Skip to main content

Natural deduction in connectionist systems

Abstract

The relation between logic and thought has long been controversial, but has recently influenced theorizing about the nature of mental processes in cognitive science. One prominent tradition argues that to explain the systematicity of thought we must posit syntactically structured representations inside the cognitive system which can be operated upon by structure sensitive rules similar to those employed in systems of natural deduction. I have argued elsewhere that the systematicity of human thought might better be explained as resulting from the fact that we have learned natural languages which are themselves syntactically structured. According to this view, symbols of natural language are external to the cognitive processing system and what the cognitive system must learn to do is produce and comprehend such symbols. In this paper I pursue that idea by arguing that ability in natural deduction itself may rely on pattern recognition abilities that enable us to operate on external symbols rather than encodings of rules that might be applied to internal representations. To support this suggestion, I present a series of experiments with connectionist networks that have been trained to construct simple natural deductions in sentential logic. These networks not only succeed in reconstructing the derivations on which they have been trained, but in constructing new derivations that are only similar to the ones on which they have been trained.

This is a preview of subscription content, access via your institution.

References

  • Bechtel, W.: 1993, ‘Decomposing Intentionality: Perspectives on Intentionality Drawn from Language Research with Two Species of Chimpanzees’,Biology and Philosophy 8, 1–32.

    Google Scholar 

  • Bechtel, W.: in press, ‘What Knowledge Must Be in the Head that We Might Acquire Language?’, in B. Velichkovsky and D. M. Rumbaugh (eds.),Naturally Human: Origins and Destiny of Language.

  • Bechtel, W. and Abrahamsen, A.: 1991,Connectionism and the Mind. An Introduction to Parallel Processing in Networks, Basil Blackwell, Oxford.

    Google Scholar 

  • Benner, P.: 1984,From Novice to Expert: Excellence and Power in Clinical Nursing Practice, Addison-Wesley, Boston.

    Google Scholar 

  • Black, F.: 1968, ‘A Deductive Question Answering System’, in M. Minsky (ed.),Semantic Information Processing, MIT Press, Cambridge, Massachusetts, pp. 354–402.

    Google Scholar 

  • Braine, M. D. S., Reiser, B. J. and Rumain, B.: 1984, ‘Some Empirical Justification for a Theory of Natural Propositional Logic’, in G. H. Bower (ed.),The Psychology of Learning and Motivation, Vol. 18, Academic Press, Orlando, pp. 313–71.

    Google Scholar 

  • Clark, A.: 1989,Microcognition: Philosophy, Cognitive Science and Parallel Distributed Processing, MIT Press, Cambridge, Massachusetts.

    Google Scholar 

  • Dreyfus, H. L. and Dreyfus, S. E.: 1986,Mind over Machine: The Power of Human Intuition and Expertise in the Era of the Computer, Free Press, New York.

    Google Scholar 

  • Elman, J. L.: 1992, ‘Grammatical Structure and Distributed Representations’, in S. Davis (ed.),Connectionism; Theory and Practice, Oxford University Press, New York.

    Google Scholar 

  • Fodor, J. A:. 1975,The Language of Thought, Crowell, New York.

    Google Scholar 

  • Fodor, J. A 1987,Psychosemantics: The Problem of Meaning in the Philosophy of Mind, MIT Press, Cambridge, Massachusetts.

    Google Scholar 

  • Fodor, J. A. and Pylyshyn, Z. A.: 1988, ‘Connectionism and Cognitive Architecture: A Critical Analysis’,Cognition 28, 3–71.

    Google Scholar 

  • Johnson-Laird, P. N. and Byrne, R. M. J.: 1991,Deduction, Erlbaum, Hillsdale, New Jersey.

    Google Scholar 

  • Margolis, H.: 1987,Patterns, Thinking and Cognition: A Theory of Judgment, University of Chicago Press, Chicago.

    Google Scholar 

  • Newell, A.: 1989,Unified Theories of Cognition, Harvard University Press, Cambridge, Massachusetts.

    Google Scholar 

  • Osherson, D. N.: 1975,Logical Abilities in Children, Vol. 3, Erlbaum, Hillsdale, New Jersey.

    Google Scholar 

  • Osherson, D. N.: 1976,Logical Abilities in Children, Vol. 4, Erlbaum, Hillsdale, New Jersey.

    Google Scholar 

  • Pollack, J.: 1990, ‘Recursive Distributed Representations’,Artificial Intelligence 46, 77–105.

    Google Scholar 

  • Rips, L. J.: 1983, ‘Cognitive Processes in Propositional Reasoning’,Psychological Review 90, 38–71.

    Google Scholar 

  • Rips, L. J.: 1990, ‘Reasoning’,Annual Review of Psychology 41, 321–53.

    Google Scholar 

  • Rumelhart, D. E.: 1989, ‘Towards a Microstructural Account of Human Reasoning’, in S. Vosniadou and A. Ortony (eds.),Similarity and Analogical Reasoning, Cambridge University Press, New York.

    Google Scholar 

  • Rumelhart, D. E., McClelland, J. L. and the PDP Research Group: 1986,Parallel Distributed Processing: Explorations in the Microstructure of Cognition, MIT Press, Cambridge, Massachusetts.

    Google Scholar 

  • Rumelhart, D. E., Smolensky, P., McClelland, J. L. and Hinton, G.E.: 1986, ‘Schemas and Sequential Thought Processes in PDP Models’, in J. L. McClelland, D. E. Rumelhart and the PDP Research Group (eds.),Parallel Distributed Processing: Explorations in the Microstructure of Cognition, MIT Press, Cambridge, Massachusetts.

    Google Scholar 

  • Smith, E. E., Langston, D. and Nisbett, R. E.: 1992. ‘The Case for Rules in Reasoning’,Cognitive Science 16, 1–40.

    Google Scholar 

  • Smolensky, P.: 1990, ‘Tensor Product Variable Binding and the Representation of Symbolic Structures in Connectionist Systems’,Artificial Intelligence 46 159–216.

    Google Scholar 

  • van Gelder, T.: 1990, ‘Compositionality: A Connectionist Variation on a Classical Theme’,Cognitive Science 14, 355–84.

    Google Scholar 

  • Vygotsky L.: 1962,Thought and Language, MIT Press, Cambridge, Massachusetts.

    Google Scholar 

  • Wason, P. and Johnson-Laird, P. N.: 1972,Psychology of Reasoning: Structure and Content, Harvard University Press, Cambridge, Massachusetts.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Bechtel, W. Natural deduction in connectionist systems. Synthese 101, 433–463 (1994). https://doi.org/10.1007/BF01063897

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01063897

Keywords

  • Pattern Recognition
  • Mental Process
  • Natural Language
  • Processing System
  • Internal Representation