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[joanne@theory.lcs.mit.edu: MIT TOC Seminar--Radha Jagadeesan-Thursday 10:00a.m. July 9, 1992]

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From: Joanne Talbot <joanne@theory.lcs.mit.edu>
Date: Tue, 7 Jul 92 17:10:28 EDT
To: theory-seminars@theory.lcs.mit.edu
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Subject: MIT TOC Seminar--Radha Jagadeesan-Thursday 10:00a.m. July 9, 1992

            
            MIT TOC SEMINAR
            
            Radha Jagadeesan
            Imperial College
            London, England

Title: "New Foundations for the Geometry of Interaction" 

Thursday, July 9, 1992 at 10:00am in NE43-308

Abstract:

Girard has proposed the programme of Geometry of Interaction, which
aims to to find a new middle ground between denotational and
operational semantics, capturing the essential features of
computational dynamics in a syntax-free fashion using denotational
tools.  He has implemented this programme using the formalism of
C*-algebras.

We present a new formal embodiment of Girard's programme, with the
following salient features:

1. We give a concrete computational interpretation of the Geometry of
Interaction in terms of dataflow networks.

2. Our formalisation is based on Domain Theory, rather than
C*-algebras.  We replace Girard's "execution formula" by a least
fixpoint, essentially a generalisation of Kahn's semantics for
feedback in dataflow networks.  This enables us to interpret the whole
of Classical Linear Logic, and to prove soundness in full generality,
thus addressing the technical limitations of Girard's formalisation.

3. We show how the interpretation arises from the construction of a
categorical model of Linear Logic, and identify exactly what structure
is required of the ambient category in order to carry out the
interpretation.  This makes the definition of the interpretation much
more transparent.

This is joint work with Samson Abramsky.

Host: Albert Meyer