General model theoretic semantics for Higher-Order horn logic programming

  • Mino Bai
  • Howard A. Blair
Session 11: Semantics II
Part of the Lecture Notes in Computer Science book series (LNCS, volume 624)


We introduce model-theoretic semantics [6] for Higher-Order Horn logic programming language. One advantage of logic programs over conventional non-logic programs has been that the least fixpoint is equal to the least model, therefore it is associated to logical consequence and has a meaningful declarative interpretation. In simple theory of types [9] on which Higher-Order Horn logic programming language is based, domain is dependent on interpretation [10]. To define T P operator for a logic program P, we need a fixed domain without regard to interpretation which is usually taken to be a set of atomic propositions. We build a semantics where we can fix a domain while changing interpretations. We also develop a fixpoint semantics based on our model, and show that we can get the least fixpoint which is the least model. Using this fixpoint we prove the completeness of the interpreter of our language in [14].


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Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • Mino Bai
    • 1
  • Howard A. Blair
    • 1
  1. 1.School of Computer and Information Science, Center for Science and Technology/Fourth FloorSyracuse UniversitySyracuseUSA

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