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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
CMU-CS-10-147
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
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 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