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Algebraic Theories over Nominal Sets

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Nominal sets were introduced by Gabbay/Pitts. Two different notions of equational logic over nominal sets were studied by Gabbay/Mathijssen and Clouston/Pitts. In this talk, we introduce the general notion of a based monad and show that finitary based monads give rise to equational theories in the standard sense of many-sorted set-based universal algebra. We further show that restricting these many-sorted equational theories to ‘uniform’ ones brings us back to the equational logics of Gabbay/Mathijssen and Clouston/Pitts. A benefit of our approach is that it allows to apply known results from universal algebra to algebras over nominal sets.

(joint work with D. Petrisan and J. Velebil)

This talk is part of the Logic and Semantics Seminar (Computer Laboratory) series.

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