Non-determinism in logic-based languages

  • Serge Abiteboul
  • Victor Vianu
Article

Abstract

The use of non-determinism in logic-based languages is motivated using pragmatic and theoretical considerations. Non-deterministic database queries and updates occur naturally, and there exist non-deterministic implementations of various languages. It is shown that non-determinism resolves some difficulties concerning the expressive power of deterministic languages: there are non-deterministic languages expressing low complexity classes of queries/updates, whereas no such deterministic languages are known. Various mechanisms yielding non-determinism are reviewed. The focus is on two closely related families of non-deterministic languages. The first consists of extensions of Datalog with negations in bodies and/or heads of rules, with non-deterministic fixpoint semantics. The second consists of non-deterministic extensions of first-order logic and fixpoint logics, using thewitness operator. The expressive power of the languages is characterized. In particular, languages expressing exactly the (deterministic and non-deterministic) queries/updates computable in polynomial time are exhibited, whereas it is conjectured that no analogous deterministic language exists. The connection between non-deterministic languages and determinism is also explored. Several problems of practical interest are examined, such as checking (statically or dynamically) if a given program is deterministic, detecting coincidence of deterministic and non-deterministic semantics, and verifying termination for non-deterministic programs.

Keywords

Neural Network Artificial Intelligence Complex System Nonlinear Dynamics Polynomial Time 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Copyright information

© J.C. Baltzer A.G. Scientific Publishing Company 1991

Authors and Affiliations

  • Serge Abiteboul
    • 1
  • Victor Vianu
    • 2
  1. 1.INRIA, Rocquencourtle Chesnay CedexFrance
  2. 2.University of California at San DiegoSan DiegoUSA

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