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# 15-815 Automated Theorem Proving

# Lecture 18: Forward Sequent Calculus

The sequent calculus presented so far was motivated by search for natural
deductions, starting from a goal sequent towards the initial sequents. The
advantage of such a method is that it is immediately goal-directed. The
disdvantage is the disjunctive non-determinism which in practice forces a
backtracking implementation.

We now develop a sequent calculus appropriate for forward reasoning, from
the initial sequents to the goal sequent. This sequent calculus in itself is
not yet useful for theorem proving, because the space of all possible proofs
is too large. However, in a second step we take advantage of the subformula
property for cut-free derivations to specialize the rules of the
sequent calculus to the goal sequent, thereby obaining the basis for
the *inverse method*.

### Reading

- Handout 12 on
*Forward Sequent
Calculus* (also availabe in PDF
format).

### Key Concepts

- Forward sequent calculus
- Weakening
- Contraction

### Links

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Frank Pfenning
fp@cs