Final answer:
No modal logic uses an anti-symmetric accessibility relation because it violates the transitivity property.
Step-by-step explanation:
No modal logic uses an anti-symmetric (partial order) accessibility relation because it would violate the transitivity property of modal logic. Modal logic relies on the principle of transitivity, which states that if 'A' is accessible from 'B' and 'B' is accessible from 'C', then 'A' should be accessible from 'C'. An anti-symmetric relation implies that if 'A' is accessible from 'B', then 'B' cannot be accessible from 'A', which contradicts the transitivity principle.
For example, if we have a modal logic system with a relation R such that 'A' is accessible from 'B', but 'B' is not accessible from 'A', and 'B' is accessible from 'C', but 'C' is not accessible from 'B', under an anti-symmetric relation, we cannot conclude that 'A' is accessible from 'C', which violates the transitivity property.