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# 15-815 Automated Theorem Proving

# Lecture 7: Quantification

We review the development of the class so far, now considering
quantifiers and negation. This requires the notion of a
parametric judgment, that is, a judgment with a free parameter
for which we can substitute arbitrary objects from the right
syntactic class.

We then discuss the annotation of sequent derivations with
proof terms, and a first simple search strategies which is
shown to be sound and complete. This is the restriction
to atomic initial sequents.

### Reading

The material on parametric judgments, quantification, and
negation is distributed throughout the notes handed
out so far (collected in the file atp.ps).
Parametric judgment are introduction on page 3, negation on page 10,
the quantifiers on pages 12-14. Material on proof term assignment for
the sequent calculus is in the handout below.

- Handout 6 on
*Proof Terms for
Sequents* (also available in PDF
format).

### Key Concepts

- Parametric judgments
- Universal quantification
- Existential quantification
- Negation as a connective
- Atomic initial sequents

### Links

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Frank Pfenning
fp@cs