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Least and greatest fixed points in linear logic (2007)
| Content Provider | CiteSeerX |
|---|---|
| Author | Baelde, David Miller, Dale |
| Description | david.baelde at ens-lyon.org dale.miller at inria.fr Abstract. The first-order theory of MALL (multiplicative, additive linear logic) over only equalities is an interesting but weak logic since it cannot capture un-bounded (infinite) behavior. Instead of accounting for unbounded behavior via the addition of the exponentials (! and?), we add least and greatest fixed point operators. The resulting logic, which we call µMALL=, satisfies two fundamental proof theoretic properties. In particular, µMALL = satisfies cut-elimination, which implies consistency, and has a complete focused proof system. This second result about focused proofs provides a strong normal form for cut-free proof structures that can be used, for example, to help automate proof search. We then consider applying these two results about µMALL = to derive a focused proof system for an intuitionistic logic extended with induction and co-induction. The traditional approach to encoding intuitionistic logic into linear logic relies heavily on us-ing the exponentials, which unfortunately weaken the focusing discipline. We get a better focused proof system by observing that certain fixed points satisfy the structural rules of weakening and contraction (without using exponentials). The resulting focused proof system for intuitionistic logic is closely related to the one implemented in Bedwyr, a recent model checker based on logic programming. We discuss how our proof theory might be used to build a computational system that can partially automate induction and co-induction. 1 International Conference on Logic for Programming and Automated Reasoning (LPAR), volume 4790 of LNCS |
| File Format | |
| Language | English |
| Publisher Date | 2007-01-01 |
| Access Restriction | Open |
| Subject Keyword | Linear Logic Focused Proof First-order Theory Intuitionistic Logic Recent Model Checker Fundamental Proof Theoretic Property Strong Normal Form Linear Logic Relies Unbounded Behavior Fr Abstract Org Dale Focused Proof System Proof Theory Focusing Discipline Additive Linear Logic Traditional Approach Logic Programming Proof System Computational System Point Operator Cut-free Proof Structure Weak Logic Second Result Proof Search Structural Rule Certain Fixed Point |
| Content Type | Text |
| Resource Type | Article |
