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- Carlos Areces, Patrick Blackburn, Maarten Marx
- CSL
- 1999

Hybrid languages are extended modal languages which can refer to (or even quantify over) states. Such languages are better behaved proof theoretically than ordinary modal languages for they internalize the apparatus of labeled deduction. Moreover, they arise naturally in a variety of applications, including description logic and temporal reasoning. Thus it… (More)

- Carlos Areces, Patrick Blackburn, Maarten Marx
- J. Symb. Log.
- 2001

Hybrid languages are expansions of propositional modal languages which can refer to (or even quantify over) worlds. The use of strong hybrid languages dates back to at least [Pri67], but recent work (for example [BS98, BT98a, BT99]) has focussed on a more constrained system called H(↓,@). We show in detail that H(↓,@) is modally natural. We begin by… (More)

- Carlos Areces, Patrick Blackburn, Maarten Marx
- Logic Journal of the IGPL
- 2000

In their simplest form, hybrid languages are propositional modal languages which can refer to states. They were introduced by Arthur Prior, the inventor of tense logic, and played an important role in his work: because they make reference to specific times possible, they remove the most serious obstacle to developing modal approaches to temporal… (More)

- Carlos Areces
- 2002

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- Guillaume Hoffmann, Carlos Areces
- Electr. Notes Theor. Comput. Sci.
- 2009

Hybrid logic is a formalism that is closely related to both modal logic and description logic. A variety of proof mechanisms for hybrid logic exist, but the only widely available implemented proof system, HyLoRes, is based on the resolution method. An alternative to resolution is the tableaux method, already widely used for both modal and description… (More)

Hybrid languages are modal languages that have special symbols for naming individual states in models. Their history can be traced back to work of Arthur Prior in the fifties. The subject has recently regained interest, resulting in many new results and techniques. This chapter contains a modern overview of the field. We sketch its history, and survey the… (More)

- Carsten Lutz, Carlos Areces, Ian Horrocks, Ulrike Sattler
- IJCAI
- 2003

Many description logics (DLs) combine knowledge representation on an abstract, logical level with an interface to “concrete” domains like numbers and strings with built-in predicates such as <, +, and prefix-of. These hybrid DLs have turned out to be useful in several application areas, such as providing the basis for expressive ontology languages. We… (More)

- Carlos Areces, Patrick Blackburn, Bernadette Martínez Hernández, Maarten Marx
- Description Logics
- 2003

We consider description logic knowledge bases in which the ABox can contain Boolean combinations of traditional ABox assertions (represented as clauses or sequents). A linear reduction of such knowledge bases into a standard format (allowing only conjunctive assertions) is described which preserves knowledge base satisfiability. Similar results are… (More)

- Carlos Areces, Alexander Koller, Kristina Striegnitz
- INLG
- 2008

In this paper, we propose to reinterpret the problem of generating referring expressions (GRE) as the problem of computing a formula in a description logic that is only satisfied by the referent. This view offers a new unifying perspective under which existing GRE algorithms can be compared. We also show that by applying existing algorithms for computing… (More)

- Carlos Areces, Maarten de Rijke, Hans de Nivelle
- J. Log. Comput.
- 2001

We provide a resolution-based proof procedure for modal, description and hybrid logic that improves on previous proposals in important ways. It avoids translations into large undecidable logics, and works directly on modal, description or hybrid logic formulas instead. In addition, by using the hybrid machinery it avoids the complexities of earlier… (More)