Communication: Positive First-Order Logic is NP-Complete

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 φ is a positive first-order sentence, then the problem of determining whether φ is true in all models of Σ is NP-complete.

[1]  B. Dreben,et al.  The decision problem: Solvable classes of quantificational formulas , 1979 .

[2]  Harry R. Lewis,et al.  Complexity of solvable cases of the decision problem for the predicate calculus , 1978, 19th Annual Symposium on Foundations of Computer Science (sfcs 1978).

[3]  Dexter Kozen,et al.  Complexity of Boolean Algebras , 1980, Theor. Comput. Sci..

[4]  Dexter Kozen,et al.  Complexity of finitely presented algebras , 1977, STOC '77.

[5]  Elbert Ernest Sibert.  A machine-oriented logic incorporating the equality relation , 1967 .

[6]  L. Wos,et al.  Paramodulation and Theorem-Proving in First-Order Theories with Equality , 1983 .

[7]  Mike Paterson,et al.  Linear unification , 1976, STOC '76.

[8]  Harry R. Lewis,et al.  Unsolvable classes of quantificational formulas , 1979 .

[9]  J. Ferrante,et al.  The computational complexity of logical theories , 1979 .

[10]  Derek C. Oppen,et al.  A 2^2^2^pn Upper Bound on the Complexity of Presburger Arithmetic , 1978, J. Comput. Syst. Sci..

[11]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[12]  M. Fischer,et al.  SUPER-EXPONENTIAL COMPLEXITY OF PRESBURGER ARITHMETIC , 1974 .

[13]  David S. Johnson,et al.  Computers and In stractability: A Guide to the Theory of NP-Completeness. W. H Freeman, San Fran , 1979 .

[14]  Charles Rackoff.  On the complexity of the theories of weak direct products (Preliminary Report) , 1974, STOC '74.