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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
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.
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.
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.
Aristotle, Works, Loeb Library, Cambridge, MA: Harvard University Press.
Austin, J.L. 1962. How to do things with words, eds. J.O. Urmson, and M. Sbisá, 2nd edn. Cambridge, MA: Harvard University Press.
Barwise, J., and J. Perry. 1983. Situations and attitudes. Cambridge, MA: MIT Press.
Bartlett, F.C. 1932. Remembering. Cambridge: Cambridge University Press.
Bharati, A., V. Chaitanya, and R. Sangal. 1995. Natural language processing: A Paninian perspective. New Delhi: Prentice-Hall of India.
Bohnert, H., and P. Backer. 1967. Automatic English-to-logic translation in a simplified model. Technical report RC-1744. Yorktown Heights, NY: IBM.
Boole, G. 1854. An Investigation into the laws of thought. Reprinted. New York, NY: Dover.
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.
Bundy, A. 2007. Cooperating reasoning processes: More than just the sum of their parts. Proceedings of IJCAI-07, 2–11.
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.
Ceccato, S. 1961. Linguistic analysis and programming for mechanical translation. New York, NY: Gordon and Breach.
Chomsky, N. 1957. Syntactic structures. The Hague: Mouton.
Chomsky, N. 1965. Aspects of the theory of syntax. Cambridge, MA: MIT Press.
Chomsky, N. 1995. The minimalist program. Cambridge, MA: MIT Press.
Croft, W., and D.A. Cruse. 2004. Cognitive linguistics. Cambridge: Cambridge University Press.
Cruse, D.A. 1986. Lexical semantics. New York, NY: Cambridge University Press.
Cruse, D.A. 2002. Microsenses, default specificity and the semantics-pragmatics boundary. Axiomathes 1:1–20.
Fillmore, C. 1988. The mechanisms of construction grammar. Berkeley Linguistics Society 35:35–55.
Förster, E. 2000. Kant’s final synthesis: An essay on the opus postumum. Cambridge, MA: Harvard University Press.
Frege, G. 1879. Begriffsschrift. English translation in J. van Heijenoort, ed. 1967. From Frege to Gödel. Cambridge, MA: Harvard University Press. 1–82.
Goldberg, A.E. 1995. Constructions: A construction grammar approach to argument structure. Chicago, IL: University of Chicago Press.
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.
Halliday, M.A.K. 1978. Language as social semiotic: The social interpretation of language and meaning. Baltimore: University Park Press.
Halliday, M.A.K. and C.M.I.M. Matthiessen. 1999. Construing experience through meaning: A language-based approach to cognition. London: Cassell.
Harris, Z.S. 1951. Methods in structural linguistics. Chicago: University of Chicago Press.
ISO/IEC. 2007. Common logic (CL)—A framework for a family of logic-based languages. IS 24707. Geneva: International Organisation for Standardisation.
Jackendoff, R. 1983. Semantics and cognition. Cambridge, MA: MIT Press.
Kant, I. 1787. Kritik der reinen Vernunft. Critique of pure reason (trans: N. Kemp Smith). New York, NY: St. Martin’s Press.
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.
Lakoff, G. 1987. Women, fire, and dangerous things. Chicago: University of Chicago Press.
Langacker, R.W. 1999. Grammar and conceptualization. Berlin: de Gruyter.
Lenat, D.B. 1995. CYC: A large-scale investment in knowledge infrastructure. Communications of the ACM 38(11):33–38.
Lord, A.B. 1960. The singer of tales. Cambridge, MA: Harvard University Press.
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.
Makinson, D. 2005. Bridges from classical to nonmonotonic logic. London: King’s College Publications.
Mann, W.C., and S.A. Thompson. 1988. Rhetorical structure theory: Towards a functional theory of text organization. Text 8(3):243–281.
Masterman, M. 2005. Language, chohesion and form. ed. Y. Wilks. Cambridge: Cambridge University Press.
Miller, G.A. 1995. WordNet: A lexical database for English. Communications of the ACM 38(11):39–41.
Minsky, M. 1975. A framework for representing knowledge. In The psychology of computer vision, ed. P. Winston, 211–280. New York, NY: McGraw-Hill.
Minsky, M. 1987. The society of mind. New York, NY: Simon & Schuster.
Minsky, M. 2006. The emotion machine: Commonsense thinking, artificial intelligence, and the future of the human mind. New York, NY: Simon & Schuster.
Mohanty, J.N. 1982. Husserl and frege. Bloomington: Indiana University Press.
Montague, R. 1970. English as a formal language. reprinted In Formal philosophy, ed. R. Montague, 188–221.New Haven: Yale University Press.
Newell, A., and H.A. Simon. 1972. Human problem solving. Englewood Cliffs, NJ: Prentice-Hall.
Ockham, William of (1323) Summa logicae, Paris: Johannes Higman. 1488 (the edition owned by C.S. Peirce).
