Skip to main content

The Role of Logic and Ontology in Language and Reasoning

  • Chapter
  • First Online:
Theory and Applications of Ontology: Philosophical Perspectives

Abstract

Natural languages have words for all the operators of first-order logic, modal logic, and many logics that have yet to be invented. They also have words and phrases for everything that anyone has ever discovered, assumed, or imagined. Aristotle invented formal logic as a tool (organon) for analyzing and reasoning about the ontologies implicit in language. Yet some linguists and logicians took a major leap beyond Aristotle: they claimed that there exists a special kind of logic at the foundation of all NLs, and the discovery of that logic would be the key to harnessing their power and implementing them in computer systems. Projects in artificial intelligence developed large systems based on complex versions of logic, yet those systems are fragile and limited in comparison to the robust and immensely expressive natural languages. Formal logics are too inflexible to be the foundation for language; instead, logic and ontology are abstractions from language. This reversal turns many theories about language upside down, and it has profound implications for the design of automated systems for reasoning and language understanding. This article analyzes these issues in terms of Peirce’s semiotics and Wittgenstein’s language games. The resulting analysis leads to a more dynamic, flexible, and extensible basis for ontology and its use in formal and informal reasoning.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  • Ajdukiewicz, K. 1935. Die syntaktische Konnexität. Studia Philosophica 1:1–27; translated as Syntactic Connexion. In Polish logic 1920–1939, ed. S. McCall. Oxford: Clarendon Press, 1967.

    Google Scholar 

  • Alchourrón, C., P. Gärdenfors, and D. Makinson. 1985. On the logic of theory change: Partial meet contraction and revision functions. Journal of Symbolic Logic 50(2):510–530.

    Article  Google Scholar 

  • Arieti, S. 1978. The psychobiology of sadness. In Severe and mild depression. eds. S. Arieti, and J. Bemporad, 109–128. New York, NY: Basic Books.

    Google Scholar 

  • Aristotle, Works, Loeb Library, Cambridge, MA: Harvard University Press.

    Google Scholar 

  • Austin, J.L. 1962. How to do things with words, eds. J.O. Urmson, and M. Sbisá, 2nd edn. Cambridge, MA: Harvard University Press.

    Google Scholar 

  • Barwise, J., and J. Perry. 1983. Situations and attitudes. Cambridge, MA: MIT Press.

    Google Scholar 

  • Bartlett, F.C. 1932. Remembering. Cambridge: Cambridge University Press.

    Google Scholar 

  • Bharati, A., V. Chaitanya, and R. Sangal. 1995. Natural language processing: A Paninian perspective. New Delhi: Prentice-Hall of India.

    Google Scholar 

  • Bohnert, H., and P. Backer. 1967. Automatic English-to-logic translation in a simplified model. Technical report RC-1744. Yorktown Heights, NY: IBM.

    Google Scholar 

  • Boole, G. 1854. An Investigation into the laws of thought. Reprinted. New York, NY: Dover.

    Google Scholar 

  • Brentano, F. 1874. Psychologie vom empirischen Standpunkte. translated as Psychology from an empirical standpoint (trans: A.C. Rancurello, D.B. Terrell, and L.L. McAlister). London: Routledge.

    Google Scholar 

  • Bundy, A. 2007. Cooperating reasoning processes: More than just the sum of their parts. Proceedings of IJCAI-07, 2–11.

    Google Scholar 

  • Bundy, A., and F. McNeill. 2006. Representation as a fluent: An AI challenge for the next half century. IEEE Intelligent Systems 21(3):85–87.

    Article  Google Scholar 

  • Ceccato, S. 1961. Linguistic analysis and programming for mechanical translation. New York, NY: Gordon and Breach.

    Google Scholar 

  • Chomsky, N. 1957. Syntactic structures. The Hague: Mouton.

    Google Scholar 

  • Chomsky, N. 1965. Aspects of the theory of syntax. Cambridge, MA: MIT Press.

    Google Scholar 

  • Chomsky, N. 1995. The minimalist program. Cambridge, MA: MIT Press.

    Google Scholar 

  • Croft, W., and D.A. Cruse. 2004. Cognitive linguistics. Cambridge: Cambridge University Press.

