Logical and psychological relations between the ‘False Belief Task’ and counterfactual reasoninga

Keith Stenning Universitiy of Edinburgh

DIPLEAP Workshop 26 - 28 November, 2010. Vienna, Austria

aThis work is a joint project with Michiel van Lambalgen of the University of Amsterdam Counterfactuals in logic and psychology • there is much psychological interest in children’s counterfactual rea- soning • 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 Counterfactuals, nonmonotonic logics, and false-belief • an alternative logical response is to use non-monotonic logics for rea- soning 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 counterfac- tual 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 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 assump- tion 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 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 dis- course • 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 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 pos- sible world).” [any relevant regularity whether mentioned or not?] What would nonmonotonic logic say here? • basic conditional reasoning is discourse processing with the closed- world assumption (otherwise no explanation of suppression phenom- ena) • 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- ing fictions 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 inter- pretation) • 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 psycholog- ical process than possible worlds semantics False-belief principles in a defeasible logic framework The formal treatment is given in [Stenning and van Lambalgen, 2008, pps. 249–262] 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’) Benefits of analysis: logical and psychological • the false-belief task is about beliefs—why not logics of belief then?

• there is an operator Ba 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, per- sistence, 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 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. 259–262] section 9.5 ex- tends the FBT analysis just described to Peterson’s mother-bakes-a- cake example 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 < t0 ∧ ¬ab(t, t0) → HoldsAt(p, t0) 2. Happens(a, s) ∧ t < s < t0 → ab(t, t0) 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, t0), so that rule 1 applies; moreover rule 3 is disabled • the second case answers the counterfactual question [Stenning and van Lambalgen, 2008, p. 261–262]

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. 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 reason- ing 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 al- ternatives • so it shouldn’t be surprising if there is a correlation, or that the FBT is harder 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 ex- perimental paper dissociating counterfactuals and the FBT • the experiment and its interpretation are complex—it contrasts sim- ple 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 Figure 1: From [Perner et al., 2004] 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?] The detail [Perner et al., 2004], from the Discussion: The need to relate the derivation process to actual events makes counterfactual reasoning prob- lems 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. [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?; . . . ) 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

HUMAN REASONING AND COGNITIVE SCIENCE AN D

HUMAN REASONING REASONING HUMAN Keith Stenning and Michiel van Lambalgen COGNITIVE

In Human Reasoning and Cognitive Science, Keith HUMAN Stenning and Michiel van Lambalgen—a cognitive scientist and a logician—argue for the indispensability Keith Stenning is Professor of Human “Once in a while there is a body of work that reconceptualizes a topic of research. of modern mathematical logic to the study of human Communication in the School of Informatics at This book reports and reviews such a body of work. The result is a framing and REASONING reasoning. Logic and cognition were once closely SC the . He is author of Seeing hypotheses about reasoning that, in my judgment, fundamentally reconstructs the AND connected, they write, but were “divorced” in the past psychology of inferential reasoning.... This book will be regarded as the major IEN century; the psychology of deduction went from being Reason and coauthor of Introduction to Cognition turning point in the field’s development.” central to the cognitive revolution to being the subject of and Communication (MIT Press, 2006). C widespread skepticism about whether human reasoning

E COGNITIVE James Greeno, LRDC, University of Pittsburgh really happens outside the academy. Stenning and

van Lambalgen argue that logic and reasoning have V Michiel van Lambalgen is Professor of Logic and S been separated because of a series of unwarranted AN TENNING SCIENCE “This deep and stimulating book, by a leading psychologist and a leading logician, assumptions about logic. Cognitive Science at the University of Amsterdam L

is about the choice of logical formalisms for representing actual reasoning. There AMBALGEN and coauthor of The Proper Treatment of Events. are two interlocking questions: what are the right formalisms to represent how people Stenning and van Lambalgen contend that psychology cannot ignore processes of interpretation in which people, reason, and what forms do the reasoners themselves bring to the world in order to AN wittingly or unwittingly, frame problems for subsequent reason about it? The authors’ answer to the first question, using closed-world D reasoning. The authors employ a neurally implementable reasoning, allows them to analyze the wide range of strategies that people use for defeasible logic for modeling part of this framing process, shaping their thinking. For example, the book uncovers important links between and show how it can be used to guide the design of autism and nonmonotonic reasoning. This may be the first book in cognitive experiments and interpret results. They draw examples science that logicians can learn some new logic from.” from deductive reasoning, from the child’s development of understandings of mind, from analysis of a psychiatric Wilfrid Hodges, Queen Mary, University of London disorder (autism), and from the search for the evolutionary origins of human higher mental processes.

The picture proposed is one of fast, cheap, automatic A BRADFORD BOOK THE MIT PRESS but logical processes bringing to bear general knowledge AND Massachusetts Institute of Technology KEITH STENNING on the interpretation of task, language, and context, thus Cambridge, Massachusetts 02142 978-0-262-19583-6 enabling human reasoners to go beyond the information http://mitpress.mit.edu MICHIEL VAN LAMBALGEN given. This proposal puts reasoning back at center stage.

Figure 2: [Stenning and van Lambalgen, 2008] References

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