Conterfactuals

1. Conterfactuals Srini Narayanan ICSI NTL Meeting 10/30/2009

2. Alterations to reality • If Ted Kennedy were alive, universal health care would have an unshakable champion. • If only we had left earlier, we would have avoided the traffic. • He almost made it to the track on time. • I hope we find a gas station soon. • He never would have made it without my help. • If only I had ten dollars more, I could have bought that shirt. • If this had been an actual emergency, the signal you just heard would have been followed by official information, news or instructions.

3. Counterfactuals • Counterfactuals are mental simulations of “variations on a theme”. • They refer to imagined alternatives to something that has actually occurred. • Basic to human cognition • ubiquitous in commonsense reasoning as well as in formalized discourse. • They play a significant role in other cognitive processes such as • conceptual learning, planning, decision making, social cognition, mood adjustment, and performance improvement.

4. Computational treatments of counterfactuals • Material implication doesn’t work • P => Q = ~P or Q • Costello and McCarthy (circumscription) • Ginsburg (minimal worlds) • Structural equation semantics • Graphical • Interventions (Pearl) vs. Observation • The calculus of do(x) • Basic point: Structural theories must be enhanced by content to capture the richness of human counterfactual reasoning.

5. Activation of counterfactuals • (Markaman, Roese, Medvec, Bryne) • Behavior regulation • Make salient a relationship between resources, actions, and outcomes. • Upward vs. downward counterfactuals. • Affect regulation • Contrast effects

6. Minimal rewrite rule • Tetlock and Belkin (1996), Kahneman and Miller (Norm theory) • Small, minor changes to reality are acceptable, whereas bigger changes may be less so. • Regrets with which people chastise themselves also follow this minimal rewrite rule (Roese and Sommerville, 2005). • People typically focus on just one action to alter within the counterfactual. All other aspects of reality remain within the counterfactual exactly as they truly are. • Alternative histories: • Few key differences between the story’s setting and reality, framed by innumerable similarities, such as the laws of physics and basic characteristics of human nature.

7. Summary of background research on counterfactual content • Counterfactuals manipulate the connection between actions, outcomes and goals (desired outcomes). • A proper understanding of counterfactual processes thus depends on a model of (the relationship between) goals, actions, and their outcomes.

8. Basic Assumption • Proposition 1. Counterfactuals exploit rich shared structure of human event and action representation. • Encoding this structure provides the basis for generating and simulating the effect of counterfactual reasoning. • The minimal rewrite rule pertains to locality in the space of actions and events

9. Preconditions, resources, fine control structure are important aspects of events

10. Active representations walker at goal energy walker=Harry goal=home • Many inferences about actions derive from what we know about executing them • X-net representation based on stochastic Petri nets captures dynamic, parameterized nature of actions • Used for acting, recognition, planning, and language • Walking: • bound to a specific walker with a direction or goal • consumes resources (e.g., energy) • may have termination condition(e.g., walker at goal) • ongoing, iterative action

11. Basic Features • Fine grained model of actions and events • Interruption, hierarchy, concurrency, synchronization, iteration • Models resources, preconditions, state changes • Active representation • Feedback loops • Forward and backward • Extensions allow hybrid system models

12. States are DBN • Dynamic Bayesian Networks (D(T)BNs) are an extension of Bayesian networks for modeling dynamic systems. • In a DBN, the state at time t is represented by a set of random variables. The state at time t is dependent on the states at previous time steps. • Typically, we assume that each state only depends on the immediately preceding state (first-order Markovian), and thus we need to represent the transition distribution P(Zt+1 | Zt). • This can be done using a two-time-slice Bayesian network fragment (2-TBN) Bt+1, • variables from Zt+1 whose parents are variables from Ztand/or Zt+1, and variables from Ztwithout any parents. • Typically, we also assume that the process is stationary, i.e., the transition models for all time slices are identical:

13. A coordinated Model of Actions and events • Graphical Model • A factorized probabilistic model of state • Based on Probabilistic Relational Models • A fine grained model of events • Based on Stochastic Petri Nets • Models primitives for concurrency, sequence, choice, stochasticity, iteration, conditionals, synchronization. • Partial order true concurrency semantics • CPRM combines PRM based state representation with coordinated actions.

