Tarski, truth and natural languages. (English) Zbl 1055.03004
Summary: The first part of the paper traces the history of the relationship between logic and linguistics with particular emphasis on the contributions of Tarski and Ajdukiewicz. In the second part we give a brief review of current work on formal semantics for natural language systems and argue for the need for a richer geometric structure on the semantic model space.
MSC:
| 03-03 | History of mathematical logic and foundations |
| 01A60 | History of mathematics in the 20th century |
| 03B65 | Logic of natural languages |
Keywords:
Categorial grammar; Attribute-value systems; Lexical semantics; Natural language systems; Ajdukiewicz; TarskiReferences:
| [1] | K. Ajdukiewicz, Syntactic connection, in: S. MacCall (Ed.), Polish Logic 1920-1939, Oxford University Press, Oxford, UK, 1967. (This is a translation of the original article Die syntaktische Konnexität from 1935.); K. Ajdukiewicz, Syntactic connection, in: S. MacCall (Ed.), Polish Logic 1920-1939, Oxford University Press, Oxford, UK, 1967. (This is a translation of the original article Die syntaktische Konnexität from 1935.) |
| [2] | Barwise, J.; Cooper, R., Generalized quantifiers and natural languages, Language Philos., 4, 159-219 (1981) · Zbl 0473.03033 |
| [3] | J. Barwise, J. Perry, Situations and Attitudes, MIT Press, Cambridge, MA, USA, 1983.; J. Barwise, J. Perry, Situations and Attitudes, MIT Press, Cambridge, MA, USA, 1983. · Zbl 0946.03007 |
| [4] | J. van Benthem, A. ter Meulen, Handbook of Logic and Language, North-Holland, Amsterdam, Netherlands, 1997.; J. van Benthem, A. ter Meulen, Handbook of Logic and Language, North-Holland, Amsterdam, Netherlands, 1997. · Zbl 0874.03001 |
| [5] | L. Bloomfield, Linguistic Aspects of Science, in: O. Neurath et al. (Eds.), [27], pp. 219-277.; L. Bloomfield, Linguistic Aspects of Science, in: O. Neurath et al. (Eds.), [27], pp. 219-277. |
| [6] | R. Blutner, Lexical Semantics and Pragmatics, see http://www.blutner.de/; R. Blutner, Lexical Semantics and Pragmatics, see http://www.blutner.de/ · Zbl 1073.68082 |
| [7] | J. Bresnan, The Mental Representation of Grammatical Relations, MIT Press, Cambridge, MA, USA, 1982.; J. Bresnan, The Mental Representation of Grammatical Relations, MIT Press, Cambridge, MA, USA, 1982. |
| [8] | R. Carnap, Logical Syntax of Language, Routledge and Kegan Paul, London, UK, 1937. (This is a translation of the German original Logische Syntax der Sprache from 1934.); R. Carnap, Logical Syntax of Language, Routledge and Kegan Paul, London, UK, 1937. (This is a translation of the German original Logische Syntax der Sprache from 1934.) · JFM 63.0820.05 |
| [9] | B. Carpenter, Type-Logical Semantics, MIT Press, Cambridge, MA, USA, 1997.; B. Carpenter, Type-Logical Semantics, MIT Press, Cambridge, MA, USA, 1997. · Zbl 0913.68133 |
| [10] | N. Chomsky, Syntactic Structures, Mouton and Co, The Hague, Netherlands, 1957.; N. Chomsky, Syntactic Structures, Mouton and Co, The Hague, Netherlands, 1957. |
| [11] | N. Chomsky, Aspects of the Theory of Syntax, MIT Press, Cambridge, MA, USA, 1965.; N. