3 Shallow embedding of HyperCTL* 3 3.1 Kripke structures and paths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 3.2 Shallow representations of formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 3.3 Reasoning rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 3.4 More derived operators . . . . . . . . . . . . . . . . . . . ....

The interpretation of propositional dynamic logic (PDL) through Kripke models requires the relations constituting the interpreting Kripke model to closely observe the syntax of the modal operators. This poses a significant challenge for an interpretation of PDL through stochastic Kripke models, because the programs’ operations do not always have a natural counterpart in the set of stochastic re...

Given the “possible worlds” interpretation of modal logic, a refinement of a Kripke model is another Kripke model in which an agent has ruled out some possible worlds to be consistent with some new information. The refinements of a finite Kripke model have been shown to correspond to the results of applying arbitrary action models to the Kripke model [10]. Refinement modal logics add quantifier...

We present Dynamic Epistemic Temporal Logic, a framework for reasoning about operations on multi-agent Kripke models that contain a designated temporal relation. These operations are natural extensions of the well-known “action models” from Dynamic Epistemic Logic. Our “temporal action models” may be used to define a number of informational actions that can modify the “objective” temporal struc...

Logics of announcements are logics of knowledge to reason about agents that communicate by broadcasting interpreted messages. These logics are typically given a semantics in terms of updatable Kripke structures, which tend to be abstract. We revisit the semantics of logics of announcements and develop a concrete semantics using runs and systems. The advantage is that we can devise models that c...

Ordinary Kripke models are not reactive. When we evaluate (test/measure) a formula A at a model m, the model does not react, respond or change while we evaluate. The model is static and unchanged. This paper studies Kripke models which react to the evaluation process and change themselves during the process. This is reminiscent of game theoretic semantics where the two sides react to each other...

We show that given a finite, transitive and reflexive Kripke model 〈W,4, J·K〉 and w ∈ W , the property of being simulated by w (i.e., lying on the image of a literalpreserving relation satisfying the ‘forth’ condition of bisimulation) is modally undefinable within the class of S4 Kripke models. Note the contrast to the fact that lying in the image of w under a bisimulation is definable in the s...

We consider a class of Kripke Structures in which the atomic propositions are events. This enables us to represent worlds as sets of events and the transition and satisfaction relations of Kripke structures as the subset and membership relations on sets. We use this class, called event Kripke structures, to model concurrency. The obvious semantics for these structures is a true concurrency sema...

Model checking [3] is a very popular paradigm for automatic verification of properties of finite state systems like those defined by circuits or communication protocols. A system is interpreted as a finite state labeled transition system or equivalently as a finite Kripke structure. If sys contains k concurrent components, each with m states, then the Kripke structure described by sys may have ...