15. CPRM inference • Filtering • P(X_t | o_1…t,X_1…t) • Update the state based on the observation sequence and state set • MAP Estimation • Argmaxh1…hnP(X_t | o_1…t, X_1…t) • Return the best assignment of values to the hypothesis variables given the observation and states • Smoothing • P(X_t-k | o_1…t, X_1…t) • modify assumptions about previous states, given observation sequence and state set • Projection/Prediction/Reachability • P(X_t+k | o_1..t, X_1..t)

16. Counterfactual generation Principle 1. People imagine two possibilities when they generate counterfactuals. • One possibility corresponds to the actual world and the second corresponds to a variant of the actual world. This principle is adapted from (Bryne2005)). • Principle 2. The fine grained structure and evolution of events and actions includes multiple possibilities or branching points for counterfactuals. • These branching points are likely candidates for generating variants or changes to reality. • Resources, preconditions, goals are all local to the action and are altered in the generation of counterfactuals

17. Resource alterations • If I had more money, I could have gone to the game. (consumption) • If I had more energy, I could have completed the marathon. (consumption) • If you had reserved the room, you could have held the meeting here. (lock-release) • If we could produce more power, we could meet demands. (produce)

18. Remove resource Add resource Remove precondition Add precondition

19. Preconditions • If only I had not opened the gate, the dog would not have run out. • If only you had not dropped the banana peel, the old man would not have fallen. • If only I had fixed the lamp, there would have been more light. • If only I had removed the vase, it would not have been toppled.

20. Resources • Shared responsibility • Each person in a group supplies a little bit of poison to an individual • Firing squad • Consumption/Production over time • Each day the food is poisoned (accumulation)

21. Alternative choice points • Bryne (2005) points of initiation as a choice point (action versus inaction) • If the talks had continued, we would have reached an agreement. (suspended and not resumed) • If we had stopped talking, we would have been able to listen. (action not suspended) • If we had canceled the game, we could have avoided getting wet. (action not canceled) • If the intifada had not restarted, peace talks would have continued. (one action interrupts another).

22. Choice points and presuppositions

23. Restart Restart Suspended Suspended Enable Enable Disable Disable Resume Resume Suspend Suspend Iterate Iterate Stop Stop Stopped Stopped Ready Ready Done Done Ongoing Ongoing Enabled Enabled Prepare Prepare Start Start Finish Finish Cancel Cancel Canceled Canceled Undo Undo Undone Undone Event 1: Intifada restarts Event 1: Peace talks suspended

24. Temporal Order • (Bryne 2005) and colleagues have performed experiments suggesting a recency effect in counterfactual generation. • Their test scenario involved imagining two individuals who are in a game show. • They are asked to pick a square which contains a blue or red colored sports car. If they both pick the same color (red or blue), they each get to keep the car they picked. If they chose different colors, they don’t get anything. • Now suppose, the first person, John chose red. Then Jack, the second chooses blue. • When asked to complete the sentence, “The players would have won if only ...”, most people tended to say • The players would have won if only Jack had picked a red car’, even though the choices for John were equally likely.

25. Simulation • Local in the simulation space to pick the most recent • Undoing the most recent action is local in simulation • Defeasible due to other conditions • Salient resources, sub-goals, salient preconditions • For instance, in the case where you go camping and • stay an extra day you didn’t plan for, • the initial resource of not having extra food or water (which may be the usual practice) may be a more likely source of counterfactuals. • If only I had the usual extra food) than the most recent action (If only we hadn’t decided to stay longer). • Suggests many experiments of the trade-offs involved

26. Semifactives-Even-if • Even if we had stayed together then, we would have broken up by now. • Even if I had taken the higher paying job, I would not have been able to afford the house. • Even if it had been sunny, the game would have been canceled. • Even if it had stopped raining, the levee would have collapsed.

27. 90 50 80 80 80 80 60 80 Even if I had loaned you $10, you couldn’t have bought the ticket. Even if you had loaned me $10, you still could have bought the ticket

28. Concessive conditionals (Dancygier & Sweetser 2005) The would vote for him even if he were a criminal. • The concessive conditional above sets up an atypical situation in which the normal expectation is violated and an unusual situation is asserted where the people still vote for the criminal candidate.

29. Voting.enable Even-if network Default criminal(x) NOISY-OR other causes criminal(x) vote vote elected(x) elected(x)

30. Model of concessives • Concessive conditions often highlight the relative importance of canonically (in the default situation) non-salient factors for an outcome. • In the example above, this could be the background of the candidate, his past deeds, ethnicity or any number of other factors that could override the fact that he has committed a crime. • Concessive conditionals specify the extreme case of the specific value of the changed parameter that still maintains the outcome. • Thus the conditional holds not just for the situation described but for a whole range of situations which are less likely to change the outcome than the one described. • How useful is the NOISY-OR (exception independence) combination?

