On the Construction of Analytic Sequent Calculi for Sub-classical Logics

  • Ori Lahav
  • Yoni Zohar
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8652)


We study the question of when a given set of derivable rules in some basic analytic propositional sequent calculus forms itself an analytic calculus. First, a general syntactic criterion for analyticity in the family of pure sequent calculi is presented. Next, given a basic calculus admitting this criterion, we provide a method to construct weaker pure calculi by collecting simple derivable rules of the basic calculus. The obtained calculi are analytic-by-construction. While the criterion and the method are completely syntactic, our proofs are semantic, based on interpretation of sequent calculi via non-deterministic valuation functions. In particular, this method captures calculi for a wide variety of paraconsistent logics, as well as some extensions of Gurevich and Neeman’s primal infon logic.


Classical Logic Proof System Context Sequent Sequent Calculus Paraconsistent Logic 
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  1. 1.
    Anderson, A.R., Belnap, N.D.: Entailment: The Logic of Relevance and Neccessity, vol. I. Princeton University Press (1975)Google Scholar
  2. 2.
    Avron, A.: Simple consequence relations. Inf. Comput. 92(1), 105–139 (1991)CrossRefzbMATHMathSciNetGoogle Scholar
  3. 3.
    Avron, A., Konikowska, B., Zamansky, A.: Modular construction of cut-free sequent calculi for paraconsistent logics. In: Proceedings of the 27th Annual IEEE Symposium on Logic in Computer science (LICS), pp. 85–94 (2012)Google Scholar
  4. 4.
    Avron, A., Lev, I.: Non-deterministic multiple-valued structures. Journal of Logic and Computation 15(3), 241–261 (2005)CrossRefzbMATHMathSciNetGoogle Scholar
  5. 5.
    Beklemishev, L., Gurevich, Y.: Propositional primal logic with disjunction. Journal of Logic and Computation 24(1), 257–282 (2014)CrossRefzbMATHMathSciNetGoogle Scholar
  6. 6.
    Béziau, J.-Y.: Sequents and bivaluations. Logique et Analyse 44(176), 373–394 (2001)zbMATHMathSciNetGoogle Scholar
  7. 7.
    Cotrini, C., Gurevich, Y.: Basic primal infon logic. Journal of Logic and Computation (2013)Google Scholar
  8. 8.
    Kamide, N.: A hierarchy of weak double negations. Studia Logica 101(6), 1277–1297 (2013)CrossRefzbMATHMathSciNetGoogle Scholar
  9. 9.
    Lahav, O., Avron, A.: A unified semantic framework for fully structural propositional sequent systems. ACM Trans. Comput. Logic 27, 1–33 (2013)MathSciNetGoogle Scholar
  10. 10.
    Lahav, O., Zohar, Y.: Sat-based decision procedure for analytic pure sequent calculi. To appear in Proceedings of the 7th International Joint Conference on Automated Reasoning, IJCAR (2014)Google Scholar
  11. 11.
    Miller, D., Pimentel, E.: A formal framework for specifying sequent calculus proof systems. Theoretical Computer Science 474(0), 98–116 (2013)CrossRefzbMATHMathSciNetGoogle Scholar
  12. 12.
    Sette, A.M.: On the propositional calculus P1. Mathematica Japonicae 18(13), 173–180 (1973)zbMATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Ori Lahav
    • 1
  • Yoni Zohar
    • 1
  1. 1.School of Computer ScienceTel Aviv UniversityIsrael

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