Some contributions to the logical analysis of circumscription

  • Gerhard Jaeger
Nondassical Deducation
Part of the Lecture Notes in Computer Science book series (LNCS, volume 230)


After sketching the first and second order version of McCarthy's predicate circumscription, we introduce the notion of positive disjunctive circumscription as an approach to (this form of) non-monotonic reasoning which guarantees consistency. We define the positive disjunctive extension PD(T) of a first order theory T and show that it is conservative over T. Then we turn to sets defined by positive disjunctive circumscription and state a boundedness theorem concerning their stages. The last considerations refer to generalizations of positive disjunctive circumscription. We discuss the inclusion of (intersective) priority relations and extensions by iteration.


Priority Relation Order Theory Proof Theory Relation Symbol Conservative Extension 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • Gerhard Jaeger
    • 1
  1. 1.ETH-Zuerich MathematikSwitzerland

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