We propose a tableau-like decision procedure for deciding the satisfiability of set-theoretical formulae with restricted universal quantifiers and the powerset operator. Our result apply to a rather large class of set theories. The procedure we define can be used as a subroutine to decide the same class of formulae both in Set Theory and in non well-founded set theories, since we assume neither...

The recent theory of plausible and paradoxical reasoning (DSmT) developed by the authors appears to be a nice promising theoretical tools to solve many information fusion problems where the Shafer’s model cannot be used due to the intrinsic paradoxical nature of the elements of the frame of discernment and where a strong internal conflict between sources arises. The main idea of DSmT is to work...

Innnite behavior of nondeterministic nite state automata running over innnite trees or more generally over elements of an arbitrary algebraic structure is characterized by a calculus of xed point terms interpreted in powerset algebras. These terms involve the least and greatest xed point operators and disjunction as the only logical operation. A tight correspondence is established between a hie...

We present the PowerSetViewer visualization system for the lattice-based mining of powersets. Searching for items within the powerset of a universe occurs in many large dataset knowledge discovery contexts. Using a spatial layout based on a powerset provides a unified visual framework at three different levels: data mining on the filtered dataset, browsing the entire dataset, and comparing mult...

We present a determinization construction for weighted tree automata using factorizations. Among others, this result subsumes a previous result for determinization of weighted string automata using factorizations (Kirsten and Mäurer, 2005) and two previous results for weighted tree automata, one of them not using factorizations (Borchardt, 2004) and one of them restricted to nonrecursive automa...

In this paper, we study the structure of underlying automata based constructions for solving the LTL realizability problem. We show how to reduce the LTL realizability problem to a game with an observer which checks that the game visits a bounded number of times accepting states of a universal co-Büchi word automaton. We show that such an observer can be made deterministic and that this determi...

domains (§3.3) are often complete lattices, i.e., algebras over partially ordered sets. We recall in this section the fundamental notions of lattice theory, which are the basis for the soundness of over-approximations of reachable state sets computed by abstract interpretation methods. For further details and proofs we refer to textbooks on lattice theory [DP90] and static analysis [NNH05]. Fro...

The nested relational algebra is often inadequate as a tool to handle nested relations, since several important queries, such as transitive closure, cannot expressed by it. On the other hand, the powerset algebra does allow the expression of transitive closure, but in a too expensive way. Therefore, we consider various other extensions to the nested algebra, such as least tixpoint and programmi...