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Expressivity of coalgebraic modal logic: The limits and beyond
 IN FOUNDATIONS OF SOFTWARE SCIENCE AND COMPUTATION STRUCTURES, VOLUME 3441 OF LNCS
, 2005
"... Modal logic has a good claim to being the logic of choice for describing the reactive behaviour of systems modeled as coalgebras. Logics with modal operators obtained from socalled predicate liftings have been shown to be invariant under behavioral equivalence. Expressivity results stating that, c ..."
Abstract

Cited by 39 (13 self)
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Modal logic has a good claim to being the logic of choice for describing the reactive behaviour of systems modeled as coalgebras. Logics with modal operators obtained from socalled predicate liftings have been shown to be invariant under behavioral equivalence. Expressivity results stating that, conversely, logically indistinguishable states are behaviorally equivalent depend on the existence of separating sets of predicate liftings for the signature functor at hand. Here, we provide a classification result for predicate liftings which leads to an easy criterion for the existence of such separating sets, and we give simple examples of functors that fail to admit expressive normal or monotone modal logics, respectively, or in fact an expressive (unary) modal logic at all. We then move on to polyadic modal logic, where modal operators may take more than one argument formula. We show that every accessible functor admits an expressive polyadic modal logic. Moreover, expressive polyadic modal logics are, unlike unary modal logics, compositional.
Coalgebraic Symbolic Semantics
"... The operational semantics of interactive systems is usually described by labeled transition systems. Abstract semantics (that is defined in terms of bisimilarity) is characterized by the final morphism in some category of coalgebras. Since the behaviour of interactive systems is for many reasons in ..."
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Cited by 2 (1 self)
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The operational semantics of interactive systems is usually described by labeled transition systems. Abstract semantics (that is defined in terms of bisimilarity) is characterized by the final morphism in some category of coalgebras. Since the behaviour of interactive systems is for many reasons infinite, symbolic semantics were introduced as a mean to define smaller, possibly finite, transition systems, by employing symbolic actions and avoiding some sources of infiniteness. Unfortunately, symbolic bisimilarity has a different “shape” with respect to ordinary bisimilarity, and thus the standard coalgebraic characterization does not work. In this paper, we introduce its coalgebraic models.
Open Multiparty Interaction ⋆
"... Abstract. We present the linkcalculus, a process calculus based on interactions that are multiparty, i.e., that may involve more than two processes and are open, i.e., the number of involved processes is not fixed or known a priori. Communications are seen as chains of links, that record the source ..."
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Abstract. We present the linkcalculus, a process calculus based on interactions that are multiparty, i.e., that may involve more than two processes and are open, i.e., the number of involved processes is not fixed or known a priori. Communications are seen as chains of links, that record the source and the target ends of each hop of interactions. The semantics of our calculus mildly extends the one of CCS in the version without message passing, and the one of πcalculus in the full version. Cardelli and Gordon’s Mobile Ambients, whose movement interactions we show to be inherently open multiparty, is encoded in our calculus in a natural way, thus providing an illustrative example of its expressiveness.