This essay is an version of a 2011 tech report.

Abstract: A plausible definition of “reasoning” could be “algebraically manipulating previously acquired knowledge in order to answer a new question”. This definition covers first-order logical inference or probabilistic inference. It also includes much simpler manipulations commonly used to build large learning systems. For instance, we can build an optical character recognition system by first training a character segmenter, an isolated character recognizer, and a language model, using appropriate labeled training sets. Adequately concatenating these modules and fine tuning the resulting system can be viewed as an algebraic operation in a space of models. The resulting model answers a new question, that is, converting the image of a text page into a computer readable text. This observation suggests a conceptual continuity between algebraically rich inference systems, such as logical or probabilistic inference, and simple manipulations, such as the mere concatenation of trainable learning systems.

@article{bottou-mlj-2013,
  author = {Bottou, L\'{eon}},
  title = {From machine learning to machine reasoning: an essay},
  journal = {Machine Learning},
  month = {January},
  year = {2014},
  volume = {94},
  pages = {133--149},
  url = {http://leon.bottou.org/papers/bottou-mlj-2013},
}