Lectures on Hybrid Logic

Patrick Blackburn

INRIA Lorraine
(Patrick.Blackburn@loria.fr)

Prerequisites: The course will be relatively self-contained, and I will attempt to make the material as accessible as possible to an interdisciplinary audience (that is, the course is not targeted solely at logicians). Nonetheless, I will be presupposing a certain level of logical literacy. Roughly speaking, to follow this course you should have a reasonable grasp of first-order logic and its semantics. Prior acquaintance with the basics of modal logic would be helpful, but is not essential.

Prospective students might like to browse through the Preface and Chapter 1 of

Modal Logic, by P. Blackburn, M. de Rijke and Y. Venema,
Cambridge University Press, 2001.

This will give you an idea of the stance on modal logic adopted in the course. For overviews of hybrid logic, try

Representation, Reasoning, and Relational Structures:
a Hybrid Logic Manifesto, by P. Blackburn,
Logic Journal of the IGPL, 8(3), 339-625, 2000

or

Bringing them all Together, by C. Areces and P. Blackburn,
Journal of Logic and Computation, 11(5), 657-669, 2001.

You can find both papers (and lots of other relevant material) on the hybrid logic homepage:

http://www.hylo.net

Summary: This course introduces hybrid logic, a form of modal logic in which it is possible to name worlds (or times, or computational states, or situations, or nodes in parse trees, or people --- indeed, whatever it is that the elements of Kripke Models are taken to represent). The course has two major goals. The first is to convey, as clearly as possible, the ideas and intuitions that have guided the development of hybrid logic. The second is to teach a concrete skill: tableau-based hybrid deduction. By the end of the course you will have seen ample evidence that modal logic is useful in a wide range of circumstances, and that hybrid logic is a particularly simple way of doing modal logic.

INRIA, France's national research organisation in computer science, provided fianancial support for this course as part of the INRIA-funded research collaboration between the Langue et Dialogue group (INRIA Lorraine, Nancy) and the Language and Inference Technology group (University of Amsterdam). The course material was developed during an INRIA-funded visit by Maarten Marx to Nancy, France.

Course Outline: Lecture 1: From modal logic to hybrid logic

Lecture 2: Hybrid deduction

Lecture 3: The downarrow binder

Lecture 4: First-order hybrid logic

Lecture 5: The Priorean perspective

Each lecture is one hour long. The slides (developed by Patrick Blackburn and Maarten Marx) on which the course is based will be made available at this site.

Course Notes:
Course Reader
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