Ogden, C.K., and I.A. Richards. 1923. The meaning ofmeaning, 8th edn, 1946. New York, NY: Harcourt, Brace, and World.
Peirce, C.S. 1880. On the algebra of logic. American Journal of Mathematics 3:15–57.
Peirce, C.S. 1885. On the algebra of logic. American Journal of Mathematics 7:180–202.
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.
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.
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.
Peppas, P. 2008. Belief revision. In Handbook of knowledge representation, eds. F. van Harmelen, V. Lifschitz, and B. Porter, 317–359. Amsterdam: Elsevier.
Post, E.L. 1943. Formal reductions of the general combinatorial decision problem. American Journal of Mathematics 65:197–268.
Propp, V. 1928. Morfologia Skazki. translated as Morphology of the folktale, 1958. Austin: University of Texas Press.
Reid, T. 1785. Essays on the intellectual power of man. Edinburgh: Edinburgh University Press.
de Saussure, F. 1916. Cours de Linguistique Générale. Course in general linguistics (trans: Baskin, W., 1959). New York, NY: Philosophical Library.
Schank, R.C., ed. 1975. Conceptual information processing. Amsterdam: North-Holland Publishing Co.
Schank, R.C., and R.P. Abelson. 1977. Scripts, plans, goals and understanding. Hilsdale, NJ: Erlbaum
Selz, O. 1913. Über die Gesetze des geordneten Denkverlaufs. Stuttgart: Spemann.
Shanker, S.G. 1987. Wittgenstein and the turning point in the philosophy of mathematics. Albany: SUNY Press.
Sowa, J.F. 1976. Conceptual graphs for a data base interface. IBM Journal of Research and Development 20(4):336–357.
Sowa, J.F. 1984. Conceptual structures: Information processing in mind and machine. Reading, MA: Addison-Wesley.
Sowa, J.F. 2000. Knowledge representation: Logical, philosophical, and computational foundations. Pacific Grove, CA: Brooks/Cole Publishing Co.
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.
Sowa, J.F. 2008. Conceptual graphs. In Handbook of knowledge representation, eds. F. van Harmelen, V. Lifschitz, and B. Porter, 213–237. Amsterdam: Elsevier.
Sperber, D., and D. Wilson. 1986. Relevance: Communication and cognition. Oxford: Blackwell.
Talmy, L. 2000. Toward a cognitive semantics, Volume I: Concept structuring systems, Volume II: Typology and process in concept structure. Cambridge, MA: MIT Press.
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.
Tesnière, L. 1959. Éléments de Syntaxe structurale, 2nd edn, 1965. Paris: L.C. Klincksieck.
Tolman, E.C. 1948. Cognitive maps in rats and men. Psychological Review 55(4):189–208.
van Deemter, K., and S. Peters. 1996. Semantic ambiguity and underspecification. Stanford, CA: CSLI.
Vygotsky, L.S. (Original work published 1934) 1962. Thought and language. Cambridge, MA: MIT Press.
Waismann, F. 1979. Ludwig Wittgenstein and the Vienna circle: Conversations recorded by friedrich waismann. Oxford: Blackwell.
Wertheimer, M. 1925. Über Gestalttheorie. Gestalt theory (trans: Ellis, W.D., 1938). Source book of Gestalt psychology. New York, NY: Harcourt, Brace and Co.
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.
Wierzbicka, A. 1996. Semantics: Primes and universals. Oxford: Oxford University Press.
Wilks, Y. 2006. Thesauri and ontologies. In Perspectives on cognition: A Festshrift for Manfred Wettler, eds. S. Rapp, and G. Zunker-Rapp. Lengerich: Pabst.
Wilks, Y. 2008a. The semantic web as the apotheosis of annotation, but what are its semantics? IEEE Transactions on Intelligent Systems. May/June 2008.
Wilks, Y. 2008b. What would a wittgensteinian computational linguistics be like? Proceedings of AISB’08, Workshop on Computers and Philosophy, Aberdeen.
Winograd, T. 1972. Understanding natural language. New York, NY: Academic Press.
Wittgenstein, L. 1921. Tractatus logico-philosophicus. London: Routledge & Kegan Paul.
Wittgenstein, L. 1953. Philosophical investigations. Oxford: Basil Blackwell.
Wittgenstein, L. 1964. Philosophische Bemerkungen. ed. R. Rhees, Philosophical remarks (trans: Hargreaves, R., and White, R., 1980). Chicago: University of Chicago Press.
Woods, W.A. 1968. Procedural semantics for a question-answering machine. AFIPS Conference Proceedings. 1968 FJCC, 457–471.
Zadeh, L.A. 1975. Fuzzy logic and approximate reasoning. Synthése 30:407–428.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights 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
DOI: https://doi.org/10.1007/978-90-481-8845-1_11
Published:
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-8844-4
Online ISBN: 978-90-481-8845-1
eBook Packages: Humanities, Social Sciences and LawPhilosophy and Religion (R0)