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Studia Logica

, Volume 101, Issue 4, pp 713–747 | Cite as

The Proof by Cases Property and its Variants in Structural Consequence Relations

  • Petr Cintula
  • Carles NogueraEmail author
Article

Abstract

This paper is a contribution to the study of the rôle of disjunction in Abstract Algebraic Logic. Several kinds of (generalized) disjunctions, usually defined using a suitable variant of the proof by cases property, were introduced and extensively studied in the literature mainly in the context of finitary logics. The goals of this paper are to extend these results to all logics, to systematize the multitude of notions of disjunction (both those already considered in the literature and those introduced in this paper), and to show several interesting applications allowed by the presence of a suitable disjunction in a given logic.

Keywords

Abstract Algebraic Logic Generalized disjunction Proof by cases properties Consequence relations Filter-distributive logics Protoalgebraic logics 

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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Institute of Computer Science Academy of Sciences of the Czech RepublicPragueCzech Republic
  2. 2.Faculty of Mathematics and GeoinformaticsVienna University of TechnologyViennaAustria
  3. 3.Artificial Intelligence Research Institute, IIIASpanish National Research Council, CSIC Campus de la Universitat Autònoma de BarcelonaBellaterraSpain
  4. 4.Institute of Information Theory and Automation Academy of Sciences of the Czech RepublicPrague 8Czech Republic

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