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IBM Journal of Research and Development  
Volume 25, Number 4, Page 327 (1981)
Finite Element Analysis
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Positive First-Order Logic Is NP-Complete

by D. Kozen
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.
Related Subjects: Complexity; Mathematics (applied)