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249
Dynamic Epistemic Logic
 Logic, Language, and Information 2, Stanford University, CSLI Publication
, 1997
"... This paper is the result of combining two traditions in formal logic: epistemic logic and dynamic semantics. Dynamic semantics is a branch of formal semantics that is concerned with ..."
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Cited by 43 (1 self)
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This paper is the result of combining two traditions in formal logic: epistemic logic and dynamic semantics. Dynamic semantics is a branch of formal semantics that is concerned with
Computing Anticipatory Systems with Incursion and Hyperincursion
 American Institute of Physics
, 1998
"... An anticipatory system is a system which contains a model of itself and/or of its environment in view of computing its present state as a function of the prediction of the model. With the concepts of incursion and hyperincursion, anticipatory discrete systems can be modelled, simulated and controlle ..."
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Cited by 43 (1 self)
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An anticipatory system is a system which contains a model of itself and/or of its environment in view of computing its present state as a function of the prediction of the model. With the concepts of incursion and hyperincursion, anticipatory discrete systems can be modelled, simulated and controlled. By definition an incursion, an inclusive or implicit recursion, can be written as: x(t+1) = F [..., x(t1), x(t), x(t+1),...] where the value of a variable x(t+1) at time t+1 is a function of this variable at past, present and future times. This is an extension of recursion. Hyperincursion is an incursion with multiple solutions. For example, chaos in the PearlVerhulst map model: x(t+1) = a.x(t).[1 x(t)] is controlled by the following anticipatory incursive model: x(t+1) = a.x(t).[1 x(t+1)] which corresponds to the differential anticipatory equation: dx(t)/dt = a.x(t).[1 x(t+1)] x(t). The main part of this paper deals with the discretisation of differential equation systems of linear and nonlinear oscillators. The nonlinear oscillator is based on the LotkaVolterra equations model. The discretisation is made by incursion. The incursive discrete equation system gives the same stability
A Coinduction Principle for Recursive Data Types Based on Bisimulation
, 1996
"... This paper provides foundations for a reasoning principle (coinduction) for establishing the equality of potentially infinite elements of selfreferencing (or circular) data types. As it is wellknown, such data types not only form the core of the denotational approach to the semantics of programmin ..."
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Cited by 37 (3 self)
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This paper provides foundations for a reasoning principle (coinduction) for establishing the equality of potentially infinite elements of selfreferencing (or circular) data types. As it is wellknown, such data types not only form the core of the denotational approach to the semantics of programming languages [SS71], but also arise explicitly as recursive data types in functional programming languages like Standard ML [MTH90] or Haskell [HPJW92]. In the latter context, the coinduction principle provides a powerful technique for establishing the equality of programs with values in recursive data types (see examples herein and in [Pit94]).
From bisimulation to simulation: coarsest partition problems
 J. Automated Reasoning
, 2003
"... Abstract. The notions of bisimulation and simulation are used for graph reduction and are widely employed in many areas: modal logic, concurrency theory, set theory, formal verification, and so forth. In particular, in the context of formal verification they are used to tackle the socalled stateex ..."
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Abstract. The notions of bisimulation and simulation are used for graph reduction and are widely employed in many areas: modal logic, concurrency theory, set theory, formal verification, and so forth. In particular, in the context of formal verification they are used to tackle the socalled stateexplosion problem. The faster algorithms to compute the maximum bisimulation on a given labeled graph are based on the crucial equivalence between maximum bisimulation and relational coarsest partition problem. As far as simulation is concerned, many algorithms have been proposed that turn out to be relatively inexpensive in terms of either time or space. In this paper we first revisit the state of the art about bisimulation and simulation, pointing out the analogies and differences between the two problems. Then, we propose a generalization of the relational coarsest partition problem, which is equivalent to the simulation problem. Finally, we present an algorithm that exploits such a characterization and improves on previously proposed algorithms for simulation. Key words: bisimulation, simulation, partition refinement problems. 1.
Distributivity for Endofunctors, Pointed and CoPointed Endofunctors, Monads and Comonads
, 2000
"... We generalise the notion of a distributive law between a monad and a comonad to consider weakened structures such as pointed or copointed endofunctors, or endofunctors. We investigate EilenbergMoore and Kleisli constructions for each of these possibilities. Then we consider two applications of the ..."
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Cited by 31 (1 self)
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We generalise the notion of a distributive law between a monad and a comonad to consider weakened structures such as pointed or copointed endofunctors, or endofunctors. We investigate EilenbergMoore and Kleisli constructions for each of these possibilities. Then we consider two applications of these weakened notions of distributivity in detail. We characterise Turi and Plotkin's model of GSOS as a distributive law of a monad over a copointed endofunctor, and we analyse generalised coiteration and coalgebraic coinduction \upto" in terms of a distributive law of the underlying pointed endofunctor of a monad over an endofunctor. 1 Work supported by Esprit Working Group \Types", MURST'99 Con. \Sistemi Formali. .." grant. 2 This work is supported by EPSRC grants GR/J84205: Frameworks for programming language semantics and logic and GR/M56333: The structure of programming languages : syntax and semantics, and British Council grant 747 FCS R34807: Data and program renement using alg...
