Forbus, K. D. (2011). Qualitative modeling. Wiley Interdisciplinary Reviews: Cognitive Science, 2(4), 374–391. doi:10.1002/wcs.115

Summary

In this article, Forbus summarizes the state of the field of qualitative reasoning, explaining how qualitative reasoning works and what it can be applied to. He begins by outlining three principles that are core to qualitative modeling:

Discretization – qualitative representations are almost always discrete.
Relevance – the manner in which the discretization is chosen (an in general how the model is set up) depends on the relevance of different aspects of the situation that is being modeled.
Ambiguity – predictions made by qualitative models are ambiguous and there may be multiple possible predictions.

Next, Forbus describes what a qualitative representation is. I won’t go into detail on this, since it’s mostly covered by my notes on Kuipers.

Given the definitions for qualitative representations, Forbus describes the qualitative mathematical operations that can be applied to them. One of qualitative proportionality, which is that “all else being equal, if $B$ increases, then $A$ will increase, and if $B$ decreases, then $A$ will decrease” (pg. 4). To get around the fact that not all functions are monotonic, Forbus describes to options. First, functions can be broken up into model fragments where monotonicity holds within a given fragment. Second, a compositional modeling language can be used instead. The notation used in the explanation of the compositional modeling language isn’t explained, though, so I’m not entirely clear on how it works. Same thing goes for confluences.

Forbus moves on to describe the pieces of a qualitative model, which include processes (e.g., heat flow), components (individual discrete parts that can be combined), and fields (a division of space in qualitatively distinct regions where some qualitative parameter is constant). These pieces, represented as model fragments, are assembed in the compositional modeling methodology to form a domain theory. There are also modeling assumptions which represent choices that need to be made depending on their relevance to the situation (for example, whether a thermal object should be considered a regular thermal object or just a temperature source).

The qualitative model can then be used in a qualitative simulation. I also won’t go into details here as I already wrote about it in my notes on Kuipers.

Forbus discusses how qualitative modeling can be used to model causality and spatial reasoning. For spatial reasoning, there are a few considerations: topology (which can be represented using a region connection calculus), direction, position, and shape. Space itself also needs to be decomposed into discrete regions and edges; this can be done with something called place vocabularies (e.g. this is what was used by the FROB system, see Chapter 4 of Gentner).

Takeaways

The term “simulation” when used in “qualitative simulation” does seem to mean something along the lines of simulation of a physical process—though because it is discrete and approximate, it is perhaps closer to something like the simulations used in Monte-Carlo Tree Search. It would be interesting to see how qualitative simulation would do in certain reinforcement learning settings when combined with something like MCTS. For example, in playing Atari games, maybe something like qualitative simulation would be useful for efficiently determining high-level actions a player could take (rather than the low level actions of left/right/jump/etc).

One thing that is not clear to me, though, is how qualitative modeling fits into scenarios where there is uncertainty about the environment. In one sense, it’s great at doing that, because you don’t necessarily need to numerically specify every parameter. In another sense, though, it doesn’t seem like qualitative modeling would work well in an uncertain case where, for example, it might be possible for a situation to unfold in a certain way (depending on the initial conditions), but highly unlikely. It doesn’t seem like qualitative simulation is set up for being able to express the magnitude of uncertainty or quality.

Also, despite their suggestion to the contrary, qualitative models suffer from many of the same issues that are discussed by Davis & Marcus as physical simulation does. Importantly, qualitative modeling doesn’t free you from having to make hard choices about how to set the simulation up, something that Forbus explicitly notes in this paper. You still have to make the relevant decisions about which properties are important, how to do the discretization, etc.