Action Description Language - Semantics of ADL

Semantics of ADL

The formal semantic of ADL is defined by 4 constraints. The first constraint is that actions may not change the set of objects that exist in the world; this means that for every action α and every current-state/next-state pair (s, t) ∈ a, it must be the case that the domain of t should be equal to the domain of s.

The second constraint is that actions in ADL must be deterministic. If (s, t1) and (s, t2) are current-state/next-state pairs of action ∃, then it must be the case that t1 = t2.

The third constraint incorporated into ADL is that the functions introduced above must be representable as first-order formulas. For every n-ary relation symbol R, there must exist a formula Φa_R x₁,... ,x_n) with free variables x₂,...,x_n such that fa_R(s) is given by:

t(R) = fa_R(s) = (d₁,..., d_n) ∈ Dom(s)n | s

Consequently, F(n₁,...,x_n) = y will be true after performing action |= if and only if Φa_R (x₁,... ,x_n,y) was true beforehand. Note that this representability requirement relies on the first constraint ( Domain of f should be equal to domain of s).

The fourth and final constraint incorporated into ADL is that set of states in which an action is executable must also be representable as a formula. For every action α that can be represented in ADL, there must exist a formula Πa with the property that s |= Π_a if and only if there is some state t for which (s, t ) ∈ α (i.e. action α is executable in state s)