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...

kripke bas proposed a number of counteretxamples to the classic thesis, which ays that the class of necmary fropositions roincidn with the cla1ss of a priori ones. these counteretxamples involve some necessary a posten'ori trutbs as well as contingent a priori ones. om cfbis exmnplu far the loller is the 1ta11dard metre example. in thi1 paper, after presenting a brief sketch of kripke&apos...

Graded modal logic (GML) was originally presented by Kit Fine (1972) to make the modal analogue to counting quantifiers explicit. A graded modal formula ♦k is true at a state w in a Kripke model if there are at least k successor states of w where φ is true. One open problem in GML is to show a Goldblatt-Thomason theorem for it. See M. De Rijke’s notes (2000). Recently, Katsuhiko Sano and Minghu...

Alternative proofs for Guaspari and Solovay's completeness theorems for R are presented. R is an extension of the provability logic L and was developed in order to study the formal properties of the provability predicate of PA occurring in sentences that may contain connectives for witness comparison. (The primary example of sentences involving witness comparison is the Rosser sentence.) In thi...