Description

• Title:
  An Inferentially Many-Valued Two-Dimensional Notion of Entailment
• Creator:
  Blasio, Carolina;
  Marcos, João;
  Wansing, Heinrich
• Contributor:
  IFCH / UNICAMP, 13083-896 Campinas – SP, Brazil;
  DIMAp / UFRN, 59078-970 Natal – RN, Brazil;
  Ruhr University Bochum / Department of Philosophy II, Universitätsstraße 150, D-44780 Bochum, Germany;
  carolblasio@gmail.com;
  jmarcos@dimap.ufrn.br;
  Heinrich.Wansing@rub.de
• Description:
  Starting from the notions of q-entailment and p-entailment, a two-dimensional notion of entailment is developed with respect to certain generalized q-matrices referred to as B-matrices. After showing that every purely monotonic singleconclusion consequence relation is characterized by a class of B-matrices with respect to q-entailment as well as with respect to p-entailment, it is observed that, as a result, every such consequence relation has an inferentially four-valued characterization. Next, the canonical form of B-entailment, a two-dimensional multiple-conclusion notion of entailment based on B-matrices, is introduced, providing a uniform framework for studying several different notions of entailment based on designation, antidesignation, and their complements. Moreover, the two-dimensional concept of a B-consequence relation is defined, and an abstract characterization of such relations by classes of B-matrices is obtained. Finally, a contribution to the study of inferential many-valuedness is made by generalizing Suszko’s Thesis and the corresponding reduction to show that any B-consequence relation is, in general, inferentially four-valued.
• Object availability:
  free access
• Rights:
  © Copyright by Authors, Łódź 2017; © Copyright for this edition by Uniwersytet Łódzki, Łódź 2017
• Date:
  2018.06.22;
  2017
• Type:
  Article
• Language:
  English
• Format:
  application/pdf
• Publisher:
  Wydawnictwo Uniwersytetu Łódzkiego
• Relation:
  Bulletin of the Section of Logic;3/4;
  46
• Subject:
  Inferential many-valuedness;
  two-dimensional entailment;
  B-matrices;
  B-consequence relations;
  monotonic consequence relations;
  q-entailment;
  p-entailment;
  Suszko Reduction
• Identifier:
  0138-0680;
  http://hdl.handle.net/11089/25179 ;
  2449-836X;
  10.18778/0138-0680.46.3.4.05
• Data provider:
  Repozytorium Uniwersytetu Łódzkiego
• Can I use it?:
  seek permission
• Type:
  image