner. Besides, we introduce an original search algorithm that per forms a restricted amount of weighted resolution at each visited node. We empirically compare our algorithm w ith a variety of solving alternatives on several benchmarks. Our experiments, which constitute to the best of our knowledge the most comprehensive Max-sat eva luation ever reported, show that our algorithm is generally orders of magnitude faster t han any competitor. Preprint submitted to Elsevier Science 11 September 2018 1 Introduction Weighted Max-SA T is the optimization version of the SA T prob lem and many important problems can be naturally expressed as such. In recent years, there has been a considerable effort in finding efficient exact algorithms. A common drawback of all these alg orithms is that albeit the close relationship between SA T and Max-SA T, they cannot be easily described with logic terminology. For instance, the contributions of [11,12,13,14] are good quality lower bounds to be incorporated into a depth-first branch and bound procedure. These lower bounds are mostly defined in a procedural way and it is very difficult to see the logic that is behind the execution of the procedure. This is in contrast with SA T algorithms where the solving process can b e easily decomposed into atomic logical steps. In this paper we introduce an original framework for (weight ed) Max-SA T in which the notions of upper and lower bound are incorporated into the problem definition. Under this framework classical SA T is just a particular case of Max-SA T, and the main SA T solving techniques can be naturally extended. In pa rticular, we extend the basic simplification rules (for example, idempotency, absorption, unit clause reduction, etc) and introduce a new one, hardening, that does not make sense in the SA T context.

We study an alternative to the prevailing approach to modelling qualitative spatial reasoning (QSR) problems as constraint satisfaction problems. In the standard approach, a relation between objects is a constraint whereas in the alternative approach it is a variable. The relation-variable approach greatly simplifies integration and implementation of QSR. To substantiate this point, we discuss several QSR algorithms from the literature which in the relation-variable approach reduce to the customary constraint propagation algorithm enforcing generalised arc-consistency.

We introduce a constraint-based framework for studying infinite qualitative simulations concerned with contingencies such as time, space, shape, size, abstracted into a finite set of qualitative relations. To define the simulations, we combine constraints that formalize the background knowledge concerned with qualitative reasoning with appropriate inter-state constraints that are formulated using linear temporal logic. We implemented this approach in a constraint programming system by drawing on ideas from bounded model checking. The resulting system allows us to test and modify the problem specifications in a straightforward way and to combine various knowledge aspects.

Constraint propagation algorithms implement logical infe r-ence. For efficiency, it is essential to control whether and in what order basic inference steps are taken. We provide a high-level fra mework that clearly differentiates between information needed for cont rolling propagation versus that needed for the logical semantics of complex constraints composed from primitive ones. We argue for the appropriaten ess of our controlled propagation framework by showing that it captures the underlying principles of manually designed propagation algo rithms, such as literal watching for unit clause propagation and the lexi cographic ordering constraint. We provide an implementation and benchm ark results that demonstrate the practicality and efficiency of our frame work.

In this short paper we present a linear constraint solver for the UniCalc system, an environment for reliable solution of mathematical modeling problems.

We discuss here constraint programming (CP) by using a proof-theoretic perspective. To this end we identify three levels of abstraction. Each level sheds light on the essence of CP. In particular, the highest level allows us to bring CP closer to the computation as deduction paradigm. At the middle level we can explain various constraint propagation algorithms. Finally, at the lowest level we can address the issue of automatic generation and optimization of the constraint propagation algorithms.

We present a technique for the automated verification of abstract models of multithreaded programs providing fresh name generation, name mobility, and unbounded control. As high level specification language we adopt here an extension of communication finite-state machines with local variables ranging over an infinite name domain, called TDL programs. Communication machines have been proved very effective for representing communication protocols as well as for representing abstractions of multithreaded software. The verification method that we propose is based on the encoding of TDL programs into a low level language based on multiset rewriting and constraints that can be viewed as an extension of Petri Nets. By means of this encoding, the symbolic verification procedure developed for the low level language in our previous work can now be applied to TDL programs. Furthermore, the encoding allows us to isolate a decidable class of verification problems for TDL programs that still provide fresh name generation, name mobility, and unbounded control. Our syntactic restrictions are in fact defined on the internal structure of threads: In order to obtain a complete and terminating method, threads are only allowed to have at most one local variable (ranging over an infinite domain of names).

Combining a set of existing constraint solvers into an integ rated system of cooperating solvers is a useful and economic principle to solve hybrid constraint problems. In this paper we show that this approach can also be used to integrate differ ent language paradigms into a unified framework. Furthermore, we study the syntacti c, semantic and operational impacts of this idea for the amalgamation of declarative and constraint programming. To appear in Theory and Practice of Logic Programming (TPLP).