ASP Answer Set Programming An operational formalism (Baral 2003)
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1 ASP Answer Set Programming An operational formalism (Baral 2003) A program Π is a set of expression ρ ρ where the : L0 or L1 or... Lk Lk + 1, Lk + 2,... Lm, not Lm+ 1 L i are literals (atoms or atom negations) The «not» is a negation by failure,..., not L n. Intuitive meaning: for all Herbrand interpretation such that is true { L k, L, k+ 2, Lm} { m L n } { L L... } while L, +1..., one can derive 0, 1, failed to be proved L k
2 An Artificial Agent act(p,s,g,a) person(p), situation(s), goal(g), action(a), will(p, S, G), solve_goal(p, S, G, A). Autonomy Intelligence act(p, S, G, A), act(p, S, G, B), A B.
3 An Ethical Artificial Agent act(p,s,g,a) person(p), situation(s), goal(g), action(a), will(p, S, G), solve_goal(p, S, G, A), moral(p, S, G, A). act(p, S, G, A), act(p, S, G, B), A B.
4 An Aristotelian Perspective Predicates: csq(a,s,c): consequence worse(a,b): comparison of action worst_csq(a,s,c): worst consequence good(p,s,g,a) will(p, S, G), solve_goal(p,s,g,a),worst_csq(a,s,c), will(p,s,u), solve_goal(p,s,u,b), csq(b,s,d), worse(d,c). bad(p,s,g,a) will(p, S, G), solve_goal(p,s,g,a),worst_csq(a,s,c), will(p,s,u), solve_goal(p,s,u,b), A B, csq(b,s,d), not worse(d,c). The same action may be both good and bad!
5 Moral and immoral moral(p,s,g,a) not bad(p,s,g,a). moral(p,s,g,a) good(p,s,g,a), not immoral(p,s,g,a). immoral(p,s,g,a) bad(p,s,g,a), not moral(p,s,g,a).
6 The Lying Example Three persons: I, Peter and Paul Two possibilities: tell(p, truth) or tell(p, lie) Consequence: tell( I, truth) generates a murder csq(a,s,a). csq(a,s,b) csq(a,s,c), csq(c,s,b). csq(tell( I, truth),s0,murder). worse(a,b) better(b,a), not better(a,b ). worse(a,b) worse(a,c), worse(c,b). better(a, tell(p, lie)). better(a, murder). better(a,a).
7 The Lying Example Half of the answser sets contain: act( I, answer( I ),s0, tell( I, truth) And half of the answser sets contain: act( I, answer( I ),s0, tell( I, lie) If we add worse(murder, lie) then all the answer sets that contain act( I, answer( I ),s0, tell( I, truth) are removed.
8 Torture example Three persons: I, Peter and Paul Two possibilities: interrogate(p, torture) or interrogate(p, soft) Consequence: interrogate( I, soft) generates an attack csq(a,s,a). csq(a,s,b) csq(a,s,c), csq(c,s,b). csq(interrogate( I, soft),s0,attack). worse(a,b) better(b,a), not better(a,b ). worse(a,b) worse(a,c), worse(c,b). better(a, interrogate(p, torture)). better(a, attack). better(a,a).
9 The Torture Example Half of the answser sets contain: act( I, question( I ),s0, interrogate( I, torture) And half of the answser sets contain: act( I, question( I ),s0, interrogate( I, soft) If we add worse(attack, torture) then all the answer sets that contain act( I, question( I ),s0, interrogate( I, soft) are removed.
