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On the Foundations of Final Coalgebra Semantics: nonwellfounded sets, partial orders, metric spaces
, 1998
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Duality for Modal µLogics
 Theoret. Comput. Sci
, 1998
"... 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 infini ..."
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Cited by 4 (2 self)
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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 Stonetype 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 negationfree case, (2) a presentation of the algebraic models of the logics in a syntaxfree manner, (3) an explicit duality for the case of the finitary calculus, missing in [3], and (4) a completeness result for the (negationfree or not) finitary modal calculus in Kripke semantics. The special case of completeness for the...
The Semantics Of Fair Recursion With Divergence
, 1996
"... 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 f ..."
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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...
A Fixpoint Approach to Finite Delay and Fairness
, 1998
"... We introduce a language SCCS oe with a restriction operation on recursion. This involves a relativization of processes to formal environments which can be seen as a simple typing of processes. The fragment SCCS ¯ of SCCS oe drops explicit typing by introducing both least and greatest fixpoint operat ..."
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We introduce a language SCCS oe with a restriction operation on recursion. This involves a relativization of processes to formal environments which can be seen as a simple typing of processes. The fragment SCCS ¯ of SCCS oe drops explicit typing by introducing both least and greatest fixpoint operators. SCCS ¯ is expressive enough so that both SCCS and the Finite Delay Calculus of Milner [21] can be regarded as subcalculi. The delay operators can be defined by "P := ¯x:1x + P and ffi P := x:1x+P . Syntactic full abstractness results are proven for fortification and fair bisimilarity. We propose a collection of algebraic laws and induction rules (which imply Milner's fixpoint rule in [21]) and prove the theory sound for fair bisimilarity and fortification. The theory is strong enough so that it can prove all the laws for the delay operators taken as axioms in the Finite Delay Calculus of Milner. Finally, we sketch a semantics for SCCS oe that is fully abstract for fair bisimilarity and...