The monadic second-order quantiier alternation hierarchy over the class of nite graphs is shown to be strict. The proof is based on automata theoretic ideas and starts from a restricted class of graph-like structures, namely nite two-dimensional grids. Considering grids where the width is a function of the height, we prove that the diierence between the levels k +1 and k of the monadic hierarch...

We compare time needed for understanding di erent types of quanti ers. In the rst study, we show that the distinction between quanti ers recognized by nite-automata and push-down automata is psychologically relevant. In the second study, we compare comprehension of push-down quanti ers in universes with randomly placed objects and those where objects were ordered in some speci c way simplifying...

Diagrams have many uses in mathematics, one of the most ambitious of which is as a form of proof. The domain we consider is real analysis, where quanti cation issues are subtle but crucial. Computers o er new possibilities in diagrammatic reasoning, one of which is animation. Here we develop animated rules as a solution to problems of quanti cation. We show a simple application of this to const...

Queries containing universal quanti cation are used in many applications, including business intelligence applications and in particular data mining. We present a comprehensive survey of the structure and performance of algorithms for universal quanti cation. We introduce a framework that results in a complete classi cation of input data for universal quanti cation. Then we go on to identify th...

vascular tone as a tunable parameter to improve drug delivery. Philippe Martinive, Julie DeWever, Caroline Bouzin, *Christine Baudelet, Pierre Sonveaux, Vincent Grégoire, *Bernard Gallez and Olivier Feron. Unit of Pharmacology and Therapeutics (FATH 5349), *Laboratory of Biomedical Magnetic Resonance; Center for Molecular Imaging and Experimental Radiotherapy, University of Louvain (UCL) Medica...

Van Lambalgen (1991) proposed a translation from a language containing a generalized quanti er Q into a rst-order language enriched with a family of predicates R i , for every arity i (or an in nitary predicate R) which takes Qx (x; y 1 ; : : : ; y n ) to 8x(R(x; y 1 ; : : : ; y n ) ! (x;y 1 ; : : : ; y n )) (y 1 ; : : : ; y n are precisely the free variables of Qx ). The logic of Q (without or...

Games David Janin1 and Jerzy Mar inkowski2 1 Laboratoire Bordelais de Re her he en Informatique, Universit e de Bordeaux I, 351, ours de la Lib eration, 33 405 Talen e edex, janin labri.u-bordeaux.fr 2 Institute of Computer S ien e, University of Wro law, Przesmy kiego 20, 51151 Wro law, Poland, jma t s.uni.wro .pl Abstra t. In 1974 R. Fagin proved that properties of stru tures whi h are in NP ...

The aim of this paper is to introduce a new formalism for multi-agent systems that captures (true) concurrency and independence. We begin describing a complete and decidable propositional multi-modal logic. The language, similar to Propositional Dynamic Logic in many aspects, di ers from usual modal logic: modal operators are non-atomic (they are built out of basic actions) and capture concurre...

Restricted quanti cation poses a serious and under-appreciated challenge for non-classical approaches to both vagueness and the semantic paradoxes. It is tempting to explain All A are B as For all x, if x is A then x is B ; but in the non-classical logics typically used in dealing with vagueness and the semantic paradoxes (even those where 'if ... then' is a special conditional not de nable in ...

Recently there has been a lot of activity in algorithms that work over real closed elds, and that perform such calculations as quanti er elimination or computing connected components of semi-algebraic sets. A cornerstone of this work is a symbolic sign determination algorithm due to Ben-Or, Kozen and Reif [2]. In this paper we describe a new sign determination method based on the earlier algori...