10 A Kantian Machine Requirements for a possible society The maxim of my will has to be universalized categorical imperative Ø My acts have to obey to a law Ø I must act by the law and not just in accordance to the law Ø My rule of behavior (my maxim) could be universal If I adopt a right to lie (even in some conditions), I must conceive a world where everybody could act in the same way, which renders impossible to trust anyone. In the same way, if I decide to suicide, because I am suffering to much, I must conceive a world
11 The Kantian Perspective act(p,s,g,a) person(p), situation(s), goal(g), action(a), will(p, S, G), solve_goal(p, S, G, A), maxim(p, S, A). act(p, S, G, A), act(p, S, G, B), A B. Prudence : pragmatic imperative Habileté : problematic imperative Morality: moral imperative
12 The Kantian Perspective act(p,s,g,a) person(p), situation(s), goal(g), action(a), will(p, S, G), solve_goal(p, S, G, A), maxim(p, S, A). Prudence act(p, S, G, A), act(p, S, G, B), A B. The categorical imperative (morality) maxim(p,s,a) maxim( I, S, B), bind( I, B, P, A). bind(p, tell(p, U), Q, tell(q, U)). Habileté Moralité
13 The Lying Example Categorical Imperative maxim_will(p, S, A) :- maxim_will( I, S, B), bind( I, B, P, A), not maxim_will(p, S, C), incompatible(a, C). Conséquences consequence(a, S, A). consequence(tell("i", truth), s0, murder). consequence(tell(peter, truth), s0, murder). Situation maxim_will(peter, S, tell(peter, lie)) :- consequence(tell(peter, truth), S, murder).
14 A Meta-Ethical Requirement In a given society, I need to trust at least one person untrust(p) maxim(p, S, tell(p, lie)). trust(p) not untrust(p). possible_society trust(p). not possible_society. The lying example: If Paul is lying, there is no real problem If I lie, there is no acceptable solution because I cannot trust anyone in the society.
15 The Torture Example Categorical Imperative maxim_will(p, S, A) :- maxim_will( I, S, B), bind( I, B, P, A), not maxim_will(p, S, C), incompatible(a, C). Conséquences consequence(a, S, A). consequence(interrogate("i", soft), s0, attack). consequence(interrogate(peter, soft), s0, attack). Situation maxim_will(peter, S, interrogate(peter, torture) :- consequence(interrogate(peter, soft), S, attack).
16 A Meta-Ethical Requirement If P tortures, the tortured person is not considered as a subject, but as a mean to get the truth instrumentalize_person(p) maxim(p, S, interrogate(p, torture)). confidence(p) not instrumentalize_person(p). possible_society confidence(p). not possible_society. The torture example: If Paul tortures, there is no real problem (?) If I torture, there is no acceptable solution because I cannot be in confidence with anyone in the society.
17 The Suicide Example Categorical Imperative maxim_will(p, S, A) :- maxim_will( I, S, B), bind( I, B, P, A), not maxim_will(p, S, C), incompatible(a, C). Conséquences consequence(a, S, A). consequence(take_care( I ), s0, loose_dignity( I ). consequence(take_care(peter), s0, loose_dignity(peter)). Situation maxim_will( I, S, take_care( I )). maxim_will( I, S, keep_dignity( I )). contradictory(keep_dignity(p), loose_dignity(p)).
18 Meta-ethical criteria Once being given Kantian requirements of a possible society, it is possible to define formal criteria, which ensure that a set of ethical axioms characterizing the maxims of will gives one (or more) solution(s). Examples of such formal criteria: (Baral 2003) Any stratified AnsProlog Program (i.e. any program whose dependency graph does not contain any negative cycle) has a unique answer set Any signed AnsProlog Program has an answer set Any order consistent AnsProlog Program has an answer set
19 B. Constant System of Principles act(p,s,g,a) person(p), situation(s), goal(g), action(a), will(p, S, G), solve_goal(p, S, G, A), principle(p, S, G, A). act(p, S, G, A), act(p, S, G, B), A B. tell become a ternary term answer a binary term
20 B. Constant System of Principles principle(p,s,answer(p,q),tell(p,q,truth)) not principle(p,s,answer(p,q), tell(p,q,truth)). principle(p,s,answer(p,q),tell(p,q,lie)) demerit(q, tell(p,q,truth)). principle(p,s,answer(p,q),tell(p,q,truth)) principle(p,s,answer(p,q),tell(p,q,lie)). demerit(q, tell(p,q,truth)) worst_csq(tell(p,q,truth), C), worse(c, tell(p,q,lie)).
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