SIMPLE DETERMINISTIC FREE WILL (SDF John McCarthy, Stanford University

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1 SIMPLE DETERMINISTIC FREE WILL (SDF John McCarthy, Stanford University We discuss free will using AI methodology. Formali plement the simplest, non-trivial cases before striving generality. Free will consists in having choices. The mechanism t the choices can be entirely deterministic. The human of free will is the knowledge of having choices.

2 In SDFW, decision making is split in two parts. deterministic mechanism uses a non-deterministic the termine the choices of action and their consequenc another deterministic mechanism chooses the action preferred consequences. From the common sense point of view, the above is theory of SDFW. However, we can give an axiomatic SDFW formalized in situation calculus, a first order t

3 WHAT GOOD IS FREE WILL, AND HOW DID IT E Like other aspects of consciousness, human free will of evolution. Machine free will has to be designed. It is common sense that people often need to co alternatives available to them. Bad outcomes are ofte to not comparing the expected results of available ac Predicting the consequences of actions is an aspect general ability to predict the consequences of events. A system acting only according to situation-action not exhibit SDFW. SDFW is limited and needs extension, both to expla and to build AI systems.

4 Predicting the future depends on a system s ability the present and remember the past. Our senses ha ability to observe, our brains have limited ability to rep limited ability to use this information to predict the con of actions. Robots will also be limited in all these res Humans and any robots we can build have to use ve imate representations of their environments and them Our approach to AI is based on representation of fa the world and the consequences of actions and oth in languages of mathematical logic. It depends on that do logical reasoning, including nonmonotonic rea achieve goals. However, the concepts of SDFW do n on commitment to logical AI.

5 for orientation A LOGICAL ROAD TO HUMAN LEVEL A All basic AI research should be measured according advances the goal of human level AI. This lecture is based on logical AI in which uses logica to express knowledge and logical inference to get new k [Not exclusively] This lecture uses situation calculus, an extended ve occurence axioms in addition to the conventional effe See my Actions and other events in situation calculus,

6 EFFECT AXIOMS AND OCCURRENCE AXIOM SITUATION CALCULUS Effect axioms use the function Result(a, s) giving th that results when action a is taken in situation s. (19 Occurrence axioms use the predicate Occurs(a, s) to the action a occurs in the situation s. (2002) With only effect axioms a theory is usually nondet because it isn t determined which action will occur. A nondeterministic theory with only effect axioms tended with enough occurrence axioms to make it det

7 THE SITUATION CALCULUS THEORY OF S Occurs(Does(actor, Choose(actor, a1, a2, s)), s) Next comes a nondeterministic theory showing actor s Choose(actor, a1, a2, s) = if P ref ers(actor, Result(a1, s), Result(a2, s)) then a1 else a2. (1) makes the theory deterministic. Here Prefers(actor, s1, s2) is to be understood as asse actor thinks s1 is better for him than s2. Prefers i order.

8 NON-DETERMINISTIC THEORY OF GREEDY Here s a particular non-deterministic theory. Result(A1, S0) = S1, Result(A2, S0) = S2, Wealth(John, S1) = $ , Wealth(John, S2) = $ , ( s s )(Wealth(John, s) > Wealth(John, s ) Prefers(John, s, s ). As we see, greedy John has a choice of at least tw in situation S0 and prefers a situation in which he h wealth to one in which he has lesser wealth. From equations 1 3 and some nonmonotonic reasonin infer Occurs(Does(John, A2), S0).

9 AN EXTENSION AND A GENERALIZATIO Let Actions(s) be the set of possible actions in situat Choose(s) = (ǫ a)(a Actions(s) (a )(a Actions a a Prefers(actor, Result(a, s), Result(a, s))) Occurs(Does(actor, Choose(s)), s) Here ǫ is the Hilbert operator corresponding to the w This elaboration is more complex but not essentiall from the version with just two actions.

10 An actor might compare actions rather than outcomes The formulas become where Occurs(Does(actor, Choose(actor, a1, a2, s)), s) Choose(actor, a1, a2, s) = if P ref ers(actor, a1, a2) then Some ethical theories sometimes compare actions ra their outcomes.

11 FEATURES OF SDFW A deterministic system uses a non-deterministic the cide what to do. The non-deterministic theory gives a tree of situatio by actions and other events.situation calculus is the determinism is often expressed in AI research. This system a perception of free will. The theory becomes deterministic if we add enough o axioms expressing which action occurs in each situati case, the occurrence axioms give the choices the acto

12 In SDFW the action that occurs is the one the ac leads to the best situation. This is expressed via a Choose(actor, s1, s2) meaning that actor thinks situation ter than situation s2. A system man, animal, or machine has simple de free will (SDFW) if it functions as described above. C of the situations resulting from alternative actions is th for SDFW. The usual chess programs have SDFW but don t kn Almost no animals, maybe none at all, have free will an animal does may be testable experimentally.

