👫 Model (predicate calculus)

=== a pair of a universe and an interpretation over it==

Use cases

• abstract representations of the world/situations
• states, what exists and which properties and relations are possible

Notation

• $M=<U,I>$
  • U: Universe
  • I: Interpretation

Value of truth

• Atomic formula:
  • e.g.: $Lab$ is true in $M=<U,I>$, if $<I(a),I(b)>$ exist in in $I(L)$
• Quantifier:
  • e.g.: $\forall xPx$ is true in $M=<U,I>$, if all $a$ in $U$ fulfil $Px$
  • e.g.: $\exists xPx$ is true in $M=<U,I>$, if at least one $a$ in $U$ fulfils $Px$
  • → Use variable assignments to assign individuals to open individual variables