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Inference of Abstraction for a Unified Account of Reasoning and Learning (2402.09046v1)
Published 14 Feb 2024 in cs.AI, cs.LG, and cs.LO
Abstract: Inspired by Bayesian approaches to brain function in neuroscience, we give a simple theory of probabilistic inference for a unified account of reasoning and learning. We simply model how data cause symbolic knowledge in terms of its satisfiability in formal logic. The underlying idea is that reasoning is a process of deriving symbolic knowledge from data via abstraction, i.e., selective ignorance. The logical consequence relation is discussed for its proof-based theoretical correctness. The MNIST dataset is discussed for its experiment-based empirical correctness.
- Neural module networks. In 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pages 39β48, 2016.
- A Bayesian Extension of the Description Logic πβ’ββ’ππβπ\cal{ALC}caligraphic_A caligraphic_L caligraphic_C, volume 11468, pages 339β354. Springer, Cham, JELIA 2019 lncs edition, 2019.
- Bayes in the brain: On Bayesian modelling in neuroscience. The British Journal for the Philosophy of Science, 63:697β723, 2012.
- A theory of learning to infer. Psychol Rev., 127(3):412β441, 2020.
- Learning probabilistic relational models. In Proc. 16th Int. Joint Conf. on Artif. Intell., pages 1297β1304, 1996.
- Karl Friston. The history of the future of the Bayesian brain. Neuroimage, 62-248(2):1230β1233, 2012.
- Neural substrate of dynamic Bayesian inference in the cerebral cortex. Nature Neuroscience, 19:1682β1689, 2016.
- A hierarchical Bayesian model of invariant pattern recognition in the visual cortex. In Proc. Int. Joint Conf. on Neural Networks, pages 1812β1817, 2005.
- Jakob Hohwy. The Predictive Mind. Oxford University Press, University of Oxford, 2014.
- Nils J.Nilsson. Probabilistic logic. Artificial Intelligence, 28:71β87, 1986.
- The Bayesian brain: the role of uncertainty in neural coding and computation. Trends in Neurosciences, 27:712β719, 2004.
- Human-level concept learning through probabilistic program induction. Science, 350(6266):1332β1338, 2015.
- Building machines that learn and think like people. Behavioral and Brain Sciences, 40(e253):1β72, 2017.
- Hierarchical Bayesian inference in the visual cortex. Journal of Optical Society of America, 20:1434β1448, 2003.
- Judea Pearl. Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan Kaufmann; 1st edition, Burlington, Massachusetts, 1988.
- Judea Pearl. Probabilistic Semantics for Nonmonotonic Reasoning, pages 157β188. Cambridge, MA: The MIT Press, philosophy and AI: essays at the interface edition, 1991.
- Scikit-learn: Machine learning in Python. Journal of Machine Learning Research, 12:2825β2830, 2011.
- Rajesh P.Β N. Rao and DanaΒ H. Ballard. Predictive coding in the visual cortex: a functional interpretation of some extra-classical receptive-field effects. Nature Neuroscience, 2:79β87, 1999.
- Markov logic networks. Machine Learning, 62:107β136, 2006.
- Artificial Intelligence : A Modern Approach, Third Edition. Pearson Education, Inc., London, England, 2009.
- Bayesian brains without probabilities. Trends in Cognitive Sciences, 20:883β893, 2016.
- Probabilistic inferences from conjoined to iterated conditionals. Int. Journal of Approximate Reasoning, 93:103β118, 2018.
- Taisuke Sato. A statistical learning method for logic programs with distribution semantics. In Proc. 12th int. conf. on logic programming, pages 715β729, 1995.
- Theory-based Bayesian models of inductive learning and reasoning. Trends in Cognitive Sciences, 10(7):309β318, 2006.
- Matthias Thimm. Inconsistency measures for probabilistic logics. Artif. Intell., 197:1β24, 2013.
- Hiroyuki Kido (10 papers)