# Why is Modal Logic So Robustly Decidable?

@inproceedings{Vardi1996WhyIM, title={Why is Modal Logic So Robustly Decidable?}, author={Moshe Y. Vardi}, booktitle={Descriptive Complexity and Finite Models}, year={1996} }

In the last 20 years modal logic has been applied to numerous areas of computer science, including artificial intelligence, program verification, hardware verification, database theory, and distributed computing. There are twomain computational problems associated with modal logic. The first problem is checking if a given formula is true in a given state of a given structure. This problem is known as the model-checking problem. The second problem is checking if a given formula is true in all…

## 309 Citations

### Decidability of modal logics with particular emphasis on the interval temporal logics

- Philosophy, Mathematics
- 2012

It is shown that the logic of subintervals, the fragment of the Halpern–Shoham logic where only the operator “during”, or D, is allowed, is undecidable over discrete structures, which is surprising as this, apparently very simple, logic is decidable over dense orders.

### Why are Modal Logics so Robustly Decidable?

- Computer ScienceBull. EATCS
- 1999

The question to identify the main reasons for the robust decidabil-ity properties of modal logics is discussed in the light of recent research on guarded fragments of rst-order logic and xed point logic.

### Optimised Proof Procedures for Quantitative Logics

- Computer Science
- 2010

Methods for improving the performance of satisfiability checking for graded and probabilistic modal logic using methods from linear programming, the resulting algorithms appear to offer significant rewards.

### Bounded model checking of infinite state systems

- Computer ScienceFormal Methods Syst. Des.
- 2007

A new approach to BMC is presented that extends current methods in three ways: instead of a reduction to propositional logic which restricts BMC to finite state systems, this work focuses on infinite state systems and therefore considers more powerful, yet decidable base logics.

### A Note on the Complexity of the Satisfiability Problem for Graded Modal Logics

- Philosophy2009 24th Annual IEEE Symposium on Logic In Computer Science
- 2009

Tight complexity bounds are obtained 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.

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