In the first section of this paper we show that iΠ1 ≡ W¬¬lΠ1. In the second section of the paper, we show that for equivalence of forcing and satisfaction of Πm-formulas in a linear Kripke model deciding ∆0-formulas, it is necessary and sufficient that the model be Σm-elementary. This implies that if a linear Kripke model forces PEMprenex, then it forces PEM . We also show that, for each n > 1,...

Dynamic programs, or fixpoint iteration schemes, are useful for solving many problems on state spaces, including model checking on Kripke structures (“verification”), computing shortest paths on weighted graphs (“optimization”), computing the value of games played on game graphs (“control”). For Kripke structures, a rich fixpoint theory is available in the form of the μ-calculus. Yet few connec...

In their 1936 seminal paper, Birkhoff and von Neumann made the proposal of a non-classical logic for quantum mechanics founded on the basic lattice-order properties of all closed subspaces of a Hilbert space. These lattice-order properties are captured in the orthomodular lattice structure, characterized by a weak form of distributivity called orthomodular law. This “weak distributivity”, which...

A social network service is a platform to build social relations among people sharing similar interests and activities. The underlying structure of a social networks service is the social graph, where nodes represent users and the arcs represent the users’ social links and other kind of connections. One important concern in social networks is privacy: what others are (not) allowed to know about...

We propose a new representation formalism for the multimodal logic Km, in which labels replace modalities in all formulas and subformulas: Possibility operators are represented by constants and necessity operators by anonymous variables. Our formalism gives rise to a new definition of models which can be much more compactly represented than traditional Kripke models. We describe how a Km formul...

We give a procedure for translating geometric Kripke frame axioms into structural hypersequent rules for the corresponding intermediate logics in Int/Geo that admit weakening, contraction and in some cases, cut. We give a procedure for translating labelled sequents in the corresponding logic to hypersequents that share the same linear models (which correspond to Gödel-Dummett logic). We prove t...

Dynamic programs, or xpoint iteration schemes, are useful for solving many problems on state spaces, including model checking on Kripke structures (\veri cation"), computing shortest paths on weighted graphs (\optimization"), computing the value of games played on game graphs (\control"). For Kripke structures, a rich xpoint theory is available in the form of the -calculus. Yet few connections ...

this paper proposes a new mathematical model for the integrated procurement-production-distribution problem of a fuzzy mixed integer linear programming (fmilp) type. considering the uncertainty in real problems, a number of parameters such as demand, capacity, and cost where their values are not available or known precisely, have been considered as trapezoidal fuzzy numbers. to solve fuzzy mixe...

ion reduces the state space by removing irrelevant features of a Kripke structure. Given a Kripke structure K, an abstraction is a Kripke structure K̂ such that K̂ is significantly smaller than K, and K̂ preserves a useful class of specifications for K. Consequently, the expensive task of model checking K can be reduced to the more feasible task of model checking K̂. We know from above that in orde...