Multiagent Systems

Prof. Dr. Jürgen Dix · Department of Informatics, TUC Multiagent Systems, WS 06/07 607/731
9. Agents based on FOL 1. First Order Logic (FOL)
Definition (continued)
4. if ϕ = def (ψ ∨ η), then
{
true,
A(ϕ) = def
false,
5. if ϕ = def ∀ x ψ, then
{
true,
A(ϕ) == def
false,
6. if ϕ = def ∃ x ψ, then
{
true,
A(ϕ) = def
false,
if A(ψ) = true or A(η) = true,
else.
if ∀ d ∈ UA : A [x/d] (ψ) = true,
else.
if ∃d ∈ UA : A [x/d] (ψ) = true,
else.
In the cases 5. and 6. the notation [x/d] was used. For
d ∈ U A be A [x/d] the structure A ′ , which is identical with A
except for the definition of x A′ : x A′ = def d (independently
of the fact that I A is defined for x or not).