Logical and psychological relations between the ‘False Belief

Task’ and counterfactual reasoninga

Keith StenningUniversitiy of Edinburgh

DIPLEAP Workshop26 - 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 < 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

[Stenning and van Lambalgen, 2008, p. 261–262]

If we now compare the two tasks, we see that the reasoning involved isvery similar, but that the false–belief task requires a more extensive setof principles. Thus, failure on the counterfactual task may be expectedto lead to failure on the false–belief task, because in both cases it isthe prepotent response that is assumed to be operative, perhaps as aderivative effect. Success on the counterfactual task by itself does notimply success on the false–belief task, because the calculations for thelatter involve combining reasoning about information sources, inertialproperties, and closed–world reasoning. In this sense false–belief reportsare a proper subspecies of counterfactuals, and it would be interesting ifthey 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 wouldhe 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 hehave ended up? [NB the variable]

Partial counterfactual: Peter makes his way only up to one of the stations (e.g., A) and children areasked: 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 interactwith 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? , versusIf 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 counterfactualstate of the world to an action aimed at achieving something in the real world. This is one criticalfeature of beliefs that differentiates false beliefs from pretence (Perner, 1988). This commonfeature can explain why understanding of false beliefs and answers to difficult counterfactualproblems correlate in the study by [Riggs et al., 1998], by German and Nichols (in press) and tosome degree in our alternative means of transport condition.

This explanation, however, differs from that given by [Peterson and Riggs, 1999]. It need notassume that false belief understanding is based on simulation by going counterfactually throughthe reasoning process that the mistaken believer goes through factually. This explanation wouldalso apply under a theorytheory approach, in which children acquire knowledge of how beliefsare formed and how they govern action without having to simulate the other persons mentalprocesses.

[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

HUMANREASONINGCOGNITIVESCIENCE

AND

KEITH STENNING AND MICHIEL VAN LAMBALGEN

HUMAN

REASONIN

G AN

D COGNITIVESCIEN

CESTEN

NIN

G A

ND

VAN

LAM

BA

LGEN

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.

HUMAN REASONING AND COGNITIVE SCIENCE

Keith Stenning is Professor of Human

Communication in the School of Informatics at

the University of Edinburgh. He is author of Seeing

Reason and coauthor of Introduction to Cognition

and Communication (MIT Press, 2006).

Michiel van Lambalgen is Professor of Logic and

Cognitive Science at the University of Amsterdam

and coauthor of The Proper Treatment of Events.

A BRADFORD BOOK

“Once in a while there is a body of work that reconceptualizes a topic of research.

This book reports and reviews such a body of work. The result is a framing and

hypotheses about reasoning that, in my judgment, fundamentally reconstructs the

psychology of inferential reasoning.... This book will be regarded as the major

turning point in the field’s development.”

James Greeno, LRDC, University of Pittsburgh

“This deep and stimulating book, by a leading psychologist and a leading logician,

is about the choice of logical formalisms for representing actual reasoning. There

are two interlocking questions: what are the right formalisms to represent how people

reason, and what forms do the reasoners themselves bring to the world in order to

reason about it? The authors’ answer to the first question, using closed-world

reasoning, allows them to analyze the wide range of strategies that people use for

shaping their thinking. For example, the book uncovers important links between

autism and nonmonotonic reasoning. This may be the first book in cognitive

science that logicians can learn some new logic from.”

Wilfrid Hodges, Queen Mary, University of London

COGNITIVE SCIENCE

THE MIT PRESS Massachusetts Institute of Technology Cambridge, Massachusetts 02142 http://mitpress.mit.edu

978-0-262-19583-6

Figure 2: [Stenning and van Lambalgen, 2008]

References

[Perner et al., 2004] Perner, Sprung, and Steinkogler (2004). Counterfactual conditionals and false belief:

A developmental dissociation. Cognitive Development, 19:179201.

[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, 14:80–112.

[Rafetseder et al., 2010] Rafetseder, E., Cristi-Vargas, R., and Perner, J. (2010). Counterfactual reason-

ing: Developing a sense of nearest possible world. Child Development, 81(1):376–389.

[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 87–100. 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,

13:73–90.

[Stenning and van Lambalgen, 2005] Stenning, K. and van Lambalgen, M. (2005). Semantic interpreta-

tion as reasoning in nonmonotonic logic: The real meaning of the suppression task. Cognitive Science,

29(6):919–960.

[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.

[Stenning and van Lambalgen, 2008] Stenning, K. and van Lambalgen, M. (2008). Human reasoning

and cognitive science. MIT University Press, Cambridge, MA.