This presentation focuses on the span between two early seminal papers on second-order quantifier elimination on the basis of first-order logic: Heinrich Behmann’s Habilitation thesis Beiträge zur Algebra der Logik, insbesondere zum Entscheidungsproblem (Contributions to the algebra of logic, in particular to the decision problem), published in 1922 as [4], and Wilhelm Ackermann’s Untersuchunge...

In principle, interval constraints provide tight enclosures for the solutions of several types of numerical problem. These include constrained global optimization and the solution of nonlinear systems of equalities or inequalities. Interval constraints finds these enclosures by a combination of propagation and search. The challenge is to extend the “in principle” to problems of practical intere...

The language of propositional logic is sometimes not appropriate to model real-world problems. Therefore, finite set constraints are introduced. A variable of a finite set constraint takes exactly one value out of a given set of values whereas a propositional variable is either true or false. Although the class of real-world problems which can be described using the language of propositional lo...

inventory control problem is one of the problems in decision making and management that contains non-crisp parameters in real world. economic production quantity (epq) model in fuzzy environment has been studied so far by many researchers. one of the main assumptions in all previous researches was neglecting the inventory shortage. in this research, a new multi-item epq model with fuzzy random ...

Arc-consistency algorithms are widely used to simplify Constraint Satisfaction Problems. The new notion of a double-support check is presented to improve the average performance of arc-consistency algorithms. The improvement is that, where possible, consistencychecks are used to find supports for two values, one value in the domain of each variable, which were previously known to be unsupported...

The paper provides a unifying perspective of tree-decomposition algorithms appearing in various automated reasoning areas such as join-tree clustering for constraint-satisfaction and the clique-tree algorithm for probabilistic reasoning. Within this framework, we introduce a new algorithm, called bucket-tree elimination (BTE), that extends Bucket Elimination (BE) to trees, and show that it can ...