Logic1125 - Completeness and other ZB results 1. 2. 3....

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Reading for the next week Ch.20 (skip Ch.19) HW #9 (due Monday, 11/30) 1. By applying a procedure similar to the propositional case, show the correctness of the tableau method for first-order logic. 2. Construct a systematic tableau (as defined in the textbook) for T∀x∃yRxyδ ∃x∀y~Rxy and show that it
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Hintikka set for first-order logic A set of closed formulas (sentences) sat- isfying: H0~H2 (the same as the propositional case) H3. For any γ&S and any parameter a, γ(a)“S. H4. For any δ&S and some parameter a, δ(a)“S. Hintikka’s lemma for first-order logic Every Hintikka set is satisfiable – espe-
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For every predicate P of degree n, we give the following interpretation I. P*(a1, …,an) iff TPa1…anXS. Then every element is S is true under I. (induction on the degree of elements) The basis step: all elements of degree o are of the form TPa1…an or FPa1…an, which are true under I. The inductive step: refer to Problem 18.1.
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Logic1125 - Completeness and other ZB results 1. 2. 3....

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