Proceedings of the International Workshop on Hybrid Logic (HyLo 2006), Electronic Notes in Theoretical Computer Science, Volume 174, Issue 6, Pages 1-148 (3 June 2007)

Official HyLo 2006 homepage   Ian Horrocks' Slides   Photos   HyLo 2007


International Workshop on Hybrid Logic 2006 (HyLo 2006)

Friday August 11, 2006, Seattle, USA

Affiliated with LOGIC IN COMPUTER SCIENCE (LICS 2006) and part of the Federated Logic Conference (FLoC 2006)

Aims & Scope

Hybrid logic is a branch of modal logic in which it is possible to directly refer to worlds/times/states or whatever the elements of the (Kripke) model are meant to represent. Although they date back to the late 1960s, and have been sporadically investigated ever since, it is only in the 1990s that work on them really got into its stride.

It is easy to justify interest in hybrid logic on applied grounds, because of the usefulness of the additional expressive power. For example, when reasoning about time one often wants to build up a series of assertions about what happens at a particular instant, and standard modal formalisms do not allow this. What is less obvious is that the route hybrid logic takes to overcome this problem (the basic mechanism being to add nominals --- atomic symbols true at a unique point --- together with extra modalities to exploit them) often actually improves the behavior of the underlying modal formalism. For example, it becomes far simpler to formulate modal tableau, resolution, and natural deduction in hybrid logic, and completeness and interpolation results can be proved of a generality that is not available in orthodox modal logic.

Hybrid logic is now a mature field, therefore a theme of special interest at this HyLo workshop will be the combination of hybrid logic with other logics, the basic methodological question being "what is the best way of hybridizing a given logic?" However, submissions in all areas of hybrid logic are welcome.

The workshop HyLo 2006 is likely to be relevant to a wide range of people, including those interested in description logic, feature logic, applied modal logics, temporal logic, and labelled deduction. The workshop continues a series of previous workshops on hybrid logic, for example the LICS-affiliated HyLo 2002 which was held as part of FLoC 2002, Copenhagen, Denmark. If you are unsure whether your work is of relevance to the workshop, please do not hesitate to contact the workshop organizers for more information. Contact details are given below.

For more general background on hybrid logic, and many of the key papers, see the Hybrid Logics homepage.

Invited Speakers

Patrick Blackburn (INRIA Lorraine, France)
Title: Hybrid Logic and Temporal Semantics


Hybrid logic is historically linked with temporal semantics for natural language; in fact, Arther Prior originally developed hybrid logic in order to have a modal logic of time strong enough to model the temporal expressivity of natural language. But while technical results have been obtained for various types of hybrid temporal logic (notably point-based and interval-based systems) there has been relatively little work on developing the connection with natural language; even Prior himself wrote little on the topic. The time seems ripe to start exploring this connection again. For a start, the development of temporal markup languages (such as TimeML) has lead to an explosion of interest within computational linguistics in coping reliably with temporal information. Hybrid logic seems to fit in naturally with such formalisms, and could be used to interpret them. And relatively simple adaptations make it possible for hybrid logics to cope with a wide range of temporal phenomena. But to make hybrid logic useful in this area we have to move beyond the setting of propositional hybrid logic (where most research has concentrated) to first-order and even higher-order temporal logics. In this talk I will discuss the sort of problems that need to be modelled, the sort of expressivity needed to cope with natural language applications, and will present hybrid languages suitable for this purpose (probably including a Montague-style Hybrid Intensional Logic). Time permitting, I will also discuss the links with TimeML.

Valeria de Paiva (PARC, USA)
Title: Constructive Hybrid Logics and Contexts


One of the (several) origins of hybrid logics was the early work of Seligman on a logic of correct descriptions. This work was also one of the basis for the work (by Torben BraŁner and myself) on a Natural Deduction formulation of constructive hybrid logic. The system described by Seligman seems intuitive and appealing as a logic of contexts for AI, but this intuition has not been made very precise, yet. Giving an invited talk is the perfect excuse to try to ascertain the pros and cons of a logic of contexts based on constructive hybrid logics, as opposed to one based on constructive modal logics.

Ian Horrocks (University of Manchester, UK)
Title: Hybrid Logics and Ontology Languages


Description Logics (DLs) are a family of logic based knowledge representation formalisms. Although they have a range of applications, they are perhaps best known as the basis for widely used ontology languages such as OIL, DAML+OIL and OWL, the last of which is now a World Wide Web Consortium (W3C) recommendation. SHOIN, the DL underlying OWL DL (the most widely used "species" of OWL), includes familiar features from hybrid logic. In particular, in order to support extensionally defined classes, SHOIN includes nominals: classes whose extension is a singleton set. This is an important feature for a logic that is designed for use in ontology language applications, because extensionally defined classes are very common in ontologies. Binders and state variables are another feature from Hybrid Logic that would clearly be useful in an ontology language, but it is well known that adding this feature to even a relatively weak language would lead to undecidability. However, recent work has shown that this feature could play a very useful role in query answering, where the syntactic structure of queries means that the occurrence of state variables is restricted in a way that allows for decidable reasoning.

Accepted Papers

Moritz Hardt, Gert Smolka: Higher-Order Syntax and Saturation Algorithms for Hybrid Logic

Martin Mundhenk, Thomas Schneider: Undecidability of Multi-modal Hybrid Logics

Nicole Bidoit, Dario Colazzo: Testing XML constraint satisfiability

Andrť Platzer: Towards a Hybrid Dynamic Logic for Hybrid Dynamic Systems

Balder ten Cate, Tadeusz Litak: Topological Perspective on the Hybrid Proof Rules

Katsuhiko Sano: A Hybridization of Irreflexive Modal Logics

Thomas Bolander, Jens Ulrik Hansen, Michael Reichhardt Hansen: Decidability of a Hybrid Duration Calculus

Jason Reed: Hybridizing a Logical Framework


Patrick Blackburn (INRIA Lorraine, France)
Thomas Bolander (Technical University of Denmark)
Torben BraŁner (Roskilde University, Denmark) - Chair
Valeria de Paiva (PARC, USA)
JÝrgen Villadsen (Technical University of Denmark)

Program Committee

Carlos Areces (INRIA Lorraine, France)
Patrick Blackburn (INRIA Lorraine, France)
Thomas Bolander (Technical University of Denmark)
Torben BraŁner (Roskilde University, Denmark) - Chair
Valeria de Paiva (PARC, USA)
Melvin Fitting (Lehman College, New York, USA)
Balder ten Cate (University of Amsterdam, The Netherlands)
JÝrgen Villadsen (Technical University of Denmark)


We invite the contribution of papers reporting new work from researchers interested in hybrid logic. The revised version of accepted papers will be published online in an Elsevier ENTCS volume devoted to FLoC 2006 satellite workshops. A preliminary version of the proceedings will also be distributed at the workshop. One author for each accepted paper must attend the workshop in order to present the paper.

Please use the HyLo 2006 submission page, handled by the EasyChair conference system, to submit papers. Papers should not exceed 15 pages including references. Authors are strongly encouraged to prepare their submissions according to the ENTCS guidelines.

Important Dates

Deadline for submissions: June 1, 2006 (strict)
Notification of acceptance: June 20, 2006
Deadline for final versions: July 21, 2006

Contact Information

Associate Professor, Ph.D. Torben BraŁner
Department of Computer Science
Roskilde University
P.O. Box 260
DK-4000 Roskilde, Denmark
Phone: +45 4674 3840
Fax: +45 4674 3072

The workshop is sponsored by the HyLoMOL project which is funded by the Danish Natural Science Research Council.