Studia Logica

, Volume 91, Issue 2, pp 273–293 | Cite as

Proof Systems for Reasoning about Computation Errors

  • Arnon AvronEmail author
  • Beata Konikowska


In the paper we examine the use of non-classical truth values for dealing with computation errors in program specification and validation. In that context, 3-valued McCarthy logic is suitable for handling lazy sequential computation, while 3-valued Kleene logic can be used for reasoning about parallel computation. If we want to be able to deal with both strategies without distinguishing between them, we combine Kleene and McCarthy logics into a logic based on a non-deterministic, 3-valued matrix, incorporating both options as a non-deterministic choice. If the two strategies are to be distinguished, Kleene and McCarthy logics are combined into a logic based on a 4-valued deterministic matrix featuring two kinds of computation errors which correspond to the two computation strategies described above. For the resulting logics, we provide sound and complete calculi of ordinary, two-valued sequents.


three-valued logics four-valued logics parallel computation lazy sequential computation computation errors non-deterministic matrices sequent calculi 


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Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.School of Computer ScienceTel-Aviv UniversityRamat AvivIsrael
  2. 2.Institute of Computer SciencePolish Academy of SciencesWarsawPoland

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