Niveau: Supérieur, Doctorat, Bac+8
Noname manuscript No. (will be inserted by the editor) A framework for proof systems Vivek Nigam and Dale Miller the date of receipt and acceptance should be inserted later Abstract Linear logic can be used as a meta-logic to specify a range of object-level proof systems. In particular, we show that by providing different polarizations within a focused proof system for linear logic, one can account for natural deduction (normal and non-normal), sequent proofs (with and without cut), and tableaux proofs. Armed with just a few, simple variations to the linear logic encodings, more proof systems can be accommodated, including proof system using generalized elimination and generalized introduction rules. In general, most of these proof systems are developed for both classical and intuitionistic logics. By using simple results about linear logic, we can also give simple and modular proofs of the soundness and relative completeness of all the proof systems we consider. 1 Introduction Logics and type systems have been exploited in recent years as frameworks for the specification of deduction in a number of logics. The most common such meta-logics and logical frameworks have been based on intuitionistic logic (see, for example, [Felty and Miller, 1988, Paulson, 1989]) or dependent types (see [Harper et al., 1993, Pfenning, 1989]).
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