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5 - Logic-Based Modeling of Cognition

from Part II - Cognitive Modeling Paradigms

Published online by Cambridge University Press:  21 April 2023

By
Selmer Bringsjord ,
Michael Giancola  and
Naveen Sundar Govindarajulu
Edited by
Ron Sun
Ron Sun
Affiliation:
Rensselaer Polytechnic Institute, New York
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Summary

After a brief orientation to logic-based (computational) cognitive modeling, the necessary preliminaries are discussed in this chapter (e.g., what a logic is, and what it is for one to “capture" human cognition are explained). Three “microworlds" or domains that all readers should be comfortably familiar with (natural numbers and arithmetic; everyday vehicles; and residential schools, e.g., colleges and universities) are introduced, in order to facilitate exposition in the chapter. Then the ever-expanding universe U of formal logics, with an emphasis on three categories therein, is given: deductive logics having no provision for directly modeling cognitive states; nondeductive logics suitable for modeling rational belief through time without machinery to directly model cognitive states such as believes and knows; and finally, nondeductive logics that enable the kind of direct modeling of cognitive states absent from the first two types of logic. Then, there follows a focus spcifically on two important aspects of human-level cognition to be modeled in logic-based fashion: the processing of quantification, and defeasible (or nonmonotonic) reasoning. Finally, a brief evaluation of logic-based cognitive modeling is provided, together with some comparison to other approaches to cognitive modeling, and the future of the discipline is considered. The chapter presupposes nothing more than high-school mathematics of the standard sort on the part of the reader.

Keywords

computerpsychologysimulationhistoryphilosophy
Type
Chapter
Information
The Cambridge Handbook of Computational Cognitive Sciences , pp. 173 - 209
Publisher: Cambridge University Press
Print publication year: 2023

