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Theory and Decision

, Volume 1, Issue 2, pp 179–217 | Cite as

On inference from inconsistent premisses

  • Nicholas Rescher
  • Ruth Manor
Article

Abstract

The main object of this paper is to provide the logical machinery needed for a viable basis for talking of the ‘consequences’, the ‘content’, or of ‘equivalences’ between inconsistent sets of premisses.

With reference to its maximal consistent subsets (m.c.s.), two kinds of ‘consequences’ of a propositional set S are defined. A proposition P is a weak consequence (W-consequence) of S if it is a logical consequence of at least one m.c.s. of S, and P is an inevitable consequence (I-consequence) of S if it is a logical consequence of all the m.c.s. of S. The set of W-consequences of a set S it determines (up to logical equivalence) its m.c.s. (This enables us to define a normal form for every set such that any two sets having the same W-consequences have the same normal form.) The W-consequences and I-consequences will not do to define the ‘content’ of a set S. The first is too broad, may include propositions mutually inconsistent, the second is too narrow. A via media between these concepts is accordingly defined: P is a P-consequence of S, where P is some preference criterion yielding some of the m.c.s. of S as preferred to others, and P is a consequence of all of the P-preferred m.c.s. of S. The bulk of the paper is devoted to discussion of various preference criteria, and also surveys the application of this machinery in diverse contexts - for example, in connection with the processing of mutually inconsistent reports.

Keywords

Normal Form Weak Consequence Logical Consequence Inevitable Consequence Preference Criterion 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© D. Reidel Publishing Company 1970

Authors and Affiliations

  • Nicholas Rescher
  • Ruth Manor

There are no affiliations available

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