Self-Modelling Group: 30/05/2024
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###### tags: `counterfactual` `conditional` `reasoning` `representation` `inference` `probability`

:::info
- **Reading:** Geiger, S. M., & Oberauer, K. (2010). Towards a reconciliation of mental model theory and probabilistic theories of conditionals. Cognition and conditionals: Probability and logic in human thinking, 289-307.
- [Slides](https://docs.google.com/presentation/d/1THhdYa9b7PvgIBA-aVoG-wzv9y3x0ifM/edit?usp=sharing&ouid=107154418804529940910&rtpof=true&sd=true) from Maya
- **Date:** May 30, 2024 15:30 PM (OXFORD)
- **Participants:**
- Matan
- Maya
- Nicole
- Noam
- Zoe
- OSMG team <3

:::

- [name=OSMG team] We heard from Maya about her project, looking at associations between decisions about the absence of a stimulus in a near-threshold perceptual task and behaviour in a conditional inference task. We then discusses together the Geiger & Obserauer paper. We asked whether probabilistic computations are cheaper or more expensive than logical derivations, how agents know what should be the scope of their mental search for defeating counterexamples to a rule (related to [the frame problem](https://plato.stanford.edu/entries/frame-problem/)), and the idea that some mental disorders may be related to a difficulty in propertly testing one's beliefs about logical rules (like in the Wason [card selection task](https://en.wikipedia.org/wiki/Wason_selection_task)). This also led us to a short discussion about the relation between logical entailment an causation, and Matan to go on a short rant about taking our theoretical ideas seriously.

clarification questions:
---
- [name=Nicole] Would appreciate use explicitly outlining the difference between the MMT and the conditional probability model before we begin our discussions please (personally find this is very helpful for me in terms of consolidating my understading)
- [name=Matan] 👍

### Abbreviations and definitions (please contribute):

|Term|Definition|
|---|---|
|MMT|Mental Model Theory|
|Conditional probability theory|Everyday conditional reasoning is better captured by probabilistic reasoning than normative formal logic. The probability of making an inference then depends on: the probability of the antecedent, the probability of the consequent and the probability of exceptions.|
|The suppositional Theory|Suppose the antecedent is true, consider what you think of the consequent under that supposition|
|Ramsey test|A test of how confident you should be in a conditional (if p, then q) by asking what the probability of q is if you suppose p is true.|
|MP|**modus ponens**: if all men are mortal and Socrates is a man, Socrates is mortal.|
|MT| **modus tollens**: if all men are mortal and Zeus is immortal, Zeus is not a man.|
|DA| **denying the antecedent**: if all men are mortal and Zeus is not a man, Zeus is immortal. (invalid)|
|AC| **affirming the consequent** if all men are mortal and Socrates is mortal, Socrates is a man. (invalid)|
|The principle of truth|(In mental model theory) mental models of a conditional only represent situations that are compatible with the conditional, i.e., that render it true (rather than, e.g., a counterexample)|
|Truth functional conditional|The truth value of the conditional is determined by the truth or falsity of its components|
|Disabling conditions|Counterexamples to a conditional where the antecedent is true but the consequence is not (John touched the weapon but his fingerprints aren't on it)|
|Alternative causes|Counterexamples to a conditional where the antecedent is false but the consequence is true (John didn't touch the weapon but his fingerprints are on it)|
|Necessary|...|
|Sufficient|...|

Points for discussion:
---

### Thoughts on different theories in the paper

#### MMT
- [name=Matan] That in MMT, inference depends on the ability to construct a mental model of a world state. I wonder if people are less likely to construct mental models for some propositions than others, e.g., negative ones (it is difficult to positively imagine that "there is no cat in the room").
- [name=Nicole] Perhaps more related to the foundation the paper is built on, but I find it interesting that there is a difference in acceptance / interaction with the different types of conditional reasoning (ie MP, MT and AC, DA).
- [name=Matan]
> "Two models provided an acceptable fit to both data sets. One was a version of MMT augmented by a directional bias: Inferences in forward direction, from the antecedent to the consequent (i.e., MP and DA) were assumed to be accepted more readily than inferences in backward direction."

#### Suppositional theory

- [name=Matan] The suppositional theory's conjecture that MT is dependent on System 2.

#### Dual process theory

- [name=Nicole] I find the integration of the dual process theory with probabilisitic and model based reasoning interesting.

#### MMT x probabilistic theory

- [name=Maya](According to the authors' own model) difficulty is not with representing the inverse, but with representing negations to begin with.
- [name=Zoe] I liked the idea sketched out as a hierarchical simplicity bias process in which the most minimal P(q|p) is first considered, before maybe P(p|q) - the converse or flip - and P(neither) to build up to P( q |not p). Is hierarchical difficulty a question of the starting point or the operations themselves? Any compression will be simpler, e.g. both true vs both false is easier than flip/converse?
- [name=Nicole] really interesting that they find a way to integrate the MMT and probabilisitc views, in terms of how people interpret conditionals favours the probabilistic view and how people reason with condition premises supports the MMT. Curious if anyone knows how this was recieved in the wider field?

