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Full-Text Articles in Physical Sciences and Mathematics
General Model Theoretic Semantics For Higher-Order Horn Logic Programming, Mino Bai, Howard A. Blair
General Model Theoretic Semantics For Higher-Order Horn Logic Programming, Mino Bai, Howard A. Blair
Electrical Engineering and Computer Science - Technical Reports
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 …
The Expressiveness Of Locally Stratified Programs, Howard A. Blair, Wiktor Marek, John S. Schlipf
The Expressiveness Of Locally Stratified Programs, Howard A. Blair, Wiktor Marek, John S. Schlipf
Electrical Engineering and Computer Science - Technical Reports
This paper completes an investigation of the logical expressibility of finite, locally stratified, general logic programs. We show that every hyperarithmetic set can be computed by a suitably chosen locally stratified logic program (as a set of values of a predicate over its perfect model). This is an optimal result, since the perfect model of a locally stratified program is itself an implicitly definable hyperarithmetic set (under a recursive coding of the Herbrand base); hence to obtain all hyperarithmetic sets requires something new, in this case selecting one predicate from the model. We find that the expressive power of programs …