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Least and Greatest Fixed Points in Linear Logic DAVID BAELDE, University of Minnesota The rst-order theory of MALL (multiplicative, additive linear logic) over only equalities is a well-structured but weak logic since it cannot capture unbounded (in nite) behavior. Instead of accounting for unbounded behavior via the addition of the exponentials (! and ?), we add least and greatest xed point operators. The resulting logic, which we call MALL, satis es two fundamental proof theoretic properties: we establish weak normalization for it, and we design a focused proof system that we prove complete with respect to the initial system. That second result provides a strong normal form for cut-free proof structures that can be used, for example, to help automate proof search. We show how these foundations can be applied to intuitionistic logic. Categories and Subject Descriptors: F.4.1 [Mathematical Logic and Formal Languages]: Mathematical Logic Proof theory; F.3.1 [Logics and Meanings of Programs]: Specifying and Verifying and Reasoning about Programs Speci cation techniques; F.3.3 [Logics and Meanings of Programs]: Studies of Program Constructs Program and recursion schemes General Terms: Design, Theory, Veri cation Additional Key Words and Phrases: Fixed points, linear logic, (co)induction, recursive de nitions, cut elimination,
ACM Transactions on Computational Logic (TOCL) – Association for Computing Machinery
Published: Jan 1, 2012
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