From Hypersequents to Parallel Processes
Francesco Genco (TU Wien)

February 24, 2017, 11:00am - 1:00pm
Logic Group, The University of Melbourne

G09
Old Quad
Parkville 3010
Australia

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Shawn Standefer
University of Melbourne

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Francesco Genco (TU Wien) will present "From Hypersequents to Parallel Processes" on Feb 24 at 11 in Old Quad G09. 

Abstract: The system of rules formalism combines ideas from natural deduction and sequent calculus achieving a great expressive power. Focusing on propositional intermediate logics, we prove that a rather simple restriction of such formalism (two-level systems of rules) is equivalent to the hypersequent formalism. This result has several proof-theoretical consequences and, furthermore, provides a strong connection between hypersequent calculi and natural deduction. Exploiting such connection we define a Curry--Howard correspondence for Gel logic, and prove that the resulting system enjoys normalisation and the subformula property. The lambda calculus obtained features constructs representing higher-order communication between parallel processes, and its reduction rules admit a meaningful computational interpretation in terms of code optimisation by code mobility.

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