Features and Formulae
, 1991
"... This paper shows how these structures can be axiomatized in a decidable class of firstorder logic, which can also be used to express constraints on these structures. Desirable properties, such as compactness and decidability, follow directly. Moreover, additional types of feature values, such as &q ..."
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This paper shows how these structures can be axiomatized in a decidable class of firstorder logic, which can also be used to express constraints on these structures. Desirable properties, such as compactness and decidability, follow directly. Moreover, additional types of feature values, such as "setvalued" features, can be incorporated into the system simply by axiomatizing their properties
A Cook’s tour of the finitary nonwellfounded sets
 Invited Lecture at BCTCS
, 1988
"... It is a great pleasure to contribute this paper to a birthday volume for Dov. Dov and I arrived at imperial College at around the same time, and soon he, Tom Maibaum and I were embarked on a joint project, the Handbook of Logic in Computer Science. We obtained a generous advance from Oxford Universi ..."
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Cited by 28 (1 self)
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It is a great pleasure to contribute this paper to a birthday volume for Dov. Dov and I arrived at imperial College at around the same time, and soon he, Tom Maibaum and I were embarked on a joint project, the Handbook of Logic in Computer Science. We obtained a generous advance from Oxford University Press, and a grant from the Alvey Programme, which allowed us to develop the Handbook in a rather unique, interactive way. We held regular meetings at Cosener’s House in Abingdon (a facility run by what was then the U.K. Science and Engineering Research Council), at which contributors would present their ideas and draft material for their chapters for discussion and criticism. Ideas for new chapters and the balance of the volumes were also discussed. Those were a remarkable series of meetings — a veritable education in themselves. I must confess that during this long process, I did occasionally wonder if it would ever terminate.... But the record shows that five handsome volumes were produced [6]. Moreover, I believe that the Handbook has proved to be a really valuable resource for students and researchers. It has been used as the basis for a number of summer schools. Many of the chapters have become standard references for their topics. In a field with rapidly changing fashions, most of the material has stood the test of time — thus
On the Combination of Symbolic Constraints, Solution Domains, and Constraint Solvers
 In Proceedings of the First International Conference on Principles and Practice of Constraint Programming
"... When combining languages for symbolic constraints, one is typically faced with the problem of how to treat "mixed" constraints. The two main problems are (1) how to define a combined solution structure over which these constraints are to be solved, and (2) how to combine the constraint sol ..."
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When combining languages for symbolic constraints, one is typically faced with the problem of how to treat "mixed" constraints. The two main problems are (1) how to define a combined solution structure over which these constraints are to be solved, and (2) how to combine the constraint solving methods for pure constraints into one for mixed constraints. The paper introduces the notion of a "free amalgamated product" as a possible solution to the first problem. Subsequently, we define socalled simplycombinable structures (SCstructures). For SCstructures over disjoint signatures, a canonical amalgamation construction exists, which for the subclass of strong SCstructures yields the free amalgamated product. The combination technique of [BS92, BaS94a] can be used to combine constraint solvers for (strong) SCstructures over disjoint signatures into a solver for their (free) amalgamated product. In addition to term algebras modulo equational theories, the class of SCstru...
Back and forth bisimulations
 Computer Science Report CS R9021, Centrum voor Wiskunde en Informatica
, 1990
"... This paper is concerned with bisimulation relations which do not only require related agents to simulate each others behavior in the direction of the arrows, but also to simulate each other when going back in history. First it is demonstrated that the back and forth variant of strong bisimulation le ..."
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Cited by 26 (3 self)
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This paper is concerned with bisimulation relations which do not only require related agents to simulate each others behavior in the direction of the arrows, but also to simulate each other when going back in history. First it is demonstrated that the back and forth variant of strong bisimulation leads to the same equivalence as the ordinary notion of strong bisimulation. Then it is shown that the back and forth variant of Milner's observation equivalence is different from (and finer than) observation equivalence. In fact we prove that it coincides with the branching bisimulation equivalence of Van Glabbeek & Weijland. Also the back and forth variants of branching, ~ and delay bisimulation lead to branching bisimulation equivalence. The notion of back and forth bisimulation moreover leads to characterizations of branching bisimulation in terms of abstraction homomorphisms and in terms of HencessyMilner logic with backward modalities. In our view these results support the claim that branching bisimulation is a natural and important notion. The notion of bisimulation relation has been introduced by PARK [18]. It leads to an equivalence on labelled transition systems which, in case image finiteness is assumed, coincides with the strong equivalence of ~IILNER [12]. The great importance and usefulness of bisimulalions