Abstract
Theories asserting that human reasoning is based on perceptual simulations often suppose these simulations are of concrete individual objects and the specific relations that hold among them. However, much human knowledge involves assertions about which relations do not hold, generalities over large numbers of objects and conditional facts. Can simulation theories explain how the mind represents these forms of knowledge, or are they inferior in their expressive power to knowledge representation schemes based on logical formalisms designed specifically to deal with negative, conditional and quantificational knowledge? In this paper, we show how assertions about mental simulations can in fact straightforwardly express all the concepts that comprise first-order logic, including negation, conditionals and both universal and existential quantification. We also speculate on how to extend this approach to deal with probabilistic and more expressive logics.
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Notes
As in a similar attempt (e.g., Barsalou 1999) to show the theoretical usefulness of a perceptual symbolic mechanism, it is important to be reasonably complete in our data coverage.
The implementation of logical inferences, such as the ones using Modus Ponens or its equivalent, by way of simulations is left for another paper.
Inclusion of abstract notions such as "mammal" may seem to compromise the tight correspondence between reasoning by simulation and perceptual mechanisms. However, the mammal property can be instantiated by way of a set of perceivable properties, such as the property of the female milk-feeding puppies.
Spivey (2007) simulates human mind in a more continuous manner, which may seem at odds with some of our observations here, such as the individuation of objects in simulations. However, Spivey’s continuous mechanisms also approximate the individuation of objects and the attribution of relations and predicates to those objects. Since we are not arguing that these simulation mechanisms are enabled by way of discrete logical inferences, Sipvey’s analysis is at least compatible with our observations about mental simulations.
As a support for this, see Garbarini and Adenzato (2004), which assumes that the object representation possible is a mechanism of "as-if" neural simulation. See also Hesslow (2002) for some neurological evidence that humans can simulate perceptual experiences in their mind, in a hypothetical setting that may involve assumptions. The latter work provides further physiological evidence that humans can simulate perception by activating the sensory areas of the brain so as to mimic the activity normally initiated by the sense organs.
We provide a more precise formulation of the assumption and result of simulations as well as what is true in reality in “The correspondence between mental simulations and first-order logic” section.
It is beyond the scope of this paper to study exactly how this sort of embedding of simulations is related to perceptual mechanisms, although we believe that some perceptual illusions involve an analogous chain of simulations.
The explanation of "negation" along these lines is similar to Barsalou (1999) explanation of falsity as the "failing to map the simulation into the situation."
As an intuitive example that motivates a mental simulation without an assumption introducing a new object in the conclusion, consider a simulation that a person might mentally run after hearing a gunshot. The gunshot is already heard and thus does not count as an assumption, and by way of elaboration, the person may mentally envisage an image of a (new) bullet flying in the air. Again, there is some neurological evidence (Hesslow 2002) that imagining perceiving something by way of perceptual simulations is essentially the same as actually perceiving it. As we explained earlier with regard to the perceptual attribution of properties and relations, once the formal expressive power of simulations allows us to introduce a new object without assumptions, motivated partly by an intuitive example as above, we do not need an intuitive justification as above each time our analysis posits an "empty-assumption" simulation introducing a new object.
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Acknowledgments
The authors would like to thank Paul Bello, Selmer Bringsjord, Robyn Carston, Andy Clark, Catherine Wearing and the members of the Human-Level Intelligence Laboratory at RPI for discussions on this work and for comments on earlier drafts of this paper. The authors are also grateful to the editor and the anonymous reviewers whose comments on the earlier draft have helped improve the content and the presentation of the paper. This work was supported in part by grants from the Office of Naval Research (N000140910094), the Air Force Office of Scientific Research (FA9550-10-1-0389) and MURI award (N000140911029).
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Uchida, H., Cassimatis, N.L. & Scally, J.R. Perceptual simulations can be as expressive as first-order logic. Cogn Process 13, 361–369 (2012). https://doi.org/10.1007/s10339-012-0444-1
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DOI: https://doi.org/10.1007/s10339-012-0444-1