Logical and psychological relations between the False Belief Task and counterfactual reasoning a. Keith Stenning Universitiy of Edinburgh

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2 Logical and psychological relations between the False Belief Task and counterfactual reasoning a Keith Stenning Universitiy of Edinburgh DIPLEAP Workshop November, Vienna, Austria a This work is a joint project with Michiel van Lambalgen of the University of Amsterdam

3 Counterfactuals in logic and psychology there is much psychological interest in children s counterfactual reasoning children reason differently with hypotheticals and counterfactuals a first logical response: possible worlds semantics a classical logical analysis but the tasks are discourse understanding not adversarial inference

4 Counterfactuals, nonmonotonic logics, and false-belief an alternative logical response is to use non-monotonic logics for reasoning to interpretations to explore children s discourse reasoning the relation between counterfactuals and false-belief reasoning is a further active psychological issue [Peterson and Riggs, 1999] proposed that problems with counterfactual reasoning were what made false-belief reasoning hard, and [Riggs et al., 1998] presented data to support the claim [Stenning and van Lambalgen, 2008] proposed a nonmonotonic logical analysis of false-belief reasoning which related it to reasoning with counterfactuals other data, notably [Perner et al., 2004], casts doubt on this alignment

5 Nonmonotonic logic the basic model A ab B read as If A, and nothing is abnormal, then B information that is at present unknown (φ) may turn out to constitute an abnormality (φ ab) if there is no such φ then, by the closed world assumption ab if φ is all the new information, then again by the closed world assumption φ ab in this case the conditional has the form A φ B this apparatus builds in certain assumptions about the set-up: there is a database of long-term regularities (think the active part of LongTermMemory) the discourse arrives sentence by sentence and is interpreted relative to the database, and to the discourse up to that point

6 The overall properties of this nonmonotonic logic a model of automatic rather than cogitative reasoning cheap, fast, reflexive reasoning over large databases of LTM in interpreting discourse it is neurally implementable as spreading activation [Stenning and van Lambalgen, 2005] produces a unique minimal model at every sentence addition, in time linear with the depth of spreading activation think of it as a core inference engine, but one which requires some executive management to perform many tasks although used here to model discourse, it is not particularly linguistic as planning logic, it is used for robot motor control

7 Hypothetical vs. Counterfactual reasoning Taken from [Perner and Rafetseder, ress];[rafetseder et al., 2010]: Basic (hypothetical) conditional reasoning applies regularities such as: If (whenever) it doesn t rain, the street is dry to questions such as: If it had not rained, would the street be wet or dry? without considering actual events [other possible regularities?]such as: if street cleaners have just been washing the street, the street is wet In counterfactual reasoning, however, the conditional reasoning must be constrained by actual events (according to the nearest possible world). [any relevant regularity whether mentioned or not?]

8 What would nonmonotonic logic say here? basic conditional reasoning is discourse processing with the closedworld assumption (otherwise no explanation of suppression phenomena) In counterfactual reasoning two models are relevant: the reference model, and the counterfactual model in counterfactual reasoning the world may not be simply closed we can refer to some facts and regularities of this independently specified situation without them having been explicitly mentioned so the street cleaners are an abnormality which might be introduced non-closure is constrained to the nearest model differing only at the counterfactual proposition and its consequences in the database this non-closure is a relative affair, may not be from the actual world and is certainly not specified in total detail just remember, experimental psychology is about subjects understand-

9 Nonmonotonic logic generates where possible worlds semantics searches possible worlds semantics goes with classical logic in specifying all logical possibilities relative to a fixed set of premises (with fixed interpretation) defeasible logic (at least this weak one) generates unique models as each new premise arrives so it could be seen as generating the analogue of the nearest possible world once new premises are introduced this is much closer to some implementable candidate for a psychological process than possible worlds semantics

10 False-belief principles in a defeasible logic framework The formal treatment is given in [Stenning and van Lambalgen, 2008, pps ] sections 9.4/9.5; cf. also first set of slides perceptions cause beliefs: when Maxi sees the chocolate, he believes it is in the box [theory-theory] principle of inertia: unless something happens, this belief persists [the closed world assumption is itself a form of inertia] the prepotent response: intrusion of the reference model [executive function theory: in neural implementations this shows up as a process of inhibition (or not) by abnormalities] the logic enables the fractionation of possible causes into those falling under theory-theory or executive function theory both kinds of mechanism are essential to a working system NB no need for Peterson s proposal of simulation (vs. theory )

11 Benefits of analysis: logical and psychological the false-belief task is about beliefs why not logics of belief then? there is an operator B a which is a bit like a modal operator but this close logical analysis of the task reveals that it is more about: the relation of belief to sensory information, verbal information, persistence, and belief reports. Not about how to get from belief in one proposition to belief in another the analysis has strong implications for modularity (at least in the sense of a bit of neural tissue doing ToM reasoning and nothing else) [Stenning and van Lambalgen, 2007] the analysis requires combining of rules about mental entities with notions about acting in the world, by means of a powerful inference engine controlled by executive functions analysis raises new psychological issues, and the data can raise logical modelling issues

