From Logic to Neural Networks and Back (original) (raw)

2005, English version of my French "Reseaux de neurones capables de raisonner", Dossier Pour la Science (special issue of the French edition of the Scientific American), October/December 2005, 97-101.

Abstract

This paper gives a very short (and accessible) survey of how classical and nonmonotonic logic relate to neural networks in general, and on how neural networks might be able to carry out logical reasoning in particular.

FAQs

sparkles

AI

How did McCulloch and Pitts conceptualize artificial neural networks in 1943?add

They presented a model where nodes equate to logical truth values and connections represent logical rules, proving all finite automata could be constructed from such networks.

Why do connectionists reject symbolic rule-based interpretations of neural networks?add

Connectionists argue that neural networks store information based on distributed activation patterns, not on single, localized nodes, which undermines traditional rule-based symbolic AI.

What are non-monotonic conditionals and why are they significant?add

Non-monotonic conditionals allow for reasoning under uncertainty, providing a framework to represent exceptions effectively in everyday situations, reflecting common reasoning patterns.

When did the psychologistic turn in logic begin affecting cognitive science?add

This shift emerged in the late 20th century, as logicians started to model cognitive processes using logical frameworks, contrasting earlier views of pure rationality.

How does logic influence the learning mechanisms of modern neural networks?add

Recent investigations link the logic of non-monotonic conditionals with neural network inference processes, aiding in the interpretation of their learning and operational dynamics.

Loading...

Loading Preview

Sorry, preview is currently unavailable. You can download the paper by clicking the button above.

References (8)

  1. References: McCulloch, W.S. and Pitts, W.H., "A logical calculus of the ideas immanent in nervous activity", Bulletin of Mathematical Biophysics 5 (1943), 115-133. Reprinted in: W.S. McCulloch, Embodiments of mind, Cambridge, Mass.: The MIT Press, 1965. Here is a selection of recent references on non-monotonic logic and neural networks: A.S. d'Avila Garcez, K. Broda, and D.M. Gabbay, "Symbolic knowledge extraction from trained neural networks: a sound approach", Artificial Intelligence 125 (2001): 153-205.
  2. A.S. d'Avila Garcez, D.M. Gabbay, and L.C. Lamb, Connectionist non-classical logics, to appear with Springer-Verlag.
  3. Balkenius, C. and Gärdenfors, P., "Nonmonotonic inferences in neural networks", in: J. Allen, R. Fikes, and E. Sandewall (eds.), Principles of knowledge representation and reasoning, San Mateo: Morgan Kaufmann, 1991, 32-39.
  4. Blutner, R., "Nonmonotonic inferences and neural networks", Synthese 142 (2004), 143-174.
  5. Hölldobler, S., P. Hitzler, and A.K. Seda, "Logic programs and connectionist networks", Journal of Applied Logic 2 (2004), 245-272.
  6. Leitgeb, H., "Nonmonotonic reasoning by inhibition nets", Artificial Intelligence 128 (2001), 161-201.
  7. Leitgeb, H., Inference on the low level. An investigation into deduction, nonmonotonic reasoning, and the philosophy of cognition, Dordrecht: Kluwer, Applied Logic Series, 2004.
  8. Schurz, G. and Leitgeb, H. (eds.), special volume on "Non-monotonic and uncertain reasoning in the focus of paradigms of cognition", Synthese 146/1-2 (2005).