31. Counterfactual Evaluation • Model includes the state model and event model • To evaluate “what would the value of Y be if X were a, given that X is b. • Y and X could be events transitions or state variables • Algorithm • Assert X is b (fire a transition or do(X=b)) on the PRM • Propagate to the Context (background) (P(Context | X=b) • Assert “X* is a” in the counterfactual network • Use temporal projection to compute the value of Y.

33. NYT, Sept 18, 2009 • Context: • American diplomats were unable on Friday to bridge gaps between Israel and the Palestinians onrestartingpeace talks, meaning that while their leaders will likely meet with President Obama next week at the United Nations General Assembly, they will not announce a renewal of negotiations, officials on all sides said. • Sentence 1: • The goal of the meetings this week was to produce conditions for a summit meeting in New York, led by Mr. Obama, at which Prime Minister Benjamin Netanyahu of Israel and President Abbas would say they were starting peace talks again. • Sentence 2: • Mr. Erekat and others said there were two sets of problems, the first having to do with the length and extent of an Israeli settlement freeze in the West Bank and Jerusalem, and the second having to do with the basis for the negotiations themselves. Mr. Erekat said that without a freeze in advance, negotiations were pointless. • Sentence 3: • Mr. Mitchell also met twice on Friday with Mr. Netanyahu. An aide to Mr. Netanyahu said only that the prime minister would leave for New York as planned onWednesday and that Israel was willing to restart negotiations immediately, so the difficulty lay not with Israel but with the Palestinians. • Sentence 4: • The Americans and Palestinians have been pushing Israel to agree to freeze settlement building entirely as evidence of its seriousness about peace talks. The settlements are on land that the Palestinians wantfortheir future state. But Mr. Netanyahu has declined to do so, saying that he would be willing to reduce orslowbuilding, but not freeze it, because he would not turn his back on Israelis living there.

34. Events modeled • Context: Peace talks suspended • Event 1: Preparatory meeting (week of Sept 18) • Event 2: Talks between Israel and Palestine (Context.status) • Event 2 depends on both parties agreeing to talk. • Facts/Evidence: Meeting failed, Talks remain suspended, Israel will not freeze settlements • US role can be modeled but is not in the current version.

36. Produce resource: conditions for restarting talks Restart Suspended Restart Suspended Enable Disable Resume Suspend Enable Disable Resume Suspend Iterate Stop Stopped Ready Done Iterate Stop Stopped Ready Done Ongoing Enabled Prepare Start Finish Succeed Ongoing Enabled Prepare Start Finish Cancel Canceled Fail Failed Cancel Canceled Undo Undone Event 1: Meeting This week Part 1 = Palestine Part 2 = Israel Agree(P, T) Agree(I, T) Event 1: Peacetalks suspended

37. If Israel had agreed to freeze settlements, the peace talks could restart in New York this week • If the meeting had succeeded, talks could restart in New York this week

38. Produce resource: conditions for restarting talks Restart Suspended Restart Suspended Enable Disable Resume Suspend Enable Disable Resume Suspend Iterate Stop Stopped Ready Done Iterate Stop Stopped Ready Done Ongoing Enabled Prepare Start Finish Succeed Ongoing Enabled Prepare Start Finish Cancel Canceled Fail Failed Cancel Canceled Undo Undone Event 1: Meeting This week Part 1 = Palestine Part 2 = Israel Agree(P, T) Agree(I, T) Event 1: Peacetalks suspended

39. BACKGROUND: SUSPENDED(PT) Part 1 = Palestine Part 1 = Palestine ACTUAL SPACE Part 2 = Israel Part 2 = Israel COUNTERFACTUAL SPACE F(I,S) F(I,S) A(P, T) A(P, T) A(I, T) A(I, T) Precond(T) Precond(T)

40. Evaluation Algorithm • If Israel had frozen settlements, the peace talks could have resumed in New York. • Running the algorithm on the dual network • Do ~I(F,S) • Propagate evidence to the background • Do I*(F,S) • Compute P(Precond*(T)) • Run X-net with new value of Precond*(T). • Return X-net state.

