1. Modeling Games using Probabilistic-Epistemic Processes and Modal Logic

    I introduce a notion of (discrete) probabilistic epistemic process and an associated dynamic-epistemic modal logic. I use them to redefine and analize some notions of game theory: extensive games with imperfect information, perfect recall, mixed strategies, beliefs about strategies, epistemic types, Bayesian belief-revision, rationality and rationalizability, solution concepts.  

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  2. On the Duality of Modal and Equational Logic

    Basic notions of coalgebras and modal logic are reviewed.

    A categorical description of coalgebraic semantics of modal logics is developed.

    This description turns out to dualise algebraic semantics of equational logic as given by Banaschewski and Herrlich in the paper "Subcategories defined by implications" (1976). This gives a precise meaning …

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  3. On the Duality of Observability and Reachability

    Joint work with Rolf Hennicker (University of Munich) and Michel Bidoit (Ecole Normale Sup351rieure de Cachan).

    The properties of a system being "observable" or "fully abstract" (all internal states can be distinguished by an external observer) and of being "reachable" (all internal states are relevant, i.e., can be reached …

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  4. Back To The Future: A Family of DTD Algorithms

    We discuss our work-in-progress on a number of Distributed Termination Detection Algorithms. These algorithms use message histories to construct administrative trees called message futures. These algorithms allow generalized network topologies and support dynamic changes to the network. The performance of these algorithms can be optimized with special information about the …

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  5. Stream calculus

    Exploiting the fact that the set of all streams (infinite sequences of real numbers) carries a final coalgebra structure, a few initial steps towards a coinductive stream calculus are discussed. This involves definitions in terms of behavioural differential equations, methods for solving such equations, and (generalized) nondeterministic representations of such …

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  6. A Generalized Schema for Coinductive Definitions

    For a given behavior type (functor), the carrier of a final coalgebra provides a unique representative for each possible behavior. This property immediately leads to a definition (and proof) principle - called `coiteration' here - for functions from an arbitrary set to this carrier: To define the function's value on a given …

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  7. Combinators for hyperedge replacement graph rewriting

    GS theories are generalizations of Lawvere's algebraic theories having explicit operations of sharing and garbage collection of 'interfaces'. They have been used to give functorial semantics to term graph rewriting and (for the static aspects) to concurrent and mobility calculi (like asynchronous pi-calculus). A higher order extension of them, called …

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