• Corpus ID: 15981360

Why are Modal Logics so Robustly Decidable?

@inproceedings{Grdel1999WhyAM,
  title={Why are Modal Logics so Robustly Decidable?},
  author={Erich Gr{\"a}del},
  booktitle={Bull. EATCS},
  year={1999}
}
  • E. Grädel
  • Published in Bull. EATCS 1 May 2001
  • Computer Science
Modal logics are widely used in a number of areas in computer science, in particular for the speciication and veriication of hardware and software systems, for knowledge representation, in databases, and in artiicial intelligence. The most important reason for the successful applications of these logics is that they provide a good balance between expressive power and computational complexity. In 30] Vardi adressed the question to identify the main reasons for the robust decidabil-ity properties… 

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References

SHOWING 1-10 OF 31 REFERENCES

On Logics with Two Variables

Why is Modal Logic So Robustly Decidable?

  • Moshe Y. Vardi
  • Philosophy, Computer Science
    Descriptive Complexity and Finite Models
  • 1996
TLDR
It is argued that the robust decidability of modal logic can be explained by the so-called tree- model property, and it is shown how the tree-model property leads to automata-based decision procedures.

The complexity of tree automata and logics of programs

  • E. EmersonC. Jutla
  • Computer Science
    [Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science
  • 1988
TLDR
It is shown that for tree automata with m states and n pairs nonemptiness can be tested in time O((mn)/sup 3n/), even though the problem is in general NP-complete, and it follows that satisfiability for propositional dynamic logic with a repetition construct and for the propositional mu-calculus can be tests in deterministic single exponential time.

A linear-time model-checking algorithm for the alternation-free modal mu-calculus

TLDR
A model-checking algorithm for a logic that permits propositions to be defined using greatest and least fixed points of mutually recursive systems of equations is developed, which improves on the best known algorithm for similar fixed-point logics.

On the Restraining Power of Guards

  • E. Grädel
  • Mathematics, Computer Science
    Journal of Symbolic Logic
  • 1999
TLDR
It is proved that the satisfiability problems for the guarded fragment and the loosely guarded fragment of first-order logic are complete for deterministic double exponential time and that some natural, modest extensions of the guarded fragments are undecidable.

Undecidability results on two-variable logics

TLDR
It is shown that going beyond L2 by adding any one of the following leads to an undecidable logic: very weak forms of recursion, such as transitive closure or monadic fixed-point operations.

Decision Procedures and Expressiveness in the Temporal Logic of Branching Time

TLDR
It is established that CTL has the small property by showing that any satisfiable CTL formulae is satisfiable in a small finite model obtained from a small -&-ldquo;pseudo-model-&-rdquo%; resulting from the Fischer Ladner quotient construction.

Model Checking and the Mu-calculus

  • E. Emerson
  • Computer Science
    Descriptive Complexity and Finite Models
  • 1996
TLDR
This work describes model checking algorithms and discusses their application on a particularly important type of temporal logic known as the Mu-calculus, which can provide an eecient and expressive tool for automatic veriication that a nite state system meets a correctness speciication formulated in temporal logic.

On the Expressive Completeness of the Propositional mu-Calculus with Respect to Monadic Second Order Logic

TLDR
It is shown that every formula of MSOL which does not distinguish between bisimilar models is equivalent to a formula of the propositional Μ-calculus, which implies that every logic over transition systems invariant under bisimulation and translatable into MSOL can be also translated into the Μ -calculus.

An automata-theoretic approach to branching-time model checking

TLDR
It is shown that alternating tree automata are the key to a comprehensive automata-theoretic framework for branching temporal logics, and can be used to obtain optimal decision procedures and make it possible to derive optimal model-checking algorithms.