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References

Adam, C., Herzig, A., & Longin, D. (2009). A logical formalization of the OCC theory of emotions. Synthese, 168(2), 201–248.CrossRefGoogle Scholar
Andréka, H., Madarász, J. X., Németi, I., & Székely, G. (2011). A logic road from special relativity to general relativity. Synthese, 186, 1–17. https://doi.org/10.1007/s11229–011-9914-8Google Scholar
Arkoudas, K., & Bringsjord, S. (2009). Vivid: an AI framework for heterogeneous problem solving. Artificial Intelligence, 173(15), 1367–1405. http://kryten.mm.rpi.edu/KA_SB_Vivid_offprint_AIJ.pdfCrossRefGoogle Scholar
Arora, S., & Barak, B. (2009). Computational Complexity: A Modern Approach. Cambridge: Cambridge University Press.Google Scholar
Ashcraft, M., & Radvansky, G. (2013). Cognition (6th ed.). London: Pearson.Google Scholar
Barwise, J., & Etchemendy, J. (1994). Hyperproof. Stanford, CA: CSLI.Google Scholar
Barwise, J., & Etchemendy, J. (1995). Heterogeneous logic. In Glasgow, J., Narayanan, N., & Chandrasekaran, B. (Eds.), Diagrammatic Reasoning: Cognitive and Computational Perspectives (pp. 211–234). Cambridge, MA: MIT Press.Google Scholar
Boolos, G. S., Burgess, J. P., & Jeffrey, R. C. (2003). Computability and Logic (4th ed.). Cambridge: Cambridge University Press.Google Scholar
Bringsjord, S. (2008), Declarative/logic-based cognitive modeling. In Sun, R., (Ed.), The Handbook of Computational Psychology. Cambridge: Cambridge University Press, pp. 127–169. http://kryten.mm.rpi.edu/sb_lccm_ab-toc_031607.pdfGoogle Scholar
Bringsjord, S. (2014). Review of P. Thagard’s The Brain and the Meaning of Life. Religion & Theology, 21, 421–425. http://kryten.mm.rpi.edu/SBringsjord_review_PThagard_TBTMOL.pdfGoogle Scholar
Bringsjord, S., Govindarajulu, N., & Giancola, M. (2021). Automated argument adjudication to solve ethical problems in multi-agent environments. Paladyn, Journal of Behavioral Robotics, 12, 310–335.CrossRefGoogle Scholar
Bringsjord, S., & Govindarajulu, N. S. (2018). Artificial intelligence. In Zalta, E., (Ed.), The Stanford Encyclopedia of Philosophy. Available at: https://plato.stanford.edu/entries/artificial-intelligenceGoogle Scholar
Bringsjord, S., Licato, J., & Bringsjord, A. (2016). The contemporary craft of creating characters meets today’s cognitive architectures: a case study in expressivity. In Turner, J., Nixon, M., Bernardet, U., & DiPaola, S. (Eds.), Integrating Cognitive Architectures into Virtual Character Design. Hershey, PA: IGI Global, pp. 151–180.CrossRefGoogle Scholar
Byrne, R. (1989). Suppressing valid inferences with conditionals. Journal of Memory and Language, 31, 61–83.Google ScholarPubMed
Charniak, E., & McDermott, D. (1985). Introduction to Artificial Intelligence. Reading, MA: Addison-Wesley.Google Scholar
Chisholm, R. (1966). Theory of Knowledge. Englewood Cliffs, NJ: Prentice-Hall.Google Scholar
Davis, M., Sigal, R., & Weyuker, E. (1994). Computability, Complexity, and Languages: Fundamentals of Theoretical Computer Science. New York, NY: Academic Press.Google Scholar
Dickmann, M. A. (1975). Large Infinitary Languages. Amsterdam: North-Holland.Google Scholar
Dietz, E.-A., Hölldobler, S., & Ragni, M. (2012). A computational logic approach to the suppression task. In Proceedings of the Annual Meeting of the Cognitive Science Society, vol. 34.Google Scholar
Dietz, E.-A., Hölldobler, S., & Wernhard, C. (2014). Modeling the suppression task under weak completion and well-founded semantics. Journal of Applied Non-Classical Logics, 24(1–2), 61–85.Google Scholar
Ebbinghaus, H. D., Flum, J., & Thomas, W. (1994). Mathematical Logic (2nd ed.). New York, NY: Springer-Verlag.CrossRefGoogle Scholar
Feferman, S. (1995). Turing in the Land of O(Z). In Herken, R. (Ed.), The Universal Turing Machine (2nd ed.). Secaucus, NJ: Springer-Verlag, pp. 103–134.Google Scholar
Francez, N. (2015). Proof-Theoretic Semantics. London: College Publications.Google Scholar
Genesereth, M., & Nilsson, N. (1987). Logical Foundations of Artificial Intelligence. Los Altos, CA: Morgan Kaufmann.Google Scholar
Giancola, M., Bringsjord, S., Govindarajulu, N. S., & Varela, C. (2020). Ethical reasoning for autonomous agents under uncertainty. In Tokhi, M., Ferreira, M., Govindarajulu, N., Silva, M., Kadar, E., Wang, J. Kaur, A. (Eds.), Smart Living and Quality Health with Robots. Proceedings of ICRES 2020, CLAWAR, London, pp. 26–41. The ShadowAdjudicator system can be obtained from: https://github.com/RAIRLab/ShadowAdjudicator; http://kryten.mm.rpi.edu/MG_SB_NSG_CV_LogicizationMiracleOnHudson.pdfGoogle Scholar
Glymour, C. (1992). Thinking Things Through. Cambridge, MA: MIT Press.Google Scholar
Govindarajulu, N., Bringsjord, S., & Peveler, M. (2019). On quantified modal theorem proving for modeling ethics. In Suda, M. & Winkler, S. (Eds.), Proceedings of the Second International Workshop on Automated Reasoning: Challenges, Applications, Directions, Exemplary Achievements (ARCADE 2019), vol. 311 of Electronic Proceedings in Theoretical Computer Science, Open Publishing Association, Waterloo, Australia, pp. 43–49. The ShadowProver system can be obtained here: https://naveensundarg.github.io/prover/; http://eptcs.web.cse.unsw.edu.au/paper.cgi?ARCADE2019.7.pdfCrossRefGoogle Scholar
Govindarajulu, N. S., & Bringsjord, S. (2017). Strength factors: an uncertainty system for quantified modal logic. In V. Belle, J. Cussens, M. Finger, L. Godo, H. Prade, & G. Qi (Eds.), Proceedings of the IJCAI Workshop on “Logical Foundations for Uncertainty and Machine Learning.” Melbourne, Australia, pp. 34–40. http://homepages.inf.ed.ac.uk/vbelle/workshops/lfu17/proc.pdfGoogle Scholar