12 Counterfactuals and false-belief tasks [Riggs and Peterson, 2000]; [Riggs et al., 1998] argue problems with false-belief tasks are actually with counterfactuals [Stenning and van Lambalgen, 2008, pps ] section 9.5 extends the FBT analysis just described to Peterson s mother-bakes-acake example

13 Formalising counterfactual reasoning Counterfactual question: where would the chocolate be if Mummy hadn t baked a cake? put p:= chocolate in cupboard, q:= chocolate in fridge, a:= Mummy bakes a cake; predicates HoldsAt, Happens, ab Principles 1. HoldsAt(p, t) t < t ab(t, t ) HoldsAt(p, t ) 2. Happens(a, s) t < s < t ab(t, t ) 3. HoldsAt(p, s) Happens(a, s) s < t HoldsAt(q, t) Rules 1 and 3 are in potential conflict, but if for some s, Happens(a, s), then rule 1 is disabled and rule 3 applies if for no s, Happens(a, s), it follows by CWR that ab(t, t ), so that rule 1 applies; moreover rule 3 is disabled the second case answers the counterfactual question

14 [Stenning and van Lambalgen, 2008, p ] If we now compare the two tasks, we see that the reasoning involved is very similar, but that the false belief task requires a more extensive set of principles. Thus, failure on the counterfactual task may be expected to lead to failure on the false belief task, because in both cases it is the prepotent response that is assumed to be operative, perhaps as a derivative effect. Success on the counterfactual task by itself does not imply success on the false belief task, because the calculations for the latter involve combining reasoning about information sources, inertial properties, and closed world reasoning. In this sense false belief reports are a proper subspecies of counterfactuals, and it would be interesting if they could be shown to be harder for some populations.

15 Counterfactuals vs. FBT: conclusions from the analysis the analysis captures some differences and some commonalities a difference: FBT reasoning demands the child understands causal relation between perception and belief : not so for the counterfactual examples similarities: task involves much of the machinery of discourse reasoning of FBT (e.g. inertia of closed world reasoning, nonmonotonicity,... ). Both require possibly complex inference about a minimal change in an assumption, and executive handling of interference between alternatives so it shouldn t be surprising if there is a correlation, or that the FBT is harder

16 But were we dead already? [Perner et al., 2004] in 2004, around the time we were doing this analysis of the FBT/Counterfactuals... unbeknownst to us, Perner, Sprong and Steinkogler published an experimental paper dissociating counterfactuals and the FBT the experiment and its interpretation are complex it contrasts simple and complex travel scenarios and embeds counterfactual and FB reasoning in both the upshot is that counterfactuals show clear interactions of complexity of scenario and age, whereas FBT shows interactions of reasoning and age, but without any effect of subsidiary scenario complexity however, the devil may be in the detail, as the authors acknowledge

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18 1. Counterfactuals versus Future-hypotheticals. [large effect] Peter is still at home. If Peter goes to the green station and takes the bus, where will he end up? Peter goes to A and takes the bus to M. If Peter had not taken the bus but the train, where would he have ended up? [Memory interference a la Morton?] 2. Complexity of Scenarios. [large effect] 1-many (top diagram) vs. 1-1 (bottom diagram) 3. Amount of Counterfactuality. [19% effect but not sig.] Complete counterfactual: If Peter had gone to the other station and taken the bus, where would he have ended up? [NB the variable] Partial counterfactual: Peter makes his way only up to one of the stations (e.g., A) and children are asked: If Peter had gone to the other station and takes [n] the bus from there, where will [would] he [have] end[ed] up? 4. Alternative Means of Transport versus Alternative Points of Departure. [not sig and doesn t interact with complexity of scenario] Suppose Peter has just taken the bus from A to the mountains. Children are then asked either, If Peter had taken the train, where would he have ended up?, versus If Peter had gone to B and taken the bus, where would he have ended up? [memory savings?] 5. Linguistic Expression: Indicative and Subjunctive. [no effect] If Peter had gone to station B (instead of A)... EITHER... and he takes the bus from there, where will he end up?, OR... and he took the bus from there, where would he have ended up? [Syntax OK in German, but with what semantics?]

19 [Perner et al., 2004], from the Discussion: The detail The need to relate the derivation process to actual events makes counterfactual reasoning problems akin to the false belief problem, where one has to reason from a belief in a counterfactual state of the world to an action aimed at achieving something in the real world. This is one critical feature of beliefs that differentiates false beliefs from pretence (Perner, 1988). This common feature can explain why understanding of false beliefs and answers to difficult counterfactual problems correlate in the study by [Riggs et al., 1998], by German and Nichols (in press) and to some degree in our alternative means of transport condition. This explanation, however, differs from that given by [Peterson and Riggs, 1999]. It need not assume that false belief understanding is based on simulation by going counterfactually through the reasoning process that the mistaken believer goes through factually. This explanation would also apply under a theorytheory approach, in which children acquire knowledge of how beliefs are formed and how they govern action without having to simulate the other persons mental processes.

