We propose a modal action logic that combines ideas from H.A. Simon's
bounded rationality, S. Kripke's possible world semantics, G.H. von Wr
ight's preference logic, Pratt's dynamic logic, Stalnaker's minimal ch
ange and more recent approaches to update semantics. ALX (the xth acti
on logic) is sound, complete and decidable, making it the first comple
te logic for two-place preference operators. ALX avoids important draw
backs of other action logics, especially the counterintuitive necessit
ation rule for goals (every theorem must be a goal) and the equally co
unterintuitive closure of goals under logical implication.