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 ...

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...

Quantum Kripke frames and other related kinds of Kripke frames are introduced. The inner structures of these Kripke frames are studied in detail, and many of them turn out to form nice geometries. To be precise, geometric frames, which are more general than quantum Kripke frames, correspond to projective geometries with a pure polarity; and quantum Kripke frames correspond to irreducible Hilber...

We propose a notion of the Kripke-style model for intersection logic. Using game interpretation, we prove soundness and completeness proposed semantics. In other words, formula is provable (a type inhabited) if only it forced in every model. As by-product, obtain another proof normalization Barendregt–Coppo–Dezani assignment system.

Kripke structures have been proposed as a semantic basis for modal logics of necessity and possibility. They consist of a set of states, informally interpreted as "possible worlds", and a binary accessibility relation between states. The primitive notion of a possible world in this context seems highly intuitive, since necessity can be interpreted as "truth in all possible worlds", and possibil...

The objectives of this research are to further investigate the foundations for novel SMT and SAT-based bounded model checking (BMC) algorithms for real-time and multi-agent systems. A major part of the research will involve the development of SMT-based BMC methods for standard Kripke structures, extended Kripke structures, and for different kinds of interpreted systems for different kinds of te...