CS486 Spring 1997

Lecture 5 Tuesday, Feb. 4, 1997

Relevant Reading: Smullyan Chapter XI §1 (p.101-108)

Review of consistency and completeness

consistency: follow interpretation down to build open path
completeness: build countermodel going up from open path
(open path is saturated)

Duality principle

using intuition to guide tableau proof
discover duality: goals and assumptions, sequents
inherent parallelism
dual of Tableau is Refinement Logic with multiple goals

Refinement Logics and Gentzen systems

multiple goals vs. single goal
sequent rules
Gentzen is isomorphic to Refinement with multiple goals (see Smullyan p.105-106)

Validity is decidable-handout from Constable &Howe 1990

evaluation of sequents
valid sequents: is
Theorem .

Multiple goals to (single goal and

is the only need for multiple goals?
single conclusion rules, issue of rule
(Excluded Middle Axiom, Magic)
example of simple refinement proofs
Nuprl proof forms

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