Sentence examples for introduction rules from inspiring English sources

r1 uses → E and introduction rules, r2 uses ∧E and introduction rules, and r3 uses both → E and ∧E, and introduction rules.

Now consider a one-sided sequent calculus presentation of linear logic where the only introduction rules are right-introduction rules.

(i) Either the right-introduction or or the left-introduction rules are considered to be introduction rules.

Such clauses can naturally be interpreted as describing introduction rules for atoms.

This means that not the introduction rules are considered basic but the consequences of defining conditions.

From the point of view of proof-theoretic semantics the following two points are essential: (1)  Introduction rules (clauses) for logically compound formulas are not distinguished in principle from introduction rules (clauses) for atoms.

The use of the tautology introduction rule or one of the essentially equivalent rules is the main vehicle of shortening proofs.

In some logic texts, the introduction rule is proved as a "deduction theorem".

Prawitz (1985; 2005) argues that any formally suitable introduction rule can fix the meaning for a logical constant.

As a consequence, it destroys the introduction form property that every closed derivation can be reduced to one which uses an introduction rule in the last step.

For example, the agent (B ⅋ C) becomes (by applying the ⅋-right introduction rule) the two agents B and C (now working in parallel).