Abstract
The formal semantics of a given Horn sentence is usually defined as a set of ground atoms, which is really the minimal Herbrand interpretation of the Horn sentence, by both model-theoretic and fixpoint approaches. In the present paper, we propose another denotational semantics of a Horn sentence, denoting the set of substitutions with which atoms are derivable by unit deduction from the Horn sentence to get a direct correspondence between the semantics of the Horn sentence and the answer set concerned with its computation, and give denotational semantics even when the Horn sentence is unsatisfiable. In accordance with the unit deductions from a Horn sentence, we define a continuous function from a direct product of powersets of a substitution set to itself, and regard the least fixpoint of the function as the semantics, which can provide the answer set for computations of the Horn sentence.
Published Version
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