Abstract not found

The modal -calculi are extensions of propositional modal logics with least and greatest fixpoint operators. They have significant expressive power, being capable to encode properly temporal notions alien to standard modal systems. We focus here on Kozen's [20] -calculi, both finitary and infinitary. Based on an extension of the classical modal duality to the case of positive modal algebras that we present, we prove a Stone-type duality for positive modal -calculi which specializes to a duality for the Boolean modal -logics. Thus we extend while also improving on results published by S. Ambler et al. [3]. The main improvements are: (1) extension to the negation-free case, (2) a presentation of the algebraic models of the logics in a syntax-free manner, (3) an explicit duality for the case of the finitary -calculus, missing in [3], and (4) a completeness result for the (negation-free or not) finitary modal -calculus in Kripke semantics. The special case of completeness for the...

We recast Milner's work on SCCSffl, a calculus for finite but unbounded delay based on SCCS, by giving a denotational semantics for admissibility of infinite computations on a bifinite domain K. Using Abramsky's SFP domain D for bisimulation we obtain a fully abstract model in D \Theta K for an operational preorder which generalizes Milner's fortification. Our preorder includes divergence and its restriction to finite behavior corresponds to Abramsky's finitary preorder. By virtue of bifiniteness of D \Theta K we obtain a Stone dual at the level of objects. Since Milner's delay operators ffl and ffi turn out to correspond to the greatest, respectively least, fixed point on K, we consequently enrich SCCS with an additional recursive binding modeled as the greatest fixed point. For the body 1x + p, the new recursive binding imposes finite delay, whereas the ordinary recursion admits infinite, as well as finite, delay of p. We define a notion of admissibility and a denotational semantics...