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