13 SDFW does not require that the actor know it ha indeed today s chess programs don t. In this theory actor can compare two situations, but know his set of choices. He needn t know about havin He just does. Methodological point: It is necessary for AI, and I a for philosophy, to treat the simple cases first and then them. It isn t necessary, and it may not be possible, t if-and-only-if theory of free will.

14 WARNINGS A complicated situation-action-rule, e.g. p1(s) p2(s)... p n (s) Occurs(Does(actor does not involve SDFW or any other kind of free w people I know have had difficulty making this distinct SDFW rules are often compiled into situation-ac Thus one may compare the consequences of taking sev to work and then compile the best into a situation-a i.e. into a rule telling whether to go straight or tur left at each intersection. This rule is then executed without further comparisons of consequences.

15 WANTING MORE OR FEWER CHOICES More choices: I ll take my car to work today rather cling so I can shop on the way home if I want to. I mathematics, you will more choice of scientific occ The more money I have, the more models of car I c from. If I escape from Cuba, I will have more choic to read, what I can say or write, and where to travel. Fewer choices: establishing a habit, burning one s bridg the flag to the mast, promising to love until death do The purpose of training is often to replace free will by action rules in certain situations, usually in order to Thus a fencer needs to parry a thrust automatically.

16 Military training involves getting rid of free will in s of situations and training the soldier to think before other kinds of situations. Often one reduces choices because of fear that o choices may be different from what one now prefer be or for a present or promised reward.

17 FROGS DON T HAVE SDFW: A FALSIFIABLE T A frog faced with two flies sticks out its tongue an one. My theory is that the frog doesn t compare the resulting from capturing Fly1 with that resulting from Fly2. This theory might be falsified; Karl Popper wou of that. Suppose when a frog captures a fly the taste region becomes active in a way that depends of the kind of Moreover, suppose that when the frog sees two flies region lights successively up as the frog looks at the according to the expected tastes of the two flies, i.e imagines the tastes of the two flies. If this happened, that frogs don t have SDFW would be falsified.

18 DO APES HAVE SDFW OR CAN THEY BE TRAIN Here s an experiment with apes. When the ape pres or lever 2, a goody falls onto one of two sets of baffle ape can see. The goody bounces off successive baffle up in front of this ape or in front of a rival ape. T of the baffles is randomized at each trial. If the ape c the bouncing of the goody, it can get it every time. baffles, and the ape can learn a situation-action rule. may be beyond the ability of apes to predict. If yes, the ape has SDFW. If not, maybe an ape can to have SDFW or maybe comparing possible futures the mentality of an ape.

19 TIC-TAC-TOE AND CHESS The usual tic-tac-toe program does look-ahead and h However, the number of states in tic-tac-toe is sm so that a table look-up program with exactly the sam is feasible. Such a program does not have SDFW. the criterion for a system having SDFW is not beha depends on its internal structure. Ken Thompson has generated tables for chess end g five or fewer pieces. These programs do not have SD All programs for the full game of chess do look-ahead do have SDFW. I conjecture that at least SDFW is es good chess play.

20 RELATED OPINIONS Daniel Dennett has discussed deterministic free will books, the latest being Freedom Evolves. He discu topics than I do, especially ethics. Even his basic c deterministic free will is more complicated than I cons sary. Indeed he asserts that complexity is essential fo to have free will. I don t agree. Gary Drescher s 1991 Made Up Minds contrasts situat systems with prediction-value systems. His Good and mystifying Paradoxes from Physics to Ethics discus systems which correspond subtantially to SDFW. P value systems assign numeric values to future situatio can then be compared. SDFW compares situations di

21 experience with chess and the 15-puzzle says that thes readily designed and correspond better to what humans can be made more resistant to local optima.

22 REMARKS, EXTENSIONS, AND QUESTION Humans have knowledge of their free will beyond kn specific choices. Praise and blame is relative to a moral system oft system. Extending the SDFW formalism to include th possible but difficult. What programs need at least SDFW? Chess, go, backgammon. Probably human-level driving. What programs need more? Human-level AI. SDFW treats a simple case. AI must, and philosop start with simple cases of intentional phenomena ra immediately striving for if-and-only-if definitions.