Skip to main content
SpringerLink
Log in

Learning the Semantics of Notational Systems with a Semiotic Cognitive Automaton

  • Published:
Cognitive Computation Aims and scope Submit manuscript

Abstract

Through semiotic modelling, a system can retrieve and manipulate its own representational formats to interpret a series of observations; this is in contrast to information processing approaches that require representational formats to be specified beforehand and thus limit the semantic properties that the system can experience. Our semiotic cognitive automaton is driven only by the observations it makes and therefore operates based on grounded symbols. A best-case scenario for our automaton involves observations that are univocally interpreted—i.e. distinct observation symbols—and that make reference to a reality characterised by “hard constraints”. Arithmetic offers such a scenario. The gap between syntax and semantics is also subtle in the case of calculations. Our automaton starts without any a priori knowledge of mathematical formalisms and not only learns the syntactical rules by which arithmetic operations are solved but also reveals the true meaning of numbers by means of second-order reasoning.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

Notes

  1. I learned of this use of the extended correlation from the Italian computer scientist Piero Slocovich.

  2. This exception is represented by the regular expressions that contain the impossible sequences “;0”, “=0” and so on, which are already known from the first iteration (see Table 2).

References

  1. Newell A, Simon HA. Computer science as empirical inquiry: symbols and search. Commun ACM. 1976;19:113–26.

    Article  Google Scholar 

  2. Hofstadter D. The ineradicable Eliza effect and its dangers. In Hofstadter D, editor. Fluid concepts and creative analogies: computer models of the fundamental mechanisms of thought. New York: Basic Books; 1994. p. 155–168.

    Google Scholar 

  3. Searle J. Minds, brains and programs. Behav Brain Sci. 1980;3:417–24.

    Article  Google Scholar 

  4. Harnad S. The symbol grounding problem. Phys D. 1990;42:335–46.

    Article  Google Scholar 

  5. Haikonen P. The role of the associative processing in cognitive computation. Cognit Comput. 2009;1:42–9.

    Article  Google Scholar 

  6. Wang P. Experience-grounded semantics: a theory for intelligent systems. Cogn Syst Res. 2005;6(4):282–302.

    Article  Google Scholar 

  7. Ziemke T. Rethinking grounding. In: Riegler MPA, von Stein A, editors. Understanding representation in the cognitive sciences. New York: Kluwer Academic/Plenum Publishers; 1999. p. 177–190.

    Chapter  Google Scholar 

  8. Devlin KJ. Introduction to mathematical thinking. Palo Alto: Keith Devlin; 2012.

    Google Scholar 

  9. Fetzer JH. Artificial intelligence: its scope and limits. Netherlands: Springer; 1990.

    Book  Google Scholar 

  10. Jackson SA, Sharkey NE. Grounding computational engines. In: Kevitt PMc, editor. Integration of natural language and vision processing. Netherlands: Springer; 1996. p. 167–84.

    Chapter  Google Scholar 

  11. Gomes A, Gudwin R, El-Hani C, Queiroz J. Towards the emergence of meaning processes in computers from Peircean semiotics. Mind Soc Cogn Stud Econ Soc Sci. 2007;6:173–87.

    Google Scholar 

  12. Meystel A. Multiresolutional semiotic systems. In: Proceedings of the IEEE international symposium on intelligent control/intelligent systems and semiotics; 1999. p. 198–202.

  13. Vogt P. The physical symbol grounding problem. Cogn Syst Res. 2002;3(3):429–57.

    Article  Google Scholar 

  14. Rieger BB. Semiotics and computational linguistics. On semiotic cognitive information processing. In: Zadeh LA, Kacprzyk J, editors. Computing with words in information/intelligent systems. Germany: Heidelberg; 1999. p. 93–118 (Physica).

    Chapter  Google Scholar 

  15. Bloom B, editor. Taxonomy of educational objectives: book I, cognitive domain. New York: Longman Green; 1956.

    Google Scholar 

  16. Franco L, Cannas SA. Solving arithmetic problems using feed-forward neural networks. Neurocomputing. 1998;18:61–79.

    Article  Google Scholar 

  17. Hoshen Y, Peleg S. Visual learning of arithmetic operations. CoRR, 2015; abs/1506.02264.

  18. Hofstadter D. How Raymond Smullyan inspired my 1112-year-old self. In: Smullyan R, Rosenhouse J, editors. Four lives: a celebration of Raymond Smullyan. New York: Dover Publications; 2014.

    Google Scholar 

  19. Schweizer P. Physical instantiation and the propositional attitudes. Cogn Comput. 2012;4:226–35.

    Article  Google Scholar 

  20. Kazakov D. The self-cognisant robot. Cogn Comput. 2012;4:347–53.

    Article  Google Scholar 

  21. Wang P. Embodiment: Does a laptop have a body? In: Proceedings of AGI conference, Arlington, Virginia, USA; p. 174–179; March 2009.

  22. de Saussure F. Grundfragen der allgemeinen Sprachwissenschaft. Berlin: de Gruyter; 1915. Charles Bally unter Mitw. von Albert Riedlinger, editors, translator Herman Lommel (2001).

