Discussion
Why is first order entailment only semidecidable?
Answer: A
A complete procedure will eventually derive any entailed sentence, but when the sentence is not entailed it may search forever without ever concluding that. That is the semidecidability result. Procedures are complete, and infinite domains and quantifiers are the reasons behind it rather than the statement. A guarantee that holds in one direction only is a genuine limitation rather than a defect of implementation, and no better algorithm will remove it.
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