Algebraic geometry in First Order Logic

Preprint English OPEN
Plotkin, B.;
(2003)
  • Subject: 03C05,03C98,03G99,08A70 | Mathematics - General Mathematics | Mathematics - Logic
    arxiv: Computer Science::Logic in Computer Science

In every variety of algebras $\Theta$ we can consider its logic and its algebraic geometry. In the previous papers geometry in equational logic, i.e., equational geometry has been studied. Here we describe an extension of this theory towards the First Order Logic (FOL).... View more
  • References (19)
    19 references, page 1 of 2

    Let knowledge bases KB1 = KB(G1, Φ1, F1) and KB2 = KB(G2, Φ2, F2) correspond to the given multimodels (G1, Φ1, F1) and (G2, Φ2, F2).

    Bancillon F., On the completeness of query language for relational databases, Lecture Notes in CS 64 (1978), 112-123.

    Beniaminov E., Galois theory of complete relational subalgebras of algebras of relations, logical structures, symmetry, NTI, ser. 2 (1980,), 237-261.

    Bulatov A., Jeavons, P.,, An algebraic approach to multi-sorted constraints, Proceedings of CP'03, to appear (2004), 15pp.

    Ganter B., Mineau G., Ontology, metadata, and semiotics, vol. 1867, Lecture Notes in AI, Springer-Verlag, 2000, pp. 55-81.

    Halmos P.R., Algebraic logic, New York, 1969.

    Henkin L., Monk J. D., Tarski A., Cylindric Algebras, North-Holland Publ. Co., 1985.

    Artificial Intelligence 24, 51-67.

    Krasner M., Generalisation et anlogues de la theorie de Galois, Comptes Rendus de Congress de la Victorie de l'Ass. Franc. pour l'Avancem. Sci. (1945,), 54-58.

    Lenat D., Steps to Sharing Knowledge, Toward Very Large Knowledge Bases, edited by N.J.I. Mars. IOS Press, 1995.

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