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This paper proposes to use prime implicants and prime implicates normal forms to represent belief sets. This representation is used, on the one hand, to define syntactical versions of belief change operators that also satisfy the rationality postulates but present better complexity properties than those proposed in the literature and, on the other hand, to propose a new minimal distance that adopts as a minimal belief unit a "fact", defined as a prime implicate of the belief set, instead of the usually adopted Hamming distance, i.e., the number of propositional symbols on which the models differ. Some experiments are also presented that show that this new minimal distance allows to define belief change operators that usually preserve more information of the original belief set.

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We extend hierarchical task network planning with task insertion (TIHTN) by introducing state constraints, called TIHTNS. We show that just as for TIHTN planning, all solutions of the TIHTNS planning problem can be obtained by acyclic decomposition and task insertion, entailing that its planexistence problem is decidable without any restriction on decomposition methods. We also prove that the extension by state constraints does not increase the complexity of the plan-existence problem, which stays 2-NEXPTIME-complete, based on an acyclic progression operator. In addition, we show that TIHTNS planning covers not only the original TIHTN planning but also hierarchyrelaxed hierarchical goal network planning.

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Mechanism Design aims at defining mechanisms that satisfy a predefined set of properties, and Auction Mechanisms are of foremost importance. Core properties of mechanisms, such as strategy-proofness or budget-balance, involve: (i) complex strategic concepts such as Nash equilibria, (ii) quantitative aspects such as utilities, and often (iii) imperfect information,with agents’ private valuations. We demonstrate that Strategy Logic provides a formal framework fit to model mechanisms, express such properties, and verify them. To do so, we consider a quantitative and epistemic variant of Strategy Logic. We first show how to express the implementation of social choice functions. Second, we show how fundamental mechanism properties can be expressed as logical formulas,and thus evaluated by model checking. Finally, we prove that model checking for this particular variant of Strategy Logic can be done in polynomial space.