Definition. Term evaluation (FOL) [0011]

In First Order Logic, terms are evaluated based on an interpretation \(I\) and a variable assignment \(\sigma \) within a structure \(S\) denoted as \(\langle I, \sigma \rangle (t)\). The evaluation rules are as follows:

• If \(t\) is a constant symbol \(c\), then \(\langle I, \sigma \rangle (c) = I(c)\).
• If \(t\) is a variable \(x\), then \(\langle I, \sigma \rangle (x) = \sigma (x)\).
• If \(t\) is a function application \(f(t_1, t_2, \ldots , t_n)\), then \[ \langle I, \sigma \rangle (f(t_1, t_2, \ldots , t_n)) = I(f)(\langle I, \sigma \rangle (t_1), \langle I, \sigma \rangle (t_2), \ldots , \langle I, \sigma \rangle (t_n)) \]