    Google Scholar 

  • Cruse, D.A. 1986. Lexical semantics. New York, NY: Cambridge University Press.

    Google Scholar 

  • Cruse, D.A. 2002. Microsenses, default specificity and the semantics-pragmatics boundary. Axiomathes 1:1–20.

    Google Scholar 

  • Fillmore, C. 1988. The mechanisms of construction grammar. Berkeley Linguistics Society 35:35–55.

    Google Scholar 

  • Förster, E. 2000. Kant’s final synthesis: An essay on the opus postumum. Cambridge, MA: Harvard University Press.

    Google Scholar 

  • Frege, G. 1879. Begriffsschrift. English translation in J. van Heijenoort, ed. 1967. From Frege to Gödel. Cambridge, MA: Harvard University Press. 1–82.

    Google Scholar 

  • Goldberg, A.E. 1995. Constructions: A construction grammar approach to argument structure. Chicago, IL: University of Chicago Press.

    Google Scholar 

  • Grice, H.P. 1975. Logic and conversation. In Syntax and semantics 3: Speech acts, eds. P. Cole and J. Morgan, 41–58. New York, NY: Academic Press.

    Google Scholar 

  • Halliday, M.A.K. 1978. Language as social semiotic: The social interpretation of language and meaning. Baltimore: University Park Press.

    Google Scholar 

  • Halliday, M.A.K. and C.M.I.M. Matthiessen. 1999. Construing experience through meaning: A language-based approach to cognition. London: Cassell.

    Google Scholar 

  • Harris, Z.S. 1951. Methods in structural linguistics. Chicago: University of Chicago Press.

    Google Scholar 

  • ISO/IEC. 2007. Common logic (CL)—A framework for a family of logic-based languages. IS 24707. Geneva: International Organisation for Standardisation.

    Google Scholar 

  • Jackendoff, R. 1983. Semantics and cognition. Cambridge, MA: MIT Press.

    Google Scholar 

  • Kant, I. 1787. Kritik der reinen Vernunft. Critique of pure reason (trans: N. Kemp Smith). New York, NY: St. Martin’s Press.

    Google Scholar 

  • Kamp, H. 2001. Levels of linguistic meaning and the logic of natural language. http://www.illc.uva.nl/lia/farewell_kamp.html

  • Kamp, H., and U. Reyle. 1993. From discourse to logic. Dordrecht: Kluwer.

    Google Scholar 

  • Lakoff, G. 1987. Women, fire, and dangerous things. Chicago: University of Chicago Press.

    Google Scholar 

  • Langacker, R.W. 1999. Grammar and conceptualization. Berlin: de Gruyter.

    Book  Google Scholar 

  • Lenat, D.B. 1995. CYC: A large-scale investment in knowledge infrastructure. Communications of the ACM 38(11):33–38.

    Article  Google Scholar 

  • Lord, A.B. 1960. The singer of tales. Cambridge, MA: Harvard University Press.

    Google Scholar 

  • Majumdar, A.K., and J.F. Sowa. 2009. Two paradigms are better than one and multiple paradigms are even better. In Proceedings of ICCS’09, LNAI 5662, eds. S. Rudolph, F. Dau, and S.O. Kuznetsov, 32–47. Heidelberg: Springer.

    Google Scholar 

  • Makinson, D. 2005. Bridges from classical to nonmonotonic logic. London: King’s College Publications.

    Google Scholar 

  • Mann, W.C., and S.A. Thompson. 1988. Rhetorical structure theory: Towards a functional theory of text organization. Text 8(3):243–281.

    Google Scholar 

  • Masterman, M. 2005. Language, chohesion and form. ed. Y. Wilks. Cambridge: Cambridge University Press.

    Book  Google Scholar 

  • Miller, G.A. 1995. WordNet: A lexical database for English. Communications of the ACM 38(11):39–41.

    Article  Google Scholar 

  • Minsky, M. 1975. A framework for representing knowledge. In The psychology of computer vision, ed. P. Winston, 211–280. New York, NY: McGraw-Hill.

    Google Scholar 

  • Minsky, M. 1987. The society of mind. New York, NY: Simon & Schuster.

