interpretation

Interpretation of the language with the domain assigns semantics to the symbols used in language.

In first order logic, the interpretation requires a domain and interpretation changes when domain changes.

A constant symbol $C$ is interpreted in domain $D$ to an element or an object the domain.

$$C\in D$$

A function symbol $f$ of an arity $n$ maps $n$ elements in domain $D$ to an element in $D$.

$$f(E{1}_D,E{2}_D,...,E{n}_D)\in D$$

A predicate or relation symbol $R$ of an arity $n$ is interpreted as a tuple of elements in domain $D$ for which the $R$ is $true$.

$$⟨E{1}_D,E{2}_D,...,E{n}_D⟩\subset D$$

Todo

• Verify the interpretation of predicate or relation symbol (@2024-06-20)