Lecture 19: The Subformula Property

The second step in the development of the inverse method is the restriction of initial sequents and inference rules to subformulas of the goal sequent. It is easy to see that it is complete, because every successful derivation in the forward sequent calculus naturally has this subformula property. To obtain as sharp a restriction as possible, we analyze positive and negative occurrences separately.

Reading

• Pages 88-90 of Handout 13 on The Subformula Property (also availabe in PDF format).

Key Concepts

• Subformula property
• Positive and negative occurrences
• Labeling of subformulas

Links

• Previous lecture: Forward Sequent Calculus
• Next lecture: Subsumption