Logical and psychological relations between the ‘False Belief · 2010-12-13 · Logical and...
Transcript of Logical and psychological relations between the ‘False Belief · 2010-12-13 · Logical and...
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.