  23. Wall L. Perl language reference manual—for Perl version 5.12.1. Network Theory Ltd; 2010.

  24. Burch R. Charles Sanders Peirce. In: Zalta EN, editor. The Stanford encyclopedia of philosophy (Winter 2014 edition). 2014. http://plato.stanford.edu/archives/win2014/entries/peirce/.

  25. Nozawa E. Peircean semeiotic—a 21st century scientific methodology. In: Proceedings of the international symposium on collaborative technologies and systems, Orlando, FL, USA; p. 224–235, May 2007.

  26. Barthes R. Elements of semiology. London: Jonathan Cape, 1964. trans. Lavers A and Smith C (1967).

  27. Rieger BB. Computing fuzzy semantic granules from natural language texts. A computational semiotics approach to understanding word meanings. In: Hamza M, editor. Proceedings of the IASTED international conference on artificial intelligence and soft computing, Honolulu, Hawaii, USA; p. 475–479, August 1999.

  28. Berkhin P. Survey of clustering data mining techniques. Technical report. San Jose: Accrue Software, Inc.; 2002.

  29. Ernest P. A semiotic perspective of mathematical activity: the case of number. Educ Stud Math. 2006;61:67–101.

    Article  Google Scholar 

  30. Goguen J. An introduction to algebraic semiotics, with applications to user interface design. In: Nehaniv C, editor. Computation for metaphor, analogy and agents. New York: Springer Lecture Notes in Artificial Intelligence; 1999. p. 242–291.

    Chapter  Google Scholar 

  31. Lengnink K, Schlimm D. Learning and understanding numeral systems: semantic aspects of number representations from an educational perspective. In: Löwe B, Müller T, editors. Philosophy of mathematics: sociological aspects and mathematical practice. London: College Publications; 2010. p. 235–264.

    Google Scholar 

  32. Thagard P. Abductive inference: from philosophical analysis to neural mechanisms. In: Feeney A, Heit E, editors. Inductive reasoning: cognitive, mathematical, and neuroscientific approaches. Cambridge: Cambridge University Press; 2007. p. 226–247.

    Chapter  Google Scholar 

  33. Russell B. The problems of philosophy. Oxford: Oxford University Press; 1959.

    Google Scholar 

  34. Mitchell TM. The need for biases in learning generalizations. In: Shavlik JW, Dietterich TG, editors. Readings in machine learning. Los Altos: Morgan Kauffman; 1980. p. 184–191.

    Google Scholar 

  35. Nasuto SJ, Bishop JM, Roesch EB, Spencer MC. Zombie mouse in a Chinese room. Philos Technol. 2015;28:209–23.

    Article  Google Scholar 

  36. Konderak P. On a cognitive model of semiosis. Stud Log Gramm Rhetor. 2015;40:129–44.

    Google Scholar 

  37. Colton S. Refactorable numbers: a machine invention. J Integer Sequ. 1999;2, Art. ID 99.1.2. http://eudml.org/doc/226761.

  38. D’Ulizia A, Ferri F, Grifoni P. A survey of grammatical inference methods for natural language learning. Artif Intell Rev. 2011;36(1):1–27.

    Article  Google Scholar 

  39. Harris ZS. Distributional structure. Word. 1954;10:146–62.

    Article  Google Scholar 

  40. Lamb SM. On the mechanization of syntactic analysis. In: 1961 Conference on machine translation of languages and applied language analysis, national physical laboratory symposium no. 13, London, Her Majesty’s Stationery Office, 1961. vol. 2, p. 674–685.

  41. Solan Z, Horn D, Ruppin E, Edelman S. Unsupervised learning of natural languages. Proc Natl Acad Sci. 2005;102(33):11629–34.

    Article  CAS  PubMed Central  Google Scholar 

  42. Ionin T, Matushansky O. The composition of complex cardinals. J Semant. 2006;23:315–60.

    Article  Google Scholar 

  43. Sinatra R, Condorelli D, Latora V. Networks of motifs from sequences of symbols. Phys Rev Lett. 2010;105:178702.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. European Patent Office, The Hague, The Netherlands

    Valerio Targon

Authors
  1. Valerio Targon
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Valerio Targon.

Ethics declarations

Conflict of Interest

Valerio Targon declares that he has no conflict of interest

Informed Consent

All procedures followed were in accordance with the ethical standards of the responsible committee on human experimentation (institutional and national) and with the Helsinki Declaration of 1975, as revised in 2008 (5). Additional informed consent was obtained from all patients for which identifying information is included in this article.

Human and Animal Rights

This article does not contain any studies with human participants or animals performed by the author.

Additional information

The views expressed in this article reflect my personal opinion and not that of the EPO.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Targon, V. Learning the Semantics of Notational Systems with a Semiotic Cognitive Automaton. Cogn Comput 8, 555–576 (2016). https://doi.org/10.1007/s12559-015-9378-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12559-015-9378-0

Keywords

Search

Navigation