Results 1  10
of
60
Abstract behavior types: A foundation model for components and their composition
 SCIENCE OF COMPUTER PROGRAMMING
, 2003
"... ..."
'One is a Lonely Number': on the logic of communication
, 2002
"... Logic is not just about singleagent notions like reasoning, or zeroagent notions like truth, but also about communication between two or more people. What we tell and ask each other can be just as 'logical' as what we infer in Olympic solitude. We show how such interactive phenomena can be studied ..."
Abstract

Cited by 66 (17 self)
 Add to MetaCart
Logic is not just about singleagent notions like reasoning, or zeroagent notions like truth, but also about communication between two or more people. What we tell and ask each other can be just as 'logical' as what we infer in Olympic solitude. We show how such interactive phenomena can be studied systematically by merging epistemic and dynamic logic.
Coalgebraic modal logic: Soundness, completeness and decidability of local consequence
 Theoret. Comput. Sci
, 2002
"... This paper studies finitary modal logics, interpreted over coalgebras for an endofunctor, and establishes soundness, completeness and decidability results. The logics are studied within the abstract framework of coalgebraic modal logic, which can be instantiated with arbitrary endofunctors on the ca ..."
Abstract

Cited by 51 (24 self)
 Add to MetaCart
This paper studies finitary modal logics, interpreted over coalgebras for an endofunctor, and establishes soundness, completeness and decidability results. The logics are studied within the abstract framework of coalgebraic modal logic, which can be instantiated with arbitrary endofunctors on the category of sets. This is achieved through the use of predicate liftings, which generalise atomic propositions and modal operators from Kripke models to arbitrary coalgebras. Predicate liftings also allow us to use induction along the terminal sequence of the underlying endofunctor as a proof principle. This induction principle is systematically exploited to establish soundness, completeness and decidability of the logics. We believe that this induction principle also opens new ways for reasoning about modal logics: Our proof of completeness does not rely on a canonical model construction, and the proof of the finite model property does not use filtrations. 1
A Hierarchy of Probabilistic System Types
, 2003
"... We study various notions of probabilistic bisimulation from a coalgebraic point of view, accumulating in a hierarchy of probabilistic system types. In general, a natural transformation between two Setfunctors straightforwardly gives rise to a transformation of coalgebras for the respective functors ..."
Abstract

Cited by 37 (6 self)
 Add to MetaCart
We study various notions of probabilistic bisimulation from a coalgebraic point of view, accumulating in a hierarchy of probabilistic system types. In general, a natural transformation between two Setfunctors straightforwardly gives rise to a transformation of coalgebras for the respective functors. This latter transformation preserves homomorphisms and thus bisimulations. For comparison of probabilistic system types we also need reflection of bisimulation. We build the hierarchy of probabilistic systems by exploiting the new result that the transformation also reflects bisimulation in case the natural transformation is componentwise injective and the first functor preserves weak pullbacks. Additionally, we illustrate the correspondence of concrete and coalgebraic bisimulation in the case of general Segalatype systems.
Semantical Principles in the Modal Logic of Coalgebraic
"... Coalgebras for a functor on the category of sets subsume many formulations of the notion of transition system, including labelled transition systems, Kripke models, Kripke frames and many types of automata. This paper presents a multimodal language which is bisimulation invariant and (under a natur ..."
Abstract

Cited by 30 (6 self)
 Add to MetaCart
Coalgebras for a functor on the category of sets subsume many formulations of the notion of transition system, including labelled transition systems, Kripke models, Kripke frames and many types of automata. This paper presents a multimodal language which is bisimulation invariant and (under a natural completeness condition) expressive enough to characterise elements of the underlying state space up to bisimulation. Like Moss' coalgebraic logic, the theory can be applied to an arbitrary signature functor on the category of sets. Also, an upper bound for the size of conjunctions and disjunctions needed to obtain characteristic formulas is given.
A Finite Model Construction For Coalgebraic Modal Logic
"... In recent years, a tight connection has emerged between modal logic on the one hand and coalgebras, understood as generic transition systems, on the other hand. Here, we prove that (finitary) coalgebraic modal logic has the finite model property. This fact not only reproves known completeness result ..."
Abstract