    Google Scholar 

  • Minsky, M. 2006. The emotion machine: Commonsense thinking, artificial intelligence, and the future of the human mind. New York, NY: Simon & Schuster.

    Google Scholar 

  • Mohanty, J.N. 1982. Husserl and frege. Bloomington: Indiana University Press.

    Google Scholar 

  • Montague, R. 1970. English as a formal language. reprinted In Formal philosophy, ed. R. Montague, 188–221.New Haven: Yale University Press.

    Google Scholar 

  • Newell, A., and H.A. Simon. 1972. Human problem solving. Englewood Cliffs, NJ: Prentice-Hall.

    Google Scholar 

  • Ockham, William of (1323) Summa logicae, Paris: Johannes Higman. 1488 (the edition owned by C.S. Peirce).

    Google Scholar 

  • Ogden, C.K., and I.A. Richards. 1923. The meaning ofmeaning, 8th edn, 1946. New York, NY: Harcourt, Brace, and World.

    Google Scholar 

  • Peirce, C.S. 1880. On the algebra of logic. American Journal of Mathematics 3:15–57.

    Google Scholar 

  • Peirce, C.S. 1885. On the algebra of logic. American Journal of Mathematics 7:180–202.

    Google Scholar 

  • Peirce, C.S. 1902. Logic, considered as semeiotic. MS L75, ed. J. Ransdell, http://members.door.net/arisbe/menu/library/bycsp/l75/l75.htm

  • Peirce, C.S. 1911. Assurance through reasoning. MS 670.

    Google Scholar 

  • Peirce, C.S. (CP) Collected papers of C. S. Peirce, ed. C. Hartshorne, P. Weiss, and A. Burks, 8 vols., 1931–1958. Cambridge, MA: Harvard University Press.

    Google Scholar 

  • Peirce, C.S. (EP) The essential Peirce, ed. N. Houser, C. Kloesel, and members of the Peirce Edition Project, 2 vols., 1991–1998. Bloomington: Indiana University Press.

    Google Scholar 

  • Peppas, P. 2008. Belief revision. In Handbook of knowledge representation, eds. F. van Harmelen, V. Lifschitz, and B. Porter, 317–359. Amsterdam: Elsevier.

    Chapter  Google Scholar 

  • Post, E.L. 1943. Formal reductions of the general combinatorial decision problem. American Journal of Mathematics 65:197–268.

    Article  Google Scholar 

  • Propp, V. 1928. Morfologia Skazki. translated as Morphology of the folktale, 1958. Austin: University of Texas Press.

    Google Scholar 

  • Reid, T. 1785. Essays on the intellectual power of man. Edinburgh: Edinburgh University Press.

    Google Scholar 

  • de Saussure, F. 1916. Cours de Linguistique Générale. Course in general linguistics (trans: Baskin, W., 1959). New York, NY: Philosophical Library.

    Google Scholar 

  • Schank, R.C., ed. 1975. Conceptual information processing. Amsterdam: North-Holland Publishing Co.

    Google Scholar 

  • Schank, R.C., and R.P. Abelson. 1977. Scripts, plans, goals and understanding. Hilsdale, NJ: Erlbaum

    Google Scholar 

  • Selz, O. 1913. Über die Gesetze des geordneten Denkverlaufs. Stuttgart: Spemann.

    Google Scholar 

  • Shanker, S.G. 1987. Wittgenstein and the turning point in the philosophy of mathematics. Albany: SUNY Press.

    Google Scholar 

  • Sowa, J.F. 1976. Conceptual graphs for a data base interface. IBM Journal of Research and Development 20(4):336–357.

    Article  Google Scholar 

  • Sowa, J.F. 1984. Conceptual structures: Information processing in mind and machine. Reading, MA: Addison-Wesley.

    Google Scholar 

  • Sowa, J.F. 2000. Knowledge representation: Logical, philosophical, and computational foundations. Pacific Grove, CA: Brooks/Cole Publishing Co.

    Google Scholar 

  • Sowa, J.F. 2005. The challenge of knowledge soup. In Research trends in science, technology, and mathematics education, eds. J. Ramadas, and S. Chunawala, 55–90. Mumbai: Homi Bhabha Centre.

