Substitution

Substitution may refer to:

Science and mathematics

Other uses

Substitution (song)

"Substitution" is a single by indie rock band Silversun Pickups, and is the second single from their second album, Swoon. Since its release, the song has reached number 17 and debuted at number 35 on Billboard Alternative Songs chart. It has also charted on Billboard's Rock Songs at number 26.

Music video

In an interview, the band's frontman Brian Aubert claimed that "the clip is going to be weird. We're playing the song in a surreal Moose lodge, and then there's musical chairs going on with, like, eight Amazon-type gorgeous girls. Babes, I suppose." Aubert added, "They were actually playing musical chairs for a real prize. It got pretty ugly. Everybody in the room watching it was like, 'This is the weirdest thing.' All the girls are color-coded. In one way, it's bright and sort of silly, but the way we're looking at it is sort of depressing. In fact, I have to admit: it's by far the darkest video we've ever done."

The video was produced and directed by The Malloys and it premiered on MTVu on September 15.

Substitution (logic)

Substitution is a fundamental concept in logic. A substitution is a syntactic transformation on formal expressions. To apply a substitution to an expression means to consistently replace its variable, or placeholder, symbols by other expressions. The resulting expression is called a substitution instance of the original expression.

Propositional logic

Definition

Where Ψ and Φ represent formulas of propositional logic, Ψ is a substitution instance of Φ if and only if Ψ may be obtained from Φ by substituting formulas for symbols in Φ, always replacing an occurrence of the same symbol by an occurrence of the same formula. For example:

is a substitution instance of:

and

is a substitution instance of:

In some deduction systems for propositional logic, a new expression (a proposition) may be entered on a line of a derivation if it is a substitution instance of a previous line of the derivation (Hunter 1971, p. 118). This is how new lines are introduced in some axiomatic systems. In systems that use rules of transformation, a rule may include the use of a substitution instance for the purpose of introducing certain variables into a derivation.