#### General observations(?)
- [name=Zoe] at what level of 'likely' do people approximate the frequency constraint as total/binary? Is this noisy? Surprisingly consistent across people?
- I like the sequential nature of their proposed model, the simplicity bias that it describes, which I believe to be true, and the sufficiency of a single model over two different ones. I agree that it is unlikely that all true statements come to mind at the same time and that this would not be efficient as a constraint on working memory energy expenditure. What mechanism determines whether or not someone searches and for how long?
- I can pretend that I'm in a world in which there is no way that someone's fingerprints could be on the weapon even though they did not touch the weapon. This makes me conclude p (touched) if I observe q (prints) with certainty.
- However, I can also think about or even google in what ways it might in fact be possible that p even if not q (no touch). This alters the type of computation and I now begin to assess the P(q|p) because I no longer consider it a necessity that q follows from p. But what would make me start that more expensive computation of searching for constraints and provide a frequency assessment?
- [name=Maya]This is such an interesting point and kind of has to do with the role of background or domain knowledge in the reasoning process? Which I feel like is so hard to capture in a model.
- [name=Matan] Yes! see [the frame problem](https://plato.stanford.edu/entries/frame-problem/).
- Is logic or probabilistic assessments a more efficient/fast/computationally inexpensive reasoning process?

### Open questions, ideas for future work:
- [name=Maya]Measuring inference acceptance with a graded scale vs. yes/no makes people more/less willing to take probabilities into account. Similarly, experiments directly manipulating frequencies/probabilities are more likely to reveal cognitive processes that are sensitive to this vs experiments that just ask you to make an inference. How often do "conflicting theories" boil down to different questions being built into the design and subsequently different models being built based on that differential data? And how can we make more "neutral" tests?
- [name=Matan] slightly off topic but relevant: a similar point about the scientific study of consciousness: "Third, a close relation was found between methodological choices made by researchers and the theoretical interpretations of their findings. That is, solely on the basis of certain methodological choices (for example, using report versus no-report paradigms or studying content versus state consciousness), we could predict whether the experiment would end up supporting each of the theories." (from [here](https://www.nature.com/articles/s41562-021-01284-5))
- [name=Maya](Relating to any two/three/multi-system theories) - in how far can these systems really be considered separate (especially in light of: people's expectations about visibility can influence "simple" perceptual decisions about absence)
- [name=Maya]More broadly, how informative *can* formal logic be about how people actually reason? And vice versa, what can empirical data about informal reasoning tell us about what sort of inferences are or aren't valid? By this I mean: Oaksford & Chater's observation that people are bad at formal logic but pretty good at "everyday rationality"

### Links to other papers and ideas:

- [name=Matan] Kahneman and Tversky's [dual system theory](https://thedecisionlab.com/reference-guide/philosophy/system-1-and-system-2-thinking).
- [name=Nicole] "Actual reasoners deviate from this ideal process model because they may fail to include all possibilities compatible with the premises in their models". Reminds me of the zero sum fallacy (Pilditch et al. 2019) - but this talks about when there are two possibles causes for something so slightly different. In the case of two possible causes people struggle to accept both, but when its the abscence of two causes people find it easier to accept this because neither has to be true.
- [name=Noam] Can think about conditionals WRT to safety behavior and avoidance. For example a socially anxious person who performs a long ritual (choosing the right outfit, combing the hair, etc.) before leaving the house for two hours. Then he walks outside and everything is right. He reason - if P then Q. He keeps reinforcing this link but he is afraid to explore the option of ¬ P then Q - which is the option that could make the original assumption not true. In these instances the condition that could contradict or challenge the logic is never tested, and this is why the (safety) behavior persists. and also Magical thinking - if I order my shoes in a certain order my mom would not get cancer. If P then not Q. another false logic that isn’t tested for counterexamples.
In these instances people are not testing counterexamples, so they don’t let the suppression effect happen.
- [name=Matan] Noam, I think finding that ¬ P then Q will not challenge the original assumption (it would be irrelevant). The only valid test is doing P and seeing if Q holds.
[name=Noam] wouldn't a way to disaprove the original belief would be by alternative casues? antecedent is false (ritual not performed) but the consequence is true (everything is fine, no disaster happend).
[name=Maya]I think you guys are talking about slightly different things here. If you assume the conditional "if p, then q" is true, the way to "defeat" this conditional is by saying "p, not q", because p is then no longer sufficient to conclude q. However, the person is this story believes that there is also a *necessary* connection between the two, and in order to change that belief "not p, still q" can also be a counterexample. Not sure though but that's just my two cents :)
[name=Matan] Strictly speaking, if the person in the story believes $P$ is a necessary condition for $Q$, they believe that $Q\rightarrow P$, not that $P \rightarrow Q$.
It's important not to confuse logical entailment with a causal model of what causes what.
[name=Maya] So they believe that q cannot occur without p occurring (mum not getting cancer, shoes not being ordered) -> p(P|Q) would be an expression of the level of necessity that can be defeated with a counterexample?