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...

Dependently typed programs contain an excessive amount of static terms which are necessary to please the type checker but irrelevant for computation. To separate static and dynamic code, several static analyses and type systems have been put forward. We consider Pfenning’s type theory with irrelevant quantification which is compatible with a type-based notion of equality that respects η-laws. W...

We use relational semantics to evaluate formulas. A Kripke model for L is a tuple M = (JMK , R, J·K) where JMK is a countable, non-empty set of states, R : I −→ P(JMK × JMK) assigns to each i ∈ I an accessibility relation Ri, and J·K : Φ −→ P(JMK) is a valuation, assigning to each atom a set of states. With s ∈ JMK, call Ms = (JMK , R, J·K , s) a pointed Kripke model. The used semantics are sta...

We present a version of separation logic for modular reasoning about concurrent programs with dynamically allocated storable locks and dynamic thread creation. The assertions of the program logic are modelled by a Kripke model over a recursively defined set of worlds and the program logic is proved sound through a Kripke relation to the standard operational semantics. This constitutes an elegan...

This paper develops eecient local model-checking algorithms for expressive fragments of the modal-calculus. The time complexity of our procedures matches that of the best existing global algorithms; however, in contrast to those routines, ours explore a system's state space in a need-driven fashion and do not require its a priori construction. Consequently, our algorithms should perform better ...