20 [Perner et al., 2004] compared to [Stenning and van Lambalgen, 2008] a remarkable convergence of analyses by totally different routes there are counterfactual elements in the FBT; there are also distinctive conceptual elements in the FBT; there is no need to evoke simulation the experimental route provides new data the logical analysis provides some conceptual clarity (the differences between counterfactuals and hypothetical has more to do with subtle differences in closure-of-the-world than in paying attention to the real world ; where do executive functions play a role?; memory interference between models is a likely source of difficulty with counterfactuals; what does simulation (modularity,... ) mean?;... )

21 Can logic help with the empirical and conceptual complexities? nonmonotonic logic is close to an albeit abstract theorem prover but lots of psychology left to do: what style of planning? what kinds of executive functions are involved? Nevertheless, it defines certain core processes of reasoning it forces us to model a whole reasoning process what is in common between two processes; to what extent two theories are distinct; what else needs to be controlled; what could possibly be modularised and what modules those modules would have to talk to; the relation between logic and experiment is the normal one in science between math model and data another value is that we know a lot about its computational properties

22 HUMAN REASONING AND COGNITIVESCIENCE STENNING AND VAN LAMBALGEN AND HUMAN REASONING COGNITIVE SCIENCE KEITH STENNING AND MICHIEL VAN LAMBALGEN HUMAN REASONING AND COGNITIVE SCIENCE Keith Stenning and Michiel van Lambalgen In Human Reasoning and Cognitive Science, Keith Stenning and Michiel van Lambalgen a cognitive scientist and a logician argue for the indispensability of modern mathematical logic to the study of human reasoning. Logic and cognition were once closely connected, they write, but were divorced in the past century; the psychology of deduction went from being central to the cognitive revolution to being the subject of widespread skepticism about whether human reasoning really happens outside the academy. Stenning and van Lambalgen argue that logic and reasoning have been separated because of a series of unwarranted assumptions about logic. Stenning and van Lambalgen contend that psychology cannot ignore processes of interpretation in which people, wittingly or unwittingly, frame problems for subsequent reasoning. The authors employ a neurally implementable defeasible logic for modeling part of this framing process, and show how it can be used to guide the design of experiments and interpret results. They draw examples from deductive reasoning, from the child s development of understandings of mind, from analysis of a psychiatric disorder (autism), and from the search for the evolutionary origins of human higher mental processes. The picture proposed is one of fast, cheap, automatic but logical processes bringing to bear general knowledge on the interpretation of task, language, and context, thus enabling human reasoners to go beyond the information given. This proposal puts reasoning back at center stage. Figure 2: [Stenning and van Lambalgen, 2008]

23 References [Perner et al., 2004] Perner, Sprung, and Steinkogler (2004). Counterfactual conditionals and false belief: A developmental dissociation. Cognitive Development, 19: [Perner and Rafetseder, ress] Perner, J. and Rafetseder, E. (in press). Counterfactual and other forms of conditional reasoning: Children lost in the nearest possible world. In Hoerl, C., McCormack, T., and Beck, S., editors, Understanding counterfactuals / understanding causation. Oxford University Press. [Peterson and Riggs, 1999] Peterson, D. and Riggs, K. J. (1999). Adaptive modelling and mindreading. Mind and Language, 14: [Rafetseder et al., 2010] Rafetseder, E., Cristi-Vargas, R., and Perner, J. (2010). Counterfactual reasoning: Developing a sense of nearest possible world. Child Development, 81(1): [Riggs and Peterson, 2000] Riggs, K. and Peterson, D. (2000). Counterfactual reasoning in pre-school children: Mental state and causal inferences. In Mitchell, P. and Riggs, K., editors, Children s Reasoning and the Mind, chapter 5, pages Psychology Press. [Riggs et al., 1998] Riggs, K. J., Peterson, D. M., Robinson, E. J., and Mitchell, P. (1998). Are errors in false belief tasks symptomatic of a broader difficulty with counterfactuality? Cognitive Development, 13: [Stenning and van Lambalgen, 2005] Stenning, K. and van Lambalgen, M. (2005). Semantic interpretation as reasoning in nonmonotonic logic: The real meaning of the suppression task. Cognitive Science, 29(6): [Stenning and van Lambalgen, 2007] Stenning, K. and van Lambalgen, M. (2007). Explaining the domain generality of human cognition. In Roberts, M. J., editor, Integrating the Mind. Psychology Press.

24 [Stenning and van Lambalgen, 2008] Stenning, K. and van Lambalgen, M. (2008). Human reasoning and cognitive science. MIT University Press, Cambridge, MA.