Guarded Logics: Algorithms and Bisimulation Von der Fakult¨at fur¨ Mathematik, Informatik und Naturwissenschaften der Rheinisch-Westf¨alischen Technischen Hochschule Aachen zur Erlangung des akademischen Grades eines Doktors der Naturwissenschaften genehmigte Dissertation vorgelegt von Diplom-Informatiker Colin Hirsch aus Wien, Osterreic¨ h Berichter: Universit¨atsprofessor Dr. Erich Gr¨adel Universit¨atsprofessor Dr. Wolfgang Thomas Tag der mundlic¨ hen Prufung:¨ 17.7.2002 Diese Dissertation ist auf den Internetseiten der Hochschule online verfugbar.¨ Thank You A.B., D.B., E.G., E.R., I.F., M.K., M.O., M.T., S.K., S.T., W.T., . “Waterproof Cookies” 8.82oz / 250g margerine 8.82oz / 250g wheat flour 7.05oz / 200g sugar 3.53oz / 100g coconut rasps 1.76oz / 50g chocolate rasps 1.76oz / 50g candy sugar 2-3 eggs Separate the egg whites and whisk until solid. Make pastry out of other ingredients, including egg yolks. Finally add egg whites. Prepare baking tray and form cookies approx. 2 in. in diameter, 1/4 in. thick. Bake in oven at 392◦ F / 200◦ C until golden brown. Comments to
[email protected]. Contents 1 Introduction 5 2 Logical Background 11 2.1 First and Second-Order Logic . 11 2.2 Definitions and Conventions . 13 2.3 Transition Systems and Bisimulation . 16 2.4 Basic Modal Logic . 18 2.5 The Modal µ-calculus . 20 2.6 Invariance and Safety . 21 3 Guarded Logics 25 3.1 Structures and Guards . 25 3.2 The Guarded Fragment . 26 3.3 Guarded Fixed Point Logic . 28 3.4 Guarded Bisimulation . 32 3.5 Invariance and Safety .