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Weak Focusing for Ordered Linear Logic Robert J. Simmons Frank Pfenning

Summary: Weak Focusing for Ordered Linear Logic
Robert J. Simmons Frank Pfenning
April 7, 2011
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 NGN-44 and by an X10
Innovation Award from IBM.
Keywords: Focusing, Linear Logic, Ordered Linear Logic, Cut Admissibility, Identity, Hypo-
thetical focus, Equality
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 backward-chaining
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 forward-chaining operational
semantics. In this report we give a so-called weakly focused sequent calculus for a polarized first-
order ordered linear logic with equality assumptions, generalizing and extending both of these


Source: Andrews, Peter B. - Department of Mathematical Sciences, Carnegie Mellon University
Pfenning, Frank - School of Computer Science, Carnegie Mellon University


Collections: Computer Technologies and Information Sciences; Mathematics