Archive for Mathematical Logic

, Volume 54, Issue 3–4, pp 425–437 | Cite as

The modal logic of Reverse Mathematics

  • Carl Mummert
  • Alaeddine Saadaoui
  • Sean Sovine


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.


Mathematics Modal logic Strict implication Automated reasoning 

Mathematics Subject Classification

03B30 03B45 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Marshall UniversityHuntingtonUSA
  2. 2.U.S. Army Corps of EngineersWashingtonUSA

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