On the ‘transitivity’ of consequence relations

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Abstract

A binary relation R on a set S is transitive iff for all a,b,c ∈ S, if aRb and bRc, then aRc. This almost never applies to the relations logicians tend to think of as consequence relations; where such relations are relations on a set at all, they are rarely transitive. Yet it is common to hear consequence relations described as ‘transitive’, and to see rules imposed to ensure ‘transitivity’ of these relations. This article attempts to clarify the situation.

Original languageEnglish
Pages (from-to)433-450
Number of pages18
JournalJournal of Logic and Computation
Volume28
Issue number2
DOIs
Publication statusPublished - 2018
Externally publishedYes

Keywords

  • Abstract logic
  • Consequence relations
  • Transitivity

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