    Google Scholar 

  • Sowa, J.F. 2008. Conceptual graphs. In Handbook of knowledge representation, eds. F. van Harmelen, V. Lifschitz, and B. Porter, 213–237. Amsterdam: Elsevier.

    Chapter  Google Scholar 

  • Sperber, D., and D. Wilson. 1986. Relevance: Communication and cognition. Oxford: Blackwell.

    Google Scholar 

  • Talmy, L. 2000. Toward a cognitive semantics, Volume I: Concept structuring systems, Volume II: Typology and process in concept structure. Cambridge, MA: MIT Press.

    Google Scholar 

  • Tarski, A. 1933. Der Wahrheitsbegriff in den formalisierten Sprachen. English edition: The concept of truth in formalized languages. In Logic, semantics, metamathematics, ed. A. Tarski, 152–278, 2nd edn. Indianapolis, IN: Hackett Publishing Co.

    Google Scholar 

  • Tesnière, L. 1959. Éléments de Syntaxe structurale, 2nd edn, 1965. Paris: L.C. Klincksieck.

    Google Scholar 

  • Tolman, E.C. 1948. Cognitive maps in rats and men. Psychological Review 55(4):189–208.

    Article  Google Scholar 

  • van Deemter, K., and S. Peters. 1996. Semantic ambiguity and underspecification. Stanford, CA: CSLI.

    Google Scholar 

  • Vygotsky, L.S. (Original work published 1934) 1962. Thought and language. Cambridge, MA: MIT Press.

    Google Scholar 

  • Waismann, F. 1979. Ludwig Wittgenstein and the Vienna circle: Conversations recorded by friedrich waismann. Oxford: Blackwell.

    Google Scholar 

  • Wertheimer, M. 1925. Über Gestalttheorie. Gestalt theory (trans: Ellis, W.D., 1938). Source book of Gestalt psychology. New York, NY: Harcourt, Brace and Co.

    Google Scholar 

  • Whitehead, A.N. 1937. Analysis of meaning. Philosophical review, reprinted In Essays in science and philosophy, ed. A.N. Whitehead, 122–131. New York, NY: Philosophical Library.

    Google Scholar 

  • Wierzbicka, A. 1996. Semantics: Primes and universals. Oxford: Oxford University Press.

    Google Scholar 

  • Wilks, Y. 2006. Thesauri and ontologies. In Perspectives on cognition: A Festshrift for Manfred Wettler, eds. S. Rapp, and G. Zunker-Rapp. Lengerich: Pabst.

    Google Scholar 

  • Wilks, Y. 2008a. The semantic web as the apotheosis of annotation, but what are its semantics? IEEE Transactions on Intelligent Systems. May/June 2008.

    Google Scholar 

  • Wilks, Y. 2008b. What would a wittgensteinian computational linguistics be like? Proceedings of AISB’08, Workshop on Computers and Philosophy, Aberdeen.

    Google Scholar 

  • Winograd, T. 1972. Understanding natural language. New York, NY: Academic Press.

    Google Scholar 

  • Wittgenstein, L. 1921. Tractatus logico-philosophicus. London: Routledge & Kegan Paul.

    Google Scholar 

  • Wittgenstein, L. 1953. Philosophical investigations. Oxford: Basil Blackwell.

    Google Scholar 

  • Wittgenstein, L. 1964. Philosophische Bemerkungen. ed. R. Rhees, Philosophical remarks (trans: Hargreaves, R., and White, R., 1980). Chicago: University of Chicago Press.

    Google Scholar 

  • Woods, W.A. 1968. Procedural semantics for a question-answering machine. AFIPS Conference Proceedings. 1968 FJCC, 457–471.

    Google Scholar 

  • Zadeh, L.A. 1975. Fuzzy logic and approximate reasoning. Synthése 30:407–428.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to John F. Sowa .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer Netherlands

About this chapter

Cite this chapter

Sowa, J.F. (2010). The Role of Logic and Ontology in Language and Reasoning. In: Poli, R., Seibt, J. (eds) Theory and Applications of Ontology: Philosophical Perspectives. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-8845-1_11

Download citation

Publish with us

Policies and ethics