University of Cambridge > Talks.cam > Logic and Semantics Seminar (Computer Laboratory) > An overview of nominal algebra, lattice, representation and dualities for computer science foundations

An overview of nominal algebra, lattice, representation and dualities for computer science foundations

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Nominal algebra lets us axiomatise substitution and quantifiers, and thus the new-quantifier, first-order logic, and the lambda-calculus. Nominal lattice theory lets us characterise binders as greatest and least upper bounds subject to freshness conditions; this is possible for “forall” and “exists” and surprisingly also for “lambda”.

From this follow a body of soundness, completeness, representation, and topological duality results for algebraic/lattice-theoretic theories in nominal sets and topological spaces. A great deal of structure is revealed by this, which I will outline.

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

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