Foundations of logic programming; (2nd extended ed.)
Foundations of logic programming; (2nd extended ed.)
Towards a theory of declarative knowledge
Foundations of deductive databases and logic programming
On the declarative semantics of deductive databases and logic programs
Foundations of deductive databases and logic programming
The alternating fixpoint of logic programs with negation
PODS '89 Proceedings of the eighth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Every logic program has a natural stratification and an iterated least fixed point model
PODS '89 Proceedings of the eighth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
The well-founded semantics for general logic programs
Journal of the ACM (JACM)
The alternating fixpoint of logic programs with negation
PODS '89 Selected papers of the eighth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Stratified negation in temporal logic programming and the cycle-sum test
Theoretical Computer Science
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We give a purely model-theoretic (denotational) characterization of the semantics of logic programs with negation allowed in clause bodies. In our semantics (the first of its kind) the meaning of a program is, as in the classical case, the unique minimum model in a program-independent ordering. We use an expanded truth domain that has an uncountable linearly ordered set of truth values between False (the minimum element) and True (the maximum), with a Zero element in the middle. The truth values below Zero are ordered like the countable ordinals. The values above Zero have exactly the reverse order. Negation is interpreted as reflection about Zero followed by a step towards Zero; the only truth value that remains unaffected by negation is Zero. We show that every program has a unique minimum model MP, and that this model can be constructed with a TP iteration which proceeds through the countable ordinals. Furthermore, collapsing the true and false values of the infinite-valued model MP to (the classical) True and False, gives a three-valued model identical to the well-founded one.