You look at the complexity of a problem based on the number of logical steps needed to reach a certain conclusion.
People aproach the beer-coke version and the E-Vowel differently. The latter is more difficult to perform well on, even if the logic is the same.
Content has a big effect on the difficulty of a problem.
→ Mental model theory, Johnson Laird.
is about discourse comprehension, relational reasoning and conditional reasoning. Involves a lot of different modes of reasoning. Wide applicability is why it is quite popular.
It states that the mind is not just a logical or probabilistic device, but rather makes mental simulations.
If humans reason logically or infer probabilities they rely on their bility to simulate the world in mental models. The application of simulation to reasoning is based on mental models of the possibilities to which the premises refer. We make simulations and based on these simulations and their counterexamples we find our conclusion.
Mental models are representations of what is common to a distinct set of possiblities.
Back in the day architects would usually build physical models of whatever they were wanting to build. And then you see which one can solve the problem at hand.
The complexity of a problem then is based on the amount of problems that require solving.
This makes it more likely that the models err, as well as the time it takes to complete the reasoning.
What is spatial reasoning?
Reasoning that hinges on the spatial relations between events. Something is to the left of. What’s interesting is that it does not relate to the visual system necessarily.
You make a model that captures all the ways in which a possibility holds, with basic statements like A is to the left of B etc.
Model-problem accounts can be unary, or n-nary. That is one-model problems or multiple-model problems.
Some multiple-model problems don’t lead to a necessary conclusion. This is called a no-valid-conclusion problem.
1M > MM > NVM
Mental Logic account.
Same but with logic in the form left(x,y).
MM > 1M > NVC
Prism
Indeterminate problems: people are likely to construct just a single, simple and typical model, even when a description is incompatible with severlal alternative models, this is the preferred mental model.
Simple principle for preferred mental models of spatial descriptions. New objects are added to a model without disturbing the arrangement of those tokens already represented in the model; first-free-fit strategy.
For Prism it is the number of focus operations that leads to the complexity of the model. A focus operation is an intentional focus on transforming one of the spatial tokens in the model. When you need to add another letter, you’re going to move your attention to where it needs to be moved.
Type 1 — initial premise, starting point of model construction.
Type 2 — One new token premise: one new object to the spatial array; theyre may be a determinate token, that is a fixed place, or an indeterminate token, that is it does not necessarily have a fixed place.
Type 3 — Two-new tokens premise. You get a bit of information that you need to add 2 entirely new tokens. Putting them into the model will be quite difficult, so people create a ‘second model’ which is then integrated into the actual model
Type 4 — is about connecting all the submodels.
Syllogisms
It is easier to figure syllogisms out from left to right when you read like that
We make models based on the information we receive. Sometimes it is conclusive and sometimes not.