 
Summary: Weak Focusing for Ordered Linear Logic
Robert J. Simmons Frank Pfenning
April 7, 2011
CMUCS10147
School of Computer Science
Carnegie Mellon University
Pittsburgh, PA 15213
Support for this research was provided by the Fundação para a Ciência e a Tecnologia (Portuguese Foundation
for Science and Technology) through the Carnegie Mellon Portugal Program under Grant NGN44 and by an X10
Innovation Award from IBM.
Keywords: Focusing, Linear Logic, Ordered Linear Logic, Cut Admissibility, Identity, Hypo
thetical focus, Equality
Abstract
Ever since Andreoli's pioneering work in linear logic, it has been understood that the technique of
focusing can be used to obtain the operational semantics of a logic programming language from
a logic. In previous work, Polakow presented ordered linear logic and gave a backwardchaining
operational semantics semantics for the uniform fragment of the logic, and the authors have pre
viously presented a fragment of ordered linear logic suitable to a forwardchaining operational
semantics. In this report we give a socalled weakly focused sequent calculus for a polarized first
order ordered linear logic with equality assumptions, generalizing and extending both of these
