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The Proof by Cases Property and its Variants in Structural Consequence Relations |
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| Authors: | Petr Cintula Carles Noguera |
| Institution: | 1. Institute of Computer Science Academy of Sciences of the Czech Republic, Pod vodárenskou vě?í 2, 182 07, Prague, Czech Republic 2. Faculty of Mathematics and Geoinformatics, Vienna University of Technology, Wiedner Hauptstrasse 8, 1040, Vienna, Austria 3. Artificial Intelligence Research Institute, IIIA, Spanish National Research Council, CSIC Campus de la Universitat Autònoma de Barcelona, 08193, Bellaterra, Catalonia, Spain 4. Institute of Information Theory and Automation Academy of Sciences of the Czech Republic, Pod vodárenskou vě?í 4, 182 08, Prague 8, Czech Republic |
| 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. |
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