Synonyms
True answer (Maybe answer); Validity (Satisfiability)
Definition
LetT be a finite theory expressed in a language L, and φ an L-sentence. Then T finitely entails φ, in notation T ⊧ φ, if all finite models of T also are models of φ. A theory T is said to be complete in the finite if for each L-sentence φ either T ⊧ φ or T ⊧ ¬φ. In particular, if T is incomplete (not complete in the finite), then there is an L-sentence φ, such that T ⊠φ and T ⊠¬φ. It follows from classical logic that a first order theory is complete in the finite if and only if all its finite models are isomorphic. Consider now a theory
where a, b, and c are constants. This theory is complete, and clearly for instance T ⊧ R(a, b), T ⊧ R(a, c), and T ⊠R(d, c), for all constants d different from a and b....
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Grahne, G. (2018). Certain (and Possible) Answers. In: Liu, L., Ă–zsu, M.T. (eds) Encyclopedia of Database Systems. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-8265-9_1254
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