## 141 Citations

### 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.

### On the Restraining Power of Guards

- Mathematics, Computer ScienceJournal of Symbolic Logic
- 1999

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.

### On the Complexity of Hybrid Logics with Binders

- Computer Science, PhilosophyCSL
- 2005

This work isolates large fragments of HL(@, ↓ ) for which satisfiability is decidable and model checking is below PSpace, and examines their applications to first-order logic.

### Undecidability of first-order intuitionistic and modal logics with two variables

- Philosophy, MathematicsBull. Symb. Log.
- 2005

For many quantified modal logics, including those in the standard nomenclature above, even the monadic two-variable fragments turn out to be undecidable.

### First-order logic with self-reference

- PhilosophyArXiv
- 2022

We consider an extension of ﬁrst-order logic with a recursion operator that corresponds to allowing formulas to refer to themselves. We investigate the obtained language under two diﬀerent systems of…

### Decidability Issues for Two-Variable Logics with Several Linear Orders

- MathematicsCSL
- 2011

It is shown that the satisfiability and the finite satisfiability problems for two-variable logic, FO2, over the class of structures with three linear orders, are undecidable and that GF2 with an arbitrary number of linear orders which can be used only as guards becomes decidable if except linear orders only unary relations are allowed.

### Approaches to Finite Variable Dependence: Expressiveness and Computational Complexity

- Mathematics
- 2014

In this thesis we study computational aspects, expressive power and modeltheoretic properties of fragments of various logics that are suitable for modeling diverse forms of variable dependence. In…

### Insights into Modal Slash Logic and Modal Decidability

- Philosophy
- 2012

The present paper has a two-fold task. On the one hand, it aims to provide an overview on Independence friendly modal logic as deﬁned in (Tulenheimo, 2003; Tulenheimo, 2004) and studied in a number…

### Complexity of Expanding a Finite Structure and Related Tasks

- Computer Science
- 2006

The complexities of model expansion for a number of logics, alongside those of satisfiability and model checking, are presented, as the task is equivalent to witnessing the existential quantifiers in ∃SO model checking.

## References

SHOWING 1-10 OF 41 REFERENCES

### Undecidability results on two-variable logics

- MathematicsArch. Math. Log.
- 1997

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.

### Why is Modal Logic So Robustly Decidable?

- Philosophy, Computer ScienceDescriptive Complexity and Finite Models
- 1996

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.

### On the Restraining Power of Guards

- Mathematics, Computer ScienceJournal of Symbolic Logic
- 1999

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.

### On the Decision Problem for Two-Variable First-Order Logic

- Mathematics, Computer ScienceBulletin of Symbolic Logic
- 1997

Improve Mortimer's bound by one exponential and show that every satisfiable FO2-sentence has a model whose size is at most exponential in the size of the sentence, establishing that the satisfiability problem for FO2 is NEXPTIME-complete.

### On the boundedness problem for two-variable first-order logic

- MathematicsProceedings. Thirteenth Annual IEEE Symposium on Logic in Computer Science (Cat. No.98CB36226)
- 1998

This paper asserts that the boundedness problem for FO/sup 2/ is undecidable, even when restricted to negation-free and equality-free formulas /spl phi/(X, x) in which x is the only free variable and X is a monadic relation symbol that occurs within the scopes of universal quantifiers only.

### Bounded variable logics: two, three, and more

- MathematicsArch. Math. Log.
- 1999

This paper deals with a translation that associates equivalence of structures in the k-variable fragments with bisimulation equivalence between derived structures and relates some interesting issues for the cases of an arbitrary number of variables to the case of just three variables.

### Model Checking and Transitive-Closure Logic

- Computer ScienceCAV
- 1997

We give a linear-time algorithm to translate any formula from computation tree logic (CTL or CTL*) into an equivalent expression in a variable-confined fragment of transitive-closure logic FO(TC).…

### On Model-Checking for Fragments of µ-Calculus

- Computer ScienceCAV
- 1993

It is shown that the logic L2 is as expressive as ECTL* given in [13], and the model checking problem for the μ-calculus is equivalent to the non-emptiness problem of parity tree automata.

### Automatic Veriication of Nite-state Concurrent Systems Using Temporal-logic Speciications. Acm

- Computer Science
- 1993

An algorithm for checking whether a GSMP satisses its TCTL-speciication is presented, which combines model- checking algorithm of this paper with model-checking for discrete-time Markov chains and ways to cope with the PSPACE complexity of the problem are devised.

### An automata-theoretic approach to branching-time model checking

- Computer ScienceJACM
- 2000

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.