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- Martin Otto
- J. Symb. Log.
- 2001

The satissability problem for the two-variable fragment of rst-order logic is investigated over nite and innnite linearly ordered, respectively wellordered domains, as well as over nite and innnite domains in which one or several designated binary predicates are interpreted as arbitrary wellfounded relations. It is shown that FO 2 over ordered, respectively… (More)

- Anuj Dawar, Martin Otto
- 20th Annual IEEE Symposium on Logic in Computer…
- 2005

We investigate model theoretic characterisations of the expressive power of modal logics in terms of bisimulation invariance. The paradigmatic result of this kind is van Benthem's theorem, which says that a first-order formula is invariant under bisimulation if and only if it is equivalent to a formula of basic modal logic. The present investigation… (More)

- Martin Otto
- Theor. Comput. Sci.
- 1999

Consider the class of all those properties of worlds in nite Kripke structures (or of states in inite transition systems), that are recognizable in polynomial time, and closed under bisimulation equivalence. It is shown that the class of these bisimulation-invariant Ptime queries has a natural logical characterization. It is captured by the straightforward… (More)

- Erich Grädel, Martin Otto
- Theor. Comput. Sci.
- 1999

This paper is a survey and systematic presentation of decidability and complexity issues for modal and non-modal two-variable logics. A classical result due to Mortimer says that the two-variable fragment of rst-order logic, denoted FO 2 , has the nite model property and is therefore decidable for satissability. One of the reasons for the signiicance of… (More)

- Erich Grädel, Colin Hirsch, Martin Otto
- ACM Trans. Comput. Log.
- 2000

Guarded fixed-point logic μGF extends the guarded fragment by means of least and greatest fixed points, and thus plays the same role within the domain of guarded logics as the modal μ-calculus plays within the modal domain. We provide a semantic characterization of μGF within an appropriate fragment of second-order logic, in terms of invariance… (More)

- Vince Bárány, Georg Gottlob, Martin Otto
- 2010 25th Annual IEEE Symposium on Logic in…
- 2010

Evaluating a boolean conjunctive query q over a guarded first-order theory T is equivalent to checking whether (T \& not q) is unsatisfiable. This problem is relevant to the areas of database theory and description logic. Since q may not be guarded, well known results about the decidability, complexity, and finite-model property of the guarded fragment… (More)

- Martin Otto, Jan Van den Bussche
- Inf. Process. Lett.
- 1996

We consider \generic" (isomorphism-invariant) queries on rela-tional databases embedded in an innnite background structure. Assume a generic query is expressible by a rst-order formula over the embedded domain that may involve both the relations of the database and the relations and functions of the background structure. Then this query is already… (More)

- Martin Otto
- Bulletin of Symbolic Logic
- 2000

Lyndon's Interpolation Theorem asserts that for any valid implication between two purely relational sentences of rst-order logic, there is an interpolant in which each relation symbol appears only in those polarities in which it appears in both the antecedent and the succedent of the given implication. This note proves a similar interpolation result under… (More)

- Martin Otto, Robert Piro
- Advances in Modal Logic
- 2008

abstract. We establish a Lindström type characterisation of the extension of basic modal logic by a global modality (ML[∀]) and of the guarded fragment of first-order logic (GF) as maximal among compact logics with the corresponding bisimulation invariance and the Tarski Union Property.

- Erich Grädel, Martin Otto, Eric Rosen
- LICS
- 1997