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15
Semantical considerations on FloydHoare Logic
, 1976
"... This paper deals with logics of programs. The objective is to formalize a notion of program description, and to give both plausible (semantic) and effective (syntactic) criteria for the notion of truth of a description. A novel feature of this treatment is the development of the mathematics underlyi ..."
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Cited by 212 (10 self)
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This paper deals with logics of programs. The objective is to formalize a notion of program description, and to give both plausible (semantic) and effective (syntactic) criteria for the notion of truth of a description. A novel feature of this treatment is the development of the mathematics underlying FloydHoare axiom systems independently of such systems. Other directions that such research might take are considered.
Higher Order Logic
 In Handbook of Logic in Artificial Intelligence and Logic Programming
, 1994
"... Contents 1 Introduction : : : : : : : : : : : : : : : : : : : : : : : : : : : : 2 2 The expressive power of second order Logic : : : : : : : : : : : 3 2.1 The language of second order logic : : : : : : : : : : : : : 3 2.2 Expressing size : : : : : : : : : : : : : : : : : : : : : : : : 4 2.3 Definin ..."
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Cited by 18 (0 self)
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Contents 1 Introduction : : : : : : : : : : : : : : : : : : : : : : : : : : : : 2 2 The expressive power of second order Logic : : : : : : : : : : : 3 2.1 The language of second order logic : : : : : : : : : : : : : 3 2.2 Expressing size : : : : : : : : : : : : : : : : : : : : : : : : 4 2.3 Defining data types : : : : : : : : : : : : : : : : : : : : : 6 2.4 Describing processes : : : : : : : : : : : : : : : : : : : : : 8 2.5 Expressing convergence using second order validity : : : : : : : : : : : : : : : : : : : : : : : : : 9 2.6 Truth definitions: the analytical hierarchy : : : : : : : : 10 2.7 Inductive definitions : : : : : : : : : : : : : : : : : : : : : 13 3 Canonical semantics of higher order logic : : : : : : : : : : : : 15 3.1 Tarskian semantics of second order logic : : : : : : : : : 15 3.2 Function and re
A zeroone law for logic with a fixedpoint operator
 Inform. and Control
"... The logic obtained by adding the leastfixedpoint operator to firstorder logic was proposed as a query language by Aho and Ullman (in "Proc. 6th ACM Sympos. on Principles of Programming Languages, " 1979, pp. 110120) and has been studied, particularly in connection with finite models, b ..."
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Cited by 14 (6 self)
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The logic obtained by adding the leastfixedpoint operator to firstorder logic was proposed as a query language by Aho and Ullman (in "Proc. 6th ACM Sympos. on Principles of Programming Languages, " 1979, pp. 110120) and has been studied, particularly in connection with finite models, by numerous authors. We extend to this logic, and to the logic containing the more powerful iterativefixedpoint operator, the zeroone law proved for firstorder logic in (Glebskii, Kogan, Liogonki, and Talanov (1969), Kibernetika 2, 3142; Fagin (1976), J. Symbolic Logic 41, 5058). For any sentence q ~ of the extended logic, the proportion of models of q ~ among all structures with universe {1, 2,..., n} approaches 0 or 1 as n tends to infinity. We also show that the problem of deciding, for any cp, whether this proportion approaches 1 is complete for exponential time, if we consider only q)'s with a fixed finite vocabulary (or vocabularies of bounded arity) and complete for doubleexponential time if ~0 is unrestricted. In addition, we establish some related results. © 1985 Academic Press, Inc.
The Modal µCalculus and the Logic of Common Knowledge
 PHD THESIS, INSTITUT FÜR INFORMATIK UND ANGEWANDTE MATHEMATIK, UNIVERSITÄT
, 2002
"... ..."
On Modal µCalculus and NonWellFounded Set Theory
"... A finitary characterization for nonwellfounded sets with finite transitive closure is established in terms of modal µcalculus. This result generalizes the standard approach in the literature where a finitary characterization is only provided for wellfounded sets with finite transitive closure ..."
