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Finite Model Theory and Descriptive Complexity
, 2002
"... This is a survey on the relationship between logical definability and computational complexity on finite structures. Particular emphasis is given to gamebased evaluation algorithms for various logical formalisms and to logics capturing complexity classes. In addition to the ..."
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Cited by 23 (7 self)
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This is a survey on the relationship between logical definability and computational complexity on finite structures. Particular emphasis is given to gamebased evaluation algorithms for various logical formalisms and to logics capturing complexity classes. In addition to the
Rational Dynamics and Epistemic Logic in Games
, 2002
"... I propose a barebones look at epistemic models for games, with a focus on update procedures for reaching equilibrium 'zones'. Connections are given with standard update and fixedpoint logics. This is just a 'methods' paper, as readers will want to play with models, uncertainty relations, and announ ..."
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Cited by 19 (5 self)
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I propose a barebones look at epistemic models for games, with a focus on update procedures for reaching equilibrium 'zones'. Connections are given with standard update and fixedpoint logics. This is just a 'methods' paper, as readers will want to play with models, uncertainty relations, and announcements different from those used here for the purposes of illustration.
Expressive Equivalence of Least and Inflationary FixedPoint Logic
 IN 17TH SYMP. ON LOGIC IN COMPUTER SCIENCE (LICS
, 2002
"... We study the relationship between least and inflationary fixedpoint logic. By results of Gurevich and Shelah from 1986, it has been known that on finite structures both logics have the same expressive power. On infinite structures however, the question whether there is a formula in IFP not equivale ..."
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Cited by 13 (2 self)
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We study the relationship between least and inflationary fixedpoint logic. By results of Gurevich and Shelah from 1986, it has been known that on finite structures both logics have the same expressive power. On infinite structures however, the question whether there is a formula in IFP not equivalent to any LFPformula was still open. In this
Open Problems in Logic and Games
 Logical Construction Games', Acta Philosophica Fennica 78, T. Aho & AV Pietarinen, eds., Truth and Games, essays in honour of Gabriel Sandu, 123  138. J. van Benthem, 2006B, 'The Epistemic Logic of IF Games', in
, 2005
"... Dov Gabbay is a prolific logician just by himself. But beyond that, he is quite good at making other people investigate the many further things he cares about. As a result, King's College London has become a powerful attractor in our field worldwide. Thus, it is a great pleasure to be an organizer f ..."
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Cited by 6 (2 self)
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Dov Gabbay is a prolific logician just by himself. But beyond that, he is quite good at making other people investigate the many further things he cares about. As a result, King's College London has become a powerful attractor in our field worldwide. Thus, it is a great pleasure to be an organizer for one of its flagship events: the Augustus de Morgan Workshop of 2005. Benedikt Loewe and I proposed the topic of 'interactive logic ' for this occasion, with an emphasis on social software – the logical analysis and design of social procedures – and on games, arguably the formal interactive setting par excellence. This choice reflects current research interests in our logic community at ILLC Amsterdam and beyond. In this broad area of interfaces between logic, computer science, and game theory, this paper is my own attempt at playing Dov. I am, perhaps not telling, but at least asking other people to find out for me what I myself cannot. A word of historical clarification may help here. The last time the Dutch came up the Thames (in 1667), we messed up the harbour, burnt down a few buildings, and took the English flagship the Royal Charles with us as a souvenir. The Medway Raid was still commemorated as late as 1967 in a joint ceremony. This time, however, our intentions
Backtracking games and inflationary fixed points
 THEORETICAL COMPUTER SCIENCE
, 2006
"... We define a new class of games, called backtracking games. Backtracking games are essentially parity games with an additional rule allowing players, under certain conditions, to return to an earlier position in the play and revise a choice. This new feature makes backtracking games more powerful tha ..."
