Reasoning about Unreliable Actions

We analyse the philosopher Davidson's semantics of actions, using a strongly typed logic with contexts given by sets of partial equations between the outcomes of actions. This provides a perspicuous and elegant treatment of reasoning about action, analogous to Reiter's work on artificial intelligence. We define a sequent calculus for this logic, prove cut elimination, and give a semantics based on fibrations over partial cartesian categories: we give a structure theory for such fibrations. The existence of lax comma objects is necessary for the proof of cut elimination, and we give conditions on the domain fibration of a partial cartesian category for such comma objects to exist

Coalescent tree based functional representations for some Feynman-Kac particle models

We design a theoretic tree-based functional representation of a class of Feynman-Kac particle distributions, including an extension of the Wick product formula to interacting particle systems. These weak expansions rely on an original combinatorial, and permutation group analysis of a special class of forests. They provide refined non asymptotic propagation of chaos type properties, as well as sharp \LL\_p-mean error bounds, and laws of large numbers for $U$-statistics. Applications to particle interpretations of the top eigenvalues, and the ground states of Schr\"{o}dinger semigroups are also discussed

Formula dependent model reduction through elimination of invisible transitions for checking fragments of CTL

We present a reduction algorithm which reduces Kripke structures by eliminating transitions from the model which do not affect the visible components of the model. These are exactly the variables contained in the specification formula. The reduction algorithm preserves the truth of special CTL formulae. In contrast to formula-dependent reduction algorithms presented so far, which are mostly computationally expensive, our algorithm needs only one pass through the reachable states of the model. Nevertheless, preliminary results show that models are reduced considerably, which is plausible because, in general, the number of visible components of a reactive system is small compared to the number of internal components