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Positive First-Order Logic Is NP-Complete

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1 Author(s)
Kozen, D. ; IBM Thomas J. Watson Research Center, Yorktown Heights, New York 10598, USA

The decision problem for positive first-order logic with equality is NP-complete. More generally, if Σ is a finite set of atomic sentences (i.e., atomic formulas of the form t1 = t2 or Rt1 … tn containing no variables) and negations of atomic sentences and if ɸ is a positive first-order sentence, then the problem of determining whether ɸ is true in all models of Σ is NP-complete.

Note: The Institute of Electrical and Electronics Engineers, Incorporated is distributing this Article with permission of the International Business Machines Corporation (IBM) who is the exclusive owner. The recipient of this Article may not assign, sublicense, lease, rent or otherwise transfer, reproduce, prepare derivative works, publicly display or perform, or distribute the Article.  

Published in:

IBM Journal of Research and Development  (Volume:25 ,  Issue: 4 )