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Guarded Fixed Point Logic
, 1999
"... Guarded fixed point logics are obtained by adding least and greatest fixed points to the guarded fragments of firstorder logic that were recently introduced by Andr eka, van Benthem and N emeti. Guarded fixed point logics can also be viewed as the natural common extensions of the modal µcalculus an ..."
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Cited by 81 (6 self)
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Guarded fixed point logics are obtained by adding least and greatest fixed points to the guarded fragments of firstorder logic that were recently introduced by Andr eka, van Benthem and N emeti. Guarded fixed point logics can also be viewed as the natural common extensions of the modal µcalculus and the guarded fragments. We prove that the satisfiability problems for guarded fixed point logics are decidable and complete for deterministic double exponential time. For guarded fixed point sentences of bounded width, the most important case for applications, the satisfiability problem is EXPTIMEcomplete.
Why Are Modal Logics So Robustly Decidable?
"... Modal logics are widely used in a number of areas in computer science, in particular ..."
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Cited by 31 (1 self)
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Modal logics are widely used in a number of areas in computer science, in particular
Homomorphism Preservation Theorems
, 2008
"... The homomorphism preservation theorem (h.p.t.), a result in classical model theory, states that a firstorder formula is preserved under homomorphisms on all structures (finite and infinite) if and only if it is equivalent to an existentialpositive formula. Answering a longstanding question in fin ..."
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Cited by 27 (0 self)
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The homomorphism preservation theorem (h.p.t.), a result in classical model theory, states that a firstorder formula is preserved under homomorphisms on all structures (finite and infinite) if and only if it is equivalent to an existentialpositive formula. Answering a longstanding question in finite model theory, we prove that the h.p.t. remains valid when restricted to finite structures (unlike many other classical preservation theorems, including the ̷Lo´sTarski theorem and Lyndon’s positivity theorem). Applications of this result extend to constraint satisfaction problems and to database theory via a correspondence between existentialpositive formulas and unions of conjunctive queries. A further result of this article strengthens the classical h.p.t.: we show that a firstorder formula is preserved under homomorphisms on all structures if and only if it is equivalent to an existentialpositive formula of equal quantifierrank.
Omitting types for finite variable fragments and complete representations of algebras
, 2007
"... ..."
Homomorphism Closed vs. Existential Positive
 In Proc. of the 18th IEEE Symp. on Logic in Computer Science
, 2003
"... Preservations theorems, which establish connection between syntactic and semantic properties of formulas, are a major topic of investigation in model theory. In the context of finitemodel theory, most, but not all, preservation theorems are known to fail. It is not known, however, whether the L/os ..."
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Cited by 15 (1 self)
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Preservations theorems, which establish connection between syntactic and semantic properties of formulas, are a major topic of investigation in model theory. In the context of finitemodel theory, most, but not all, preservation theorems are known to fail. It is not known, however, whether the L/osTarskiLyndon Theorem, which asserts that a 1storder sentence is preserved under homomorphisms iff it is equivalent to an existential positive sentence, holds with respect to finite structures. Resolving this is an important open question in finitemodel theory.
Some Aspects of Model Theory and Finite Structures
, 2002
"... this paper is to highlight some of these aspects of the model theory of nite structures, where the nite and in nite interact fruitfully, in order to dispel the perhaps too common perception that ( rstorder) model theory has little to say about nite structures ..."
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Cited by 11 (0 self)
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this paper is to highlight some of these aspects of the model theory of nite structures, where the nite and in nite interact fruitfully, in order to dispel the perhaps too common perception that ( rstorder) model theory has little to say about nite structures
Decidable Fragments of FirstOrder and FixedPoint Logic  From prefix vocabulary classes to guarded logics
, 2003
"... We survey decidable and undecidable satis ability problems for fragments of rstorder logic and beyond. Classical studies, related to Hilbert's programme and to which Laszlo Kalmar has made important contributions, focussed on pre xvocabulary fragments in rstorder logic; for these a com ..."
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Cited by 10 (0 self)
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We survey decidable and undecidable satis ability problems for fragments of rstorder logic and beyond. Classical studies, related to Hilbert's programme and to which Laszlo Kalmar has made important contributions, focussed on pre xvocabulary fragments in rstorder logic; for these a complete classi cation of the decidable and undecidable cases has been obtained.
On the Variable Hierarchy of the Modal µCalculus
"... We investigate the structure of the modal µcalculus L with respect to the question of how many different fixed point variables are necessary to define a given property. Most of the logics commonly used in verification, such as CTL, LTL, CTL , PDL, etc. can in fact be embedded into the twovariable ..."
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Cited by 2 (0 self)
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We investigate the structure of the modal µcalculus L with respect to the question of how many different fixed point variables are necessary to define a given property. Most of the logics commonly used in verification, such as CTL, LTL, CTL , PDL, etc. can in fact be embedded into the twovariable fragment of the µcalculus. It is also known that the twovariable fragment can express properties that occur at arbitrarily high levels of the alternation hierarchy. However, it is an open problem whether the variable hierarchy is strict.