Multiagent Systems

9. Agents based on FOL 1. First Order Logic (FOL)
Definition 9.1 (First order logic L F OL ,L ⊆ L F OL )
The language L F OL of first order logic (Praedikatenlogik
erster Stufe) is defined as follows:
x, y, z, x 1 , x 2 , . . . , x n , . . .: a countable set Var of
variables.
for each k ∈ N: P k 1 , P k 2 , . . . , P k n , . . . a countable set
Pred k of k-dimensional predicate symbols (the
0-dimensional predicate symbols are the propositional
logic constants from At of L P L . We suppose that □
and ⊤ are available.)
for each k ∈ N: f k 1 , f k 2 , . . . , f k n, . . . a countable set
Funct k of k-dimensional function symbols.
¬, ∧, ∨, →: the sentential connectives.
(, ): parentheses.
∀, ∃: quantifiers.
rof. Dr. Jürgen Dix · Department of Informatics, TUC Multiagent Systems, WS 06/07 596/731