Groarke, L. (1996/2017). Informal logic. In Zalta, E. (Ed.), The Stanford Encyclopedia of Philosophy. https://plato.stanford.edu/entries/logic-informalGoogle Scholar
Hájek, P. (1998). Metamathematics of Fuzzy Logic: Trends in Logic (vol. 4). Dordrecht: Kluwer.Google Scholar
Hayes, P. (1978). The naïve physics manifesto. In Mitchie, D. (Ed.), Expert Systems in the Microelectronics Age. Edinburgh: Edinburgh University Press, pp. 242–270.Google Scholar
Hayes, P. J. (1985). The second naïve physics manifesto. In Hobbs, J. R., & Moore, B. (Eds.), Formal Theories of the Commonsense World (pp. 1–36). Norwood, NJ: Ablex.Google Scholar
Heil, C. (2019). Introduction to Real Analysis. Cham: Springer.Google Scholar
Hendricks, V., & Symons, J. (2006). Epistemic logic. In Zalta, E. (Ed.), The Stanford Encyclopedia of Philosophy. http://plato.stanford.edu/entries/logic-epistemicGoogle Scholar
Hummel, J. (2010). Symbolic versus associative learning. Cognitive Science, 34(6), 958–965.Google Scholar
Hummel, J. E., & Holyoak, K. J. (2003). A symbolic-connectionist theory of relational inference and generalization. Psychological Review, 110, 220–264.CrossRefGoogle ScholarPubMed
Johnson, G. (2016). Argument & Inference: An Introduction to Inductive Logic. Cambridge, MA: MIT Press.Google Scholar
Kemp, C. (2009). Quantification and the language of thought. In Bengio, Y., Schuurmans, D., Lafferty, J., Williams, C., & Culotta, A. (Eds.), Advances in Neural Information Processing Systems, vol. 22. Red Hook, NY: Curran Associates. Available from: https://proceedings.neurips.cc/paper/2009/file/82161242827b703e6acf9c726942a1e4-Paper.pdfGoogle Scholar
Kleene, S. (1967). Mathematical Logic. New York, NY: Wiley & Sons.Google Scholar
Konyndyk, K. (1986). Introductory Modal Logic. Notre Dame, IN: University of Notre Dame Press.Google Scholar
Markman, A., & Gentner, D. (2001). Thinking. Annual Review of Psychology, 52, 223–247.Google Scholar
McCarthy, J. (1980). Circumscription: a form of non-monotonic reasoning. Artificial Intelligence, 13, 27–39.CrossRefGoogle Scholar
McKeon, R. (Ed.). (1941). The Basic Works of Aristotle. New York, NY: Random House.Google Scholar
McKinsey, J., Sugar, A., & Suppes, P. (1953). Axiomatic foundations of classical particle mechanics. Journal of Rational Mechanics and Analysis, 2, 253–272.Google Scholar
Nelson, M. (2015). Propositional attitude reports. In E. Zalta (Ed.), The Stanford Encyclopedia of Philosophy. https://plato.stanford.edu/entries/prop-attitude-reportsGoogle Scholar
Newell, A., & Simon, H. (1956). The logic theory machine: a complex information processing system. P-868 The RAND Corporation, pp. 25–63. Available from: http://shelf1.library.cmu.edu/IMLS/BACKUP/MindModels.pre_Oct1/logictheorymachine.pdfGoogle Scholar
Núñez, R., Murthi, M., Premaratine, K., Scheutz, M., & Bueno, O. (2018). Uncertain logic processing: logic-based inference and reasoning using Dempster-Shafer models. International Journal of Approximate Reasoning, 95, 1–21.Google Scholar
Paris, J., & Vencovská, A. (2015). Pure Inductive Logic. Cambridge: Cambridge University Press.Google Scholar
Partee, B. (2013). The starring role of quantifiers in the history of formal semantics. In Punčochář, V. & Švarný, P. (Eds.), The Logica Yearbook 2012. London: College Publications.Google Scholar
Pollock, J. (1995). Cognitive Carpentry: A Blueprint for How to Build a Person. Cambridge, MA: MIT Press.Google Scholar
Pollock, J. L. (1992). How to reason defeasibly. Artificial Intelligence, 57(1), 1–42.CrossRefGoogle Scholar
Prakken, H., & Vreeswijk, G. (2001). Logics for defeasible argumentation. In Gabbay, D. & Guenthner, F. (Eds.), Handbook of Philosophical Logic (pp. 219–318). Dordrecht: Springer.Google Scholar
Reiter, R. (1980). A logic for default reasoning. Artificial Intelligence, 13, 81–132.CrossRefGoogle Scholar
Russell, S., & Norvig, P. (2020). Artificial Intelligence: A Modern Approach (4th ed.). New York, NY: Pearson.Google Scholar
Saldanha, E.-A. D., & Kakas, A. (2020). Cognitive argumentation and the suppression task. arXiv:2002.10149Google Scholar
Simpson, S. (2010). Subsystems of Second Order Arithmetic (2nd ed.). Cambridge: Cambridge University Press.Google Scholar
Sloman, A. (1971). Interactions between philosophy and AI: the role of intuition and non-logical reasoning in intelligence. Artificial Intelligence, 2, 209–225.CrossRefGoogle Scholar
Smith, P. (2013). An Introduction to Gödel’s Theorems (2nd ed.). Cambridge: Cambridge University Press.Google Scholar
Stenning, K., & van Lambalgen, M. (2008). Human Reasoning and Cognitive Science. Cambridge, MA: MIT Press.CrossRefGoogle Scholar
Sun, R. (2002). Duality of the Mind. Mahwah, NJ: Lawrence Erlbaum Associates.Google Scholar
Sun, R., & Bringsjord, S. (2009). Cognitive systems and cognitive architectures. In Wah, B. W. (Ed.), The Wiley Encyclopedia of Computer Science and Engineering, Vol. 1 (pp. 420–428). New York, NY: Wiley. http://kryten.mm.rpi.edu/rs_sb_wileyency_pp.pdfGoogle Scholar
Szymanik, J., & Zajenkowski, M. (2009). Understanding Quantifiers in Language. Proceedings of the Annual Meeting of the Cognitive Science Society, 31, 1109–1114. Available from: https://escholarship.org/uc/item/6j17t373Google Scholar
Zadeh, L. (1965). Fuzzy sets. Information and Control, 8(3), 338–353.Google Scholar

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