Graphical Foundations for Dialogue Games

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• Cai Wingfield, University of Bath
• Friday 17 May 2013, 16:00-17:00
• UG05 Learning Centre.

If you have a question about this talk, please contact Paul Levy.

In 2007, Harmer, Hyland and Melliès gave a formal mathematical foundation for game semantics using a notion they called a schedule, a structure describing interleavings of plays in games. Their definition was combinatorial in nature, but researchers often draw pictures when describing schedules in practice. Moreover, several proofs of key properties, such as that the composition of schedules is associative, involve cumbersome combinatorial detail, whereas in terms of pictures the proofs are straightforward, reflecting the geometry of the plane. Here, we give a geometric formulation of schedules, prove that they are isomorphic to Harmer et al.’s definitions, and illustrate their value by giving such geometric proofs. Harmer et al.’s notions may be combined to describe plays in multi-component games, and researchers have similarly developed intuitive graphical representations of plays in these games. We give a characterisation of these diagrams and explicitly describe how they relate to the underlying schedules, finally using this relation to provide new, intuitive proofs of key categorical properties.

This talk is part of the Theoretical computer science seminar series.

This talk is included in these lists:

• Computer Science Departmental Series
• Computer Science Distinguished Seminars
• Theoretical computer science seminar
• UG05 Learning Centre
• computer sience

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