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Cited by 3 (0 self)
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A finitary characterization for nonwellfounded sets with finite transitive closure is established in terms of modal µcalculus. This result generalizes the standard approach in the literature where a finitary characterization is only provided for wellfounded sets with finite transitive closure. The proof relies on the concept of automaton, leading then to new interlinks between automata theory and nonwellfounded sets.
The Modal µCalculus Hierarchy over Restricted Classes of Transition Systems
, 2008
"... We study the strictness of the modal µcalculus hierarchy over some restricted classes of transition systems. First, we show that the hierarchy is strict over reflexive frames. By proving the finite model theorem for reflexive systems the same results holds for finite models. Second, we prove that o ..."
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Cited by 2 (0 self)
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We study the strictness of the modal µcalculus hierarchy over some restricted classes of transition systems. First, we show that the hierarchy is strict over reflexive frames. By proving the finite model theorem for reflexive systems the same results holds for finite models. Second, we prove that over transitive systems the hierarchy collapses to the alternationfree fragment. In order to do this the finite model theorem for transitive transition systems is also proved. Further, we verify that if symmetry is added to transitivity the hierarchy collapses to the purely modal fragment.
The beginning of model checking: A personal perspective
, 2008
"... Abstract. Model checking provides an automated method for verifying concurrent systems. Correctness specifications are given in temporal logic. The method hinges on an efficient and flexible graphtheoretic reachability algorithm. At the time of its introduction in the early 1980’s, the prevailing p ..."
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Abstract. Model checking provides an automated method for verifying concurrent systems. Correctness specifications are given in temporal logic. The method hinges on an efficient and flexible graphtheoretic reachability algorithm. At the time of its introduction in the early 1980’s, the prevailing paradigm for verification was a manual one of prooftheoretic reasoning using formal axioms and inference rules oriented towards sequential programs. The need to encompass concurrent programs, the desire to avoid the difficulties with manual deductive proofs, and the small model theorem for temporal logic motivated the development of model checking.
Sequent Calculi for the Modal µCalculus over S5
, 2008
"... We present two sequent calculi for the modal µcalculus over S5 and prove their completeness by using classical methods. One sequent calculus has an analytical cut rule and could be used for a decision procedure the other uses a modified version of the induction rule. We also provide a completeness ..."
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We present two sequent calculi for the modal µcalculus over S5 and prove their completeness by using classical methods. One sequent calculus has an analytical cut rule and could be used for a decision procedure the other uses a modified version of the induction rule. We also provide a completeness theorem for Kozen’s Axiomatisation over S5 without using the completeness result established by Walukiewicz for the modal µcalculus over arbitrary models.
Overige leden:
"... ter verkrijging van de graad van doctor aan de Universiteit van Amsterdam op gezag van de Rector Magnificus prof. dr. D. van den Boom ten overstaan van een door het college voor promoties ingestelde commissie, in het openbaar te verdedigen in de Agnietenkapel op vrijdag 17 december 2010, te 14.00 uu ..."
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ter verkrijging van de graad van doctor aan de Universiteit van Amsterdam op gezag van de Rector Magnificus prof. dr. D. van den Boom ten overstaan van een door het college voor promoties ingestelde commissie, in het openbaar te verdedigen in de Agnietenkapel op vrijdag 17 december 2010, te 14.00 uur door
Learning as Interaction
"... In formal approaches to inductive learning, the ability to learn is understood as the ability to single out a correct hypothesis from a range of possibilities. Although most of the existing research focuses on the characteristics of the learner, in many paradigms the significance of the teacher’s ab ..."
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In formal approaches to inductive learning, the ability to learn is understood as the ability to single out a correct hypothesis from a range of possibilities. Although most of the existing research focuses on the characteristics of the learner, in many paradigms the significance of the teacher’s abilities and strategies is in fact undeniable. Motivated by this observation, in this paper we highlight the interactive nature of learning by proposing a gametheoretical and logical approach. We consider learning as a game, and present different levels of cooperativeness between the players. Then, we look at different variants of Sabotage Games as learning scenarios, expressing the conditions for learnability in Sabotage Modal Logic and analyzing their complexity. Our work constitutes the first step towards a unified gametheoretical and logical approach to formal learning theory. 1