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110
Abstract behavior types: A foundation model for components and their composition
- SCIENCE OF COMPUTER PROGRAMMING
, 2003
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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 ..."
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Cited by 73 (25 self)
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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
'One is a Lonely Number': on the logic of communication
, 2002
"... Logic is not just about single-agent notions like reasoning, or zero-agent 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 ..."
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Cited by 73 (18 self)
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Logic is not just about single-agent notions like reasoning, or zero-agent 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.
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 Set-functors straightforwardly gives rise to a transformation of coalgebras for the respective functors ..."
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Cited by 51 (7 self)
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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 Set-functors 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 Segala-type systems.
Dynamic belief revision over multi-agent plausibility models
- Proceedings of LOFT 2006 (7th Conference on Logic and the Foundations of Game and Decision Theory
, 2006
"... In this paper, we develop a notion of doxastic actions, general enough to cover all examples of commu-nication actions and most other belief-changing actions encountered in the literature, but also flexible enough to deal with the issue of (static and dynamic) revision of beliefs. This can be seen a ..."
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Cited by 33 (8 self)
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In this paper, we develop a notion of doxastic actions, general enough to cover all examples of commu-nication actions and most other belief-changing actions encountered in the literature, but also flexible enough to deal with the issue of (static and dynamic) revision of beliefs. This can be seen as a natural extension of the work in [3, 4] on “epistemic actions”, incorporating ideas from the semantics of belief
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 ..."
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Cited by 33 (8 self)
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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.
Presenting Functors by Operations and Equations
, 2006
"... We take the point of view that, if transition systems are coalgebras for a functor T, then an adequate logic for these transition systems should arise from the ‘Stone dual ’ L of T. We show that such a functor always gives rise to an ‘abstract’ adequate logic for T-coalgebras and investigate under ..."
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Cited by 33 (17 self)
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We take the point of view that, if transition systems are coalgebras for a functor T, then an adequate logic for these transition systems should arise from the ‘Stone dual ’ L of T. We show that such a functor always gives rise to an ‘abstract’ adequate logic for T-coalgebras and investigate under which circumstances it gives rise to a ‘concrete ’ such logic, that is, a logic with an inductively defined syntax and proof system. We obtain a result that allows us to prove adequateness of logics uniformly for a large number of different types of transition systems and give some examples of its usefulness.
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 ..."
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Cited by 31 (15 self)
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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 Hennessy-Milner logic, graded modal logic and probabilistic modal logic.
Non-Deterministic Kleene Coalgebras
"... In this paper, we present a systematic way of deriving (1) languages of (generalised) regular expressions, and (2) sound and complete axiomatizations thereof, for a wide variety of systems. This generalizes both the results of Kleene (on regular languages and deterministic finite automata) and Miln ..."
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Cited by 25 (9 self)
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In this paper, we present a systematic way of deriving (1) languages of (generalised) regular expressions, and (2) sound and complete axiomatizations thereof, for a wide variety of systems. This generalizes both the results of Kleene (on regular languages and deterministic finite automata) and Milner (on regular behaviours and finite labelled transition systems), and includes many other systems such as Mealy and Moore machines.
Finality Regained - A Coalgebraic Study of Scott-sets 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 ..."
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Cited by 25 (1 self)
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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 AFA-universe. Wewillhave a closer look into the connection of the iterated circular multisets and arbitrary trees. Key words: multiset, non-wellfounded set, Scott-universe, 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 . . . . . . . . . . . . . . . ...
