💭Interpretation function (predicate calculus)

=== a function, which assigns a an extension (meaning) out of a universe U to each individual constant and predicate symbol==

Rules

1. For every individual constant a, $I(a)$ is an element of the universe U
2. For every n-digit predicate P, $I(P)$ is an n-digit relation (or property) in universe U

Notation

• $I$

📖 Example:

• $I(a)=a,I(b)=b,I(c)=c$
• $I(F)=\{a,c\}$
  • (F = predicate symbol designating “is female”)
• $I(L)=\{<b,c>,<c,b>\}$
  • (L = predicate symbol designating “does love”)