Journal of Philosophical Logic

, Volume 30, Issue 1, pp 51–55

Comments on Some Completeness Theorems of Urquhart and Méndez &; Salto

  • Kenneth Harris
  • Branden Fitelson

DOI: 10.1023/A:1017549804474

Cite this article as:
Harris, K. & Fitelson, B. Journal of Philosophical Logic (2001) 30: 51. doi:10.1023/A:1017549804474


Urquhart and Méndez and Salto claim to establish completeness theorems for the system C and two of its negation extensions. In this note, we do the following three things: (1) provide a counterexample to all of these alleged completeness theorems, (2) attempt to diagnose the mistakes in the reported completeness proofs, and (3) provide complete axiomatizations of the desired systems.

completeness substructural logic many-valued matrix 

Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • Kenneth Harris
    • 1
  • Branden Fitelson
    • 1
  1. 1.Department of Philosophy MadisonUniversity of Wisconsin-MadisonUSA

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