Reducing Nondeterminism in the Calculus of Structures

  • Ozan Kahramanoğulları
Conference paper

DOI: 10.1007/11916277_19

Part of the Lecture Notes in Computer Science book series (LNCS, volume 4246)
Cite this paper as:
Kahramanoğulları O. (2006) Reducing Nondeterminism in the Calculus of Structures. In: Hermann M., Voronkov A. (eds) Logic for Programming, Artificial Intelligence, and Reasoning. LPAR 2006. Lecture Notes in Computer Science, vol 4246. Springer, Berlin, Heidelberg

Abstract

The calculus of structures is a proof theoretical formalism which generalizes the sequent calculus with the feature of deep inference: In contrast to the sequent calculus, inference rules can be applied at any depth inside a formula, bringing shorter proofs than any other formalisms supporting analytical proofs. However, deep applicability of the inference rules causes greater nondeterminism than in the sequent calculus regarding proof search. In this paper, we introduce a new technique which reduces nondeterminism without breaking proof theoretical properties and provides a more immediate access to shorter proofs. We present this technique on system BV, the smallest technically non-trivial system in the calculus of structures, extending multiplicative linear logic with the rules mix, nullary mix, and a self-dual non-commutative logical operator. Because our technique exploits a scheme common to all the systems in the calculus of structures, we argue that it generalizes to these systems for classical logic, linear logic, and modal logics.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Ozan Kahramanoğulları
    • 1
  1. 1.Department of ComputingImperial College LondonUK

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