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      The modal logic of Reverse Mathematics

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          Abstract

          The implication relationship between subsystems in Reverse Mathematics has an underlying logic, which can be used to deduce certain new Reverse Mathematics results from existing ones in a routine way. We use techniques of modal logic to formalize the logic of Reverse Mathematics into a system that we name s-logic. We argue that s-logic captures precisely the "logical" content of the implication and nonimplication relations between subsystems in Reverse Mathematics. We present a sound, complete, decidable, and compact tableau-style deductive system for s-logic, and explore in detail two fragments that are particularly relevant to Reverse Mathematics practice and automated theorem proving of Reverse Mathematics results.

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          1 Modal logic: a semantic perspective

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            V -DISCUSSIONS

             C. LEWIS (1914)
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              Author and article information

              Journal
              2014-01-03
              Article
              10.1007/s00153-015-0417-z
              1401.0648

              http://arxiv.org/licenses/nonexclusive-distrib/1.0/

              Custom metadata
              03B30 (Primary) 03B45 (Secondary)
              Archive for Mathematical Logic May 2015, Volume 54, Issue 3-4, pp 425-437
              math.LO cs.LO

              Theoretical computer science, Logic & Foundation

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