A Probabilistic Modal Set Theory

Three Seminars by Professor Dana S. Scott

30th June - 8th July 2010, Edinburgh, UK

Three seminars on "A Probabilistic Modal Set Theory" associated with Professor Dana S. Scott's visit to Scotland on a SICSA distinguished visiting fellowship.

All seminars will be held in the Informatics Forum (IF), 10 Crichton Street, Edinburgh.

Although these seminars are open to all, space is limited. Please contact Alex.Simpson@ed.ac.uk if you plan to attend. First come first served.

Seminar 1

11.30-12.45, Wednesday 30th June 2010, room IF 4.31.

Slides (pdf)

Constructions of complete Boolean algebras. Boolean-valued completeness for first-order logic. Modeling Lewis S4 modal logic. Connections with intuitionistic logic.

Seminar 2

11.30-12.45, Thursday 1st July 2010, room IF 4.02.

Slides (pdf)

The Lebesgue measure algebra. Finding the modal structure. Proof of the 0-1 Law for measure-preserving automorphisms. Semantics for higher-order logic. Boolean-valued real numbers.

Seminar 3

11.30-12.45, continued 13.30-14.45, Thursday 8th July 2010, room IF 4.02.

Slides (pdf)

Defining a Boolean-valued Modal Set Theory. Derivation of first principles involving modality. Introduction of random elements and their properties. Some discussion of probabilistic logic.


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