Cited by 24 (16 self)
 Add to MetaCart
In recent years, a tight connection has emerged between modal logic on the one hand and coalgebras, understood as generic transition systems, on the other hand. Here, we prove that (finitary) coalgebraic modal logic has the finite model property. This fact not only reproves known completeness results for coalgebraic modal logic, which we push further by establishing that every coalgebraic modal logic admits a complete axiomatization of rank 1; it also enables us to establish a generic decidability result and a first complexity bound. Examples covered by these general results include, besides standard HennessyMilner logic, graded modal logic and probabilistic modal logic.
Modular construction of modal logics
 Concurrency Theory, CONCUR 04, volume 3170 of Lect. Notes Comput. Sci
, 2004
"... Abstract. We present a modular approach to defining logics for a wide variety of statebased systems. We use coalgebras to model the behaviour of systems, and modal logics to specify behavioural properties of systems. We show that the syntax, semantics and proof systems associated to such logics can ..."
Abstract

Cited by 22 (7 self)
 Add to MetaCart
Abstract. We present a modular approach to defining logics for a wide variety of statebased systems. We use coalgebras to model the behaviour of systems, and modal logics to specify behavioural properties of systems. We show that the syntax, semantics and proof systems associated to such logics can all be derived in a modular way. Moreover, we show that the logics thus obtained inherit soundness, completeness and expressiveness properties from their building blocks. We apply these techniques to derive sound, complete and expressive logics for a wide variety of probabilistic systems. 1
Finality Regained  A Coalgebraic Study of Scottsets and Multisets
 Arch. Math. Logic
, 1999
"... In this paper we study iterated circular multisets in a coalgebraic framework. We will produce two essentially different universes of suchsets. The unisets of the first universe will be shown to be precisely the sets of the Scott universe. The unisets of the second universe will be precisely the ..."
Abstract

Cited by 21 (1 self)
 Add to MetaCart
In this paper we study iterated circular multisets in a coalgebraic framework. We will produce two essentially different universes of suchsets. The unisets of the first universe will be shown to be precisely the sets of the Scott universe. The unisets of the second universe will be precisely the sets of the AFAuniverse. Wewillhave a closer look into the connection of the iterated circular multisets and arbitrary trees. Key words: multiset, nonwellfounded set, Scottuniverse, AFA, coalgebra, modal logic, graded modalities MSC2000 codes: 03B45, 03E65, 03E70, 18A15, 18A22, 18B05, 68Q85 1 Contents 1 Introduction 3 1.1 Multisets on a Given Domain . . . . . . . . . . . . . . . . . . . . 3 1.2 Iterated and Circular Multisets . . . . . . . . . . . . . . . . . . . 6 1.3 Organization of the Paper . . . . . . . . . . . . . . . . . . . . . . 7 2 Prerequisites 8 2.1 Coalgebras and Morphisms . . . . . . . . . . . . . . . . . . . . . 8 2.1.1 A Prototype: Pow . . . . . . . . . . . . . . . ...
Towards a Duality Result in the Modal Logic of Coalgebras
 In Coalgebraic Methods in Computer Science, volume 33 of ENTCS
, 2000
"... This paper forms a step in the development of the recently emerged connection between coalgebra and modal logic. It introduces (backandforth) transformations between coalgebras of simple polynomial functors and certain Boolean algebras with operators (BAOs). Categorically, these transformations ta ..."
Abstract

Cited by 21 (0 self)
 Add to MetaCart
This paper forms a step in the development of the recently emerged connection between coalgebra and modal logic. It introduces (backandforth) transformations between coalgebras of simple polynomial functors and certain Boolean algebras with operators (BAOs). Categorically, these transformations take the form of an adjunction. The BAO associated with a coalgebra can be used for specification, e.g. of classes in objectoriented languages.
Exercises in Coalgebraic Specification
, 1999
"... An introduction to coalgebraic specification is presented via examples. A coalgebraic specification describes a collection of coalgebras satisfying certain assertions. It is thus an axiomatic description of a particular class of mathematical structures. Such specifications are especially suitable fo ..."
Abstract

Cited by 16 (2 self)
 Add to MetaCart
An introduction to coalgebraic specification is presented via examples. A coalgebraic specification describes a collection of coalgebras satisfying certain assertions. It is thus an axiomatic description of a particular class of mathematical structures. Such specifications are especially suitable for statebased dynamical systems in general, and for classes in objectoriented programming languages in particular. This paper will gradually introduce the notions of bisimilarity, invariance, component classes, temporal logic and refinement in a coalgebraic setting. Besides the running example of the coalgebraic specification of (possibly infinite) binary trees, a specification of Peterson's mutual exclusion algorithm is elaborated in detail.