Summary: Games and Full Completeness for Multiplicative Linear Logic
Samson Abramsky and Radha Jagadeesan
Department of Computing
Imperial College of Science, Technology and Medicine
Technical Report DoC 92/24
September 25, 1992
Abstract
We present a game semantics for Linear Logic, in which formulas denote games and
proofs denote winning strategies. We show that our semantics yields a categorical model of
Linear Logic and prove full completeness for Multiplicative Linear Logic with the MIX rule:
every winning strategy is the denotation of a unique cut­free proof net. A key role is played
by the notion of history­free strategy; strong connections are made between history­free
strategies and the Geometry of Interaction. Our semantics incorporates a natural notion of
polarity, leading to a refined treatment of the additives. We make comparisons with related
work by Joyal, Blass et al.
1

Contents
1 Introduction 3
1.1 Overview of Results : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 3

Source: Abramsky, Samson - Computing Laboratory, University of Oxford

Collections: Computer Technologies and Information Sciences