Inference in first-order logic
Inference in first-order logic
Inference in first-order logic
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Properties of forward cha<strong>in</strong><strong>in</strong>g<br />
♦ Sound and complete for <strong>first</strong>-<strong>order</strong> def<strong>in</strong>ite clauses<br />
(proof similar to propositional proof)<br />
♦ Datalog = <strong>first</strong>-<strong>order</strong> def<strong>in</strong>ite clauses and no functions<br />
♦ FC term<strong>in</strong>ates for Datalog <strong>in</strong> poly iterations: at most p · n k<br />
literals<br />
♦ general case: may not term<strong>in</strong>ate if α is not entailed<br />
♦ unavoidable: entailment with def<strong>in</strong>ite clauses (with<br />
functions) is semidecidable<br />
<strong>Inference</strong> <strong>in</strong> <strong>first</strong>-<strong>order</strong> <strong>logic</strong> – 15
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