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...

Kripke frames (and models) provide a suitable semantics for sub-classical logics; for example Intuitionistic Logic (of Brouwer and Heyting) axiomatizes the reflexive and transitive Kripke frames (with persistent satisfaction relations), and the Basic Logic (of Visser) axiomatizes transitive Kripke frames (with persistent satisfaction relations). Here, we investigate whether Kripke frames/models...

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 ...

In this paper a method to construct Kripke models for subtheories of constructive set theory is introduced that uses constructions from classical model theory such as constructible sets and generic extensions. Under the main construction all axioms except the collection axioms can be shown to hold in the constructed Kripke model. It is shown that by carefully choosing the classical models vario...

We present a variant of Kripke models to model knowledge of large numbers, applicable to cryptographic protocols. Our Epistemic Crypto Logic is a variant of Dynamic Epistemic Logic to describe communication and computation in a multi-agent setting. It is interpreted on register models which efficiently encode larger Kripke models. As an example we formalize the well-known Diffie-Hellman key exc...

The material presented here is an exposition of an application of logical relations to the problem of full abstraction for PCF. The point is to see Kripke logical relations as introduced by Jung and Tiuryn in [5] and used by O'Hearn and Riecke in [6] to give a logical characterization of sequentiality, within the mainstream of the classical notion of logical relations. The main di erence with r...

We investigate the relation between intermediate predicate logics based on countable linear Kripke frames with constant domains and Gödel logics. We show that for any such Kripke frame there is a Gödel logic which coincides with the logic defined by this Kripke frame on constant domains and vice versa. This allows us to transfer several recent results on Gödel logics to logics based on countabl...

Computational systems are often represented by means of Kripke structures, and related using simulations. We propose rewriting logic as a flexible and executable framework in which to formally specify these mathematical models, and introduce a particular and elegant way of representing simulations in it: theoroidal maps. A categorical viewpoint is very natural in the study of these structures a...