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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
Decision Procedures for Guarded Logics
 IN AUTOMATED DEDUCTION  CADE16. PROCEEDINGS OF 16TH INTERNATIONAL CONFERENCE ON AUTOMATED DEDUCTION
, 1999
"... Different variants of guarded logics (a powerful generalization of modal logics) are surveyed and the recent decidability result for guarded fixed point logic (obtained in joint work with I. Walukiewicz) is explained. The exposition given here emphasizes the tree model property of guarded logics ..."
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Cited by 29 (0 self)
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Different variants of guarded logics (a powerful generalization of modal logics) are surveyed and the recent decidability result for guarded fixed point logic (obtained in joint work with I. Walukiewicz) is explained. The exposition given here emphasizes the tree model property of guarded logics: every satisfiable sentence has a model of bounded tree width. Based on the tree model property, different methods for reasoning with guarded fixed point sentences are presented: (1) reduction to the monadic theory of countable trees (S!S); (2) reduction to the calculus with backwards modalities; (3) the automata theoretic method (which gives theoretically optimal complexity results).
Loosely Guarded Fragment of FirstOrder Logic Has the Finite Model Property
, 2000
"... We show that the loosely guarded and packed fragments of firstorder logic have the finite model property. We use a construction of Herwig. We point out some consequences in temporal predicate logic and algebraic logic. AMS classification: Primary 03B20; Secondary 03B45, 03C07, 03C13, 03C30, 03G1 ..."
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Cited by 18 (3 self)
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We show that the loosely guarded and packed fragments of firstorder logic have the finite model property. We use a construction of Herwig. We point out some consequences in temporal predicate logic and algebraic logic. AMS classification: Primary 03B20; Secondary 03B45, 03C07, 03C13, 03C30, 03G15 Keywords: finite structures, modal logic, modal fragment, packed fragment 1 Introduction Perhaps because beginning students of modal logic are often told that modal logic is more expressive than firstorder logic and indeed has some secondorder expressive power, or perhaps because they are hoping for something new, it can come as a surprise to them that every modal formula has a `standard translation' into firstorder logic. For example, (p !q) is translated to 9y(R(x;y) ^ (P(y) ! 8z(R(y;z) ! Q(z)))): (1) The translation mimics the Kripke semantics for modal logic. Not every firstorder formula (with one free variable in the appropriate signature) is the translation of a modal formu...
Bisimulation Invariance and Finite Models
 IN LOGIC COLLOQUIUM ’02
, 2006
"... We study bisimulation invariance over finite structures. This investigation leads to a new, quite elementary proof of the van BenthemRosen characterisation of basic modal logic as the bisimulation invariant fragment of firstorder logic. The ramification of this characterisation for the finer no ..."
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We study bisimulation invariance over finite structures. This investigation leads to a new, quite elementary proof of the van BenthemRosen characterisation of basic modal logic as the bisimulation invariant fragment of firstorder logic. The ramification of this characterisation for the finer notion of global twoway bisimulation equivalence is based on bisimulation respecting constructions of models that recover in finite models some of the desirable properties of the usually in finite bisimilar unravellings.
A Note on the Complexity of the Satisfiability Problem for Graded Modal Logics
, 905
"... Abstract—Graded modal logic is the formal language obtained from ordinary modal logic by endowing its modal operators with cardinality constraints. Under the familiar possibleworlds semantics, these augmented modal operators receive interpretations such as “It is true at no fewer than 15 accessible ..."
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Cited by 6 (1 self)
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Abstract—Graded modal logic is the formal language obtained from ordinary modal logic by endowing its modal operators with cardinality constraints. Under the familiar possibleworlds semantics, these augmented modal operators receive interpretations such as “It is true at no fewer than 15 accessible worlds that... ”, or “It is true at no more than 2 accessible worlds that... ”. We investigate the complexity of satisfiability for this language over some familiar classes of frames. This problem is more challenging than its ordinary modal logic counterpart—especially in the case of transitive frames, where graded modal logic lacks the treemodel property. We obtain tight complexity bounds for the problem of determining the satisfiability of a given graded modal logic formula over the classes of frames characterized by any combination of reflexivity, seriality, symmetry, transitivity and the Euclidean property. Keywordsmodal logic; graded modalities; computational complexity I.