41. BACKGROUND: SUSPENDED(PT) Propagate Evidence to Background Part 1 = Palestine Part 1 = Palestine ACTUAL SPACE Part 2 = Israel Part 2 = Israel COUNTERFACTUAL SPACE F(I,S) F(I,S) Assert Evidence do(~F(I,S)) Assert Evidence F*(I,S) A(P, T) A(P, T) A(I, T) A(I, T) ComputeP(Precond(T)) Precond(T) Precond(T)

42. Produce resource: conditions for restarting talks Restart Suspended Restart Suspended Enable Disable Resume Suspend Precondition (T) holds Enable Disable Resume Suspend Iterate Stop Stopped Ready Done Iterate Stop Stopped Ready Done Ongoing Enabled Prepare Start Finish Succeed Ongoing Enabled Prepare Start Finish Cancel Canceled Fail Failed Cancel Canceled Undo Undone Event 1: Meeting This week Part 1 = Palestine Part 2 = Israel Agree(P, T) Agree(I, T) Event 1: Peacetalks suspended

43. Produce resource: conditions for restarting talks Restart Suspended Restart Suspended Enable Disable Resume Suspend Precondition (T) holds Enable Disable Resume Suspend Iterate Stop Stopped Ready Done Iterate Stop Stopped Ready Done Ongoing Enabled Prepare Start Finish Succeed Ongoing Enabled Prepare Start Finish Cancel Canceled Fail Failed Cancel Canceled Undo Undone Event 1: Meeting This week Restart Talks Part 1 = Palestine Part 2 = Israel Agree(P, T) Agree(I, T) Event 1: Peacetalks suspended

44. Produce resource: conditions for restarting talks Restart Suspended Restart Suspended Enable Disable Resume Suspend Precondition (T) holds Enable Disable Resume Suspend Iterate Stop Stopped Ready Done Iterate Stop Stopped Ready Done Ongoing Enabled Prepare Start Finish Succeed Ongoing Enabled Prepare Start Finish Cancel Canceled Fail Failed Cancel Canceled Undo Undone Event 1: Meeting This week Restart Talks Part 1 = Palestine Part 2 = Israel Agree(P, T) Agree(I, T) Talks ready Event 1: Peacetalks suspended

45. Evaluation Algorithm • If the meeting had succeeded, talks could restart in New York this week • Running the algorithm on the dual network • Assert Evidence: Do Fire Fail • Propagate evidence to the background context • P(talks=suspended | Fail) • Assert counterfactual (Fire Succeed) • Run X-net with new value of Precond*(T). • Return X-net state.

46. Produce resource: conditions for restarting talks Restart Suspended Restart Suspended Enable Disable Resume Suspend Enable Disable Resume Suspend Iterate Stop Stopped Ready Done Iterate Stop Stopped Ready Done Ongoing Enabled Prepare Start Finish Succeed Ongoing Enabled Prepare Start Finish Cancel Canceled Fail Failed Cancel Canceled Undo Undone Event 1: Meeting This week Part 1 = Palestine Part 2 = Israel Agree(P, T) Agree(I, T) Event 1: Peacetalks suspended

47. Produce resource: conditions for restarting talks Restart Suspended Restart Suspended Enable Disable Resume Suspend Enable Disable Resume Suspend Iterate Stop Stopped Ready Done Iterate Stop Stopped Ready Done Ongoing Enabled Prepare Start Finish Succeed Ongoing Enabled Prepare Start Finish Cancel Canceled Fail Failed Cancel Canceled Undo Undone Event 1: Meeting This week Part 1 = Palestine Part 2 = Israel Agree(P, T) Agree(I, T) Event 1: Peacetalks suspended

48. Produce resource: conditions for restarting talks Restart Suspended Restart Suspended Enable Disable Resume Suspend Precondition (T) holds Enable Disable Resume Suspend Iterate Stop Stopped Ready Done Iterate Stop Stopped Ready Done Ongoing Enabled Prepare Start Finish Succeed Ongoing Enabled Prepare Start Finish Cancel Canceled Fail Failed Cancel Canceled Undo Undone Event 1: Meeting This week Restart Talks Part 1 = Palestine Part 2 = Israel Agree(P, T) Agree(I, T) Talks ready Event 1: Peacetalks suspended

49. Conclusion • Counterfactuals depend on • The relationship between actions, outcomes and goals • The fine-grained structure of events and actions • Resources, control, and complex interactions between events and state • Interventions on both events and state (Pearl 2000) • The CPRM framework provides a computationally adequate framework. • Biological implications (in reading).