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# Logic1202 - Completeness of axiom systems 1 2 3 Axiom...

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Completeness of axiom systems 1. Axiom system U0 2. Completeness of U0 3. Other axiom systems

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Final exam: Monday (12/14) 7pm . No paper assignment: focus on the exam! HW #10 (last HW set due Wednesday, 12/9) 1. There is no ambiguity involved in the formula X1R … & Xn. Show this by proving the following claim by induction: Any formula X, in which the only
How to show an axiom system is cor- rect? For correctness, two things must be shown: 1. all axioms are tautologies (or valid for FOL). 2. for each inference rule, if all the premises (above ___) are true, then so is the conclusion (below ___). C Because a proof in an axiom system is of the inductive nature, an inference rule preserves the property of “being a tautology”. There-

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An axiom system U0 There is no ambiguity about X1& … E Xn without ( ) (why? – HW #10). Smullyan calls it a meta-schema (why?). Inference rules I-IV (call them simply Rules I-IV). U0 is correct. All axioms are tautologies, and for each inference rule, if the
U0 is complete. All tautologies are provable in U0. Toward the proof of completeness of U0,

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Logic1202 - Completeness of axiom systems 1 2 3 Axiom...

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