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Cited by 4 (4 self)
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We define a new class of games, called backtracking games. Backtracking games are essentially parity games with an additional rule allowing players, under certain conditions, to return to an earlier position in the play and revise a choice. This new feature makes backtracking games more powerful than parity games. As a consequence, winning strategies become more complex objects and computationally harder. The corresponding increase in expressiveness allows us to use backtracking games as model checking games for inflationary fixedpoint logics such as IFP or MIC. We identify a natural subclass of backtracking games, the simple games, and show that these are the “right ” model checking games for IFP by a) giving a translation of formulae ϕ and structures A into simple games such that A  = ϕ if, and only if, Player 0 wins the corresponding game and b) showing that the winner of simple backtracking games can again be defined in IFP.
The complexity of model checking higher order fixpoint logic
 In Proc. 30th Int. Symp. on Math. Foundations of Computer Science, MFCS’05, volume 3618 of LNCS
, 2005
"... Abstract. This paper analyses the computational complexity of the model checking problem for Higher Order Fixpoint Logic – the modal µcalculus enriched with a typed λcalculus. It is hard for every level of the elementary time/space hierarchy and in elementary time/space when restricted to formulas ..."
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Cited by 4 (3 self)
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Abstract. This paper analyses the computational complexity of the model checking problem for Higher Order Fixpoint Logic – the modal µcalculus enriched with a typed λcalculus. It is hard for every level of the elementary time/space hierarchy and in elementary time/space when restricted to formulas of bounded type order. 1
The Undecidability of Iterated Modal
 Relativization”, Studia Logica
"... Abstract. In dynamic epistemic logic and other fields, it is natural to consider relativization as an operator taking sentences to sentences. When using the ideas and methods of dynamic logic, one would like to iterate operators. This leads to iterated relativization. We are also concerned with the ..."
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Cited by 2 (0 self)
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Abstract. In dynamic epistemic logic and other fields, it is natural to consider relativization as an operator taking sentences to sentences. When using the ideas and methods of dynamic logic, one would like to iterate operators. This leads to iterated relativization. We are also concerned with the transitive closure operation, due to its connection to common knowledge. We show that for three fragments of the logic of iterated relativization and transitive closure, the satisfiability problems are Σ 1 1complete. Two of these fragments do not include transitive closure. We also show that the question of whether a sentence in these fragments has a finite (tree) model is Σ 0 1complete. These results go via reduction to problems concerning domino systems.
Generalising Automaticity to Modal Properties of Finite Structures
 In Proc. 22nd FSTTCS, LNCS 2556
, 2002
"... We introduce a complexity measure of modal properties of finite structures which generalises the automaticity of languages. It is based on graphautomata like devices called labelling systems. We define a measure of the size of a structure that we call rank, and show that any modal property of st ..."
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Cited by 2 (1 self)
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We introduce a complexity measure of modal properties of finite structures which generalises the automaticity of languages. It is based on graphautomata like devices called labelling systems. We define a measure of the size of a structure that we call rank, and show that any modal property of structures can be approximated up to any fixed rank n by a labelling system. The function that takes n to the size of the smallest labelling system doing this is called the labelling index of the property. We demonstrate that this is a useful and finegrained measure of complexity and show that it is especially well suited to characterise the expressive power of modal fixedpoint logics. From this we derive several separation results of modal and nonmodal fixedpoint logics, some of which are already known whereas others are new.
The expressive power of twovariable least fixedpoint logics
"... Abstract. The present paper gives a classification of the expressive power of twovariable least fixedpoint logics. The main results are: 1. The twovariable fragment of monadic least fixedpoint logic with parameters is as expressive as full monadic least fixedpoint logic (on binary structures). ..."
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Abstract. The present paper gives a classification of the expressive power of twovariable least fixedpoint logics. The main results are: 1. The twovariable fragment of monadic least fixedpoint logic with parameters is as expressive as full monadic least fixedpoint logic (on binary structures). 2. The twovariable fragment of monadic least fixedpoint logic without parameters is as expressive as the twovariable fragment of binary least fixedpoint logic without parameters. 3. The twovariable fragment of binary least fixedpoint logic with parameters is strictly more expressive than the twovariable fragment of monadic least fixedpoint logic with parameters (even on finite strings). 1.