A completeness result for the simply typed -calculus

In this paper, we define a realizability semantics for the simply typed λμ-calculus. We show that, if a term is typable, then it inhabits the interpretation of its type. This result serves to give characterizations of the computational behavior of some closed typed terms. We also prove a completeness result of our realizability semantics using a particular term model.     

Capturing k-ary existential second order logic with k-ary inclusion–exclusion logic

In this paper we analyze k-ary inclusion–exclusion logic, INEX[k], which is obtained by extending first order logic with k-ary inclusion and exclusion atoms. We show that every formula of INEX[k] can be expressed with a formula of k-ary existential second order logic, ESO[k]. Conversely, every formula of ESO[k] with at most k-ary free relation variables can be expressed with a formula of INEX[k]. From this it follows that, on the level of sentences, INEX[k] captures the expressive power of ESO[k].We also introduce several useful operators that can be expressed in INEX[k]. In particular, we define inclusion and exclusion quantifiers and so-called term value preserving disjunction which is essential for the proofs of the main results in this paper. Furthermore, we present a novel method of relativization for team semantics and analyze the duality of inclusion and exclusion atoms.     

Exhibiting Wide Families of Maximal Intermediate Propositional Logics with the Disjunction Property

We provide results allowing to state, by the simple inspection of suitable classes of posets (propositional Kripke frames), that the corresponding intermediate propositional logics are maximal among the ones which satisfy the disjunction property. Starting from these results, we directly exhibit, without using the axiom of choice, the Kripke frames semantics of 2^No maximal intermediate propositional logics with the disjunction property. This improves previous evaluations, giving rise to the same conclusion but made with an essential use of the axiom of choice, of the cardinality of the set of the maximal intermediate propositional logics with the disjunction property. Mathematics Subject Classification: 03B55, 03C90.     

A model of the executive's decision processes in new product development

This paper introduces the concept of fuzziness to deal quantitatively with the imprecision of the meaning of the executive's judgment stated in a natural language and presents a model of the executive's decision processes for the new product introduction which contain fuzzy-2 states, fuzzy-2 information systems, fuzzy-2 information signals, fuzzy-2 strategy are presented. The committee decision problem under fuzzy-2 constraints is dealt with.     

Some primitives for the portable programming of array and vector processors

A high-level language for array and vector processors is analyzed by the methods of denotational semantics. The analysis leads to the identification of a set of primitives suitable for the portable programming of array and vector processors. Discussion of the primitives includes consideration of the efficiency with which they may be implemented on different machines, and their possible application to portable programming, the design of intermeiate languages, and the design of future array and vector processors.     

Team decision theory and integral equations

The coordination of decisions under uncertainty in a team leads to optimality conditions that are integral equations. A specific example of a two-division firm is developed to illustrate these conditions. Numerical imbedding techniques are used to solve the firm's decision problem. Extensions toward more general techniques and applications are indicated.     

Sémantique de type Kripke d'un système logique basé sur un ensemble ordonné fini

In order to modelize the reasoning of intelligent agents represented by a poset T, H. Rasiowa introduced logic systems called “Approximation Logics”. In these systems the use of a set of constants constitutes a fundamental tool. We have introduced in [8] a logic system called without this kind of constants but limited to the case that T is a finite poset. We have proved a completeness result for this system w.r.t. an algebraic semantics. We introduce in this paper a Kripke‐style semantics for a subsystem of for which there existes a deduction theorem. The set of “possible worldsr is enriched by a family of functions indexed by the elements of T and satisfying some conditions. We prove a completeness result for system with respect to this Kripke semantics and define a finite Kripke structure that characterizes the propositional fragment of logic . We introduce a reational semantics (found by E. Orlowska) which has the advantage to allow an interpretation of the propositionnal logic using only binary relations. We treat also the computational complexity of the satisfiability problem of the propositional fragment of logic .     

Negation and partial axiomatizations of dependence and independence logic revisited

In this paper, we axiomatize the negatable consequences in dependence and independence logic by extending the systems of natural deduction of the logics given in [22] and [11]. We prove a characterization theorem for negatable formulas in independence logic and negatable sentences in dependence logic, and identify an interesting class of formulas that are negatable in independence logic. Dependence and independence atoms, first-order formulas belong to this class. We also demonstrate our extended system of independence logic by giving explicit derivations for Armstrong's Axioms and the Geiger-Paz-Pearl axioms of dependence and independence atoms.     

Coupling ant colony systems with strong local searches

Ant colony system is a well known metaheuristic framework, and many efficient algorithms for different combinatorial optimization problems have been derived from this general framework. In this paper some directions for improving the original framework when a strong local search routine is available, are identified. In particular, some modifications able to speed up the method and make it competitive on large problem instances, on which the original framework tends to be weaker, are described. The resulting framework, called Enhanced Ant Colony System is tested on three well-known combinatorial optimization problems arising in the transportation field. Many new best known solutions are retrieved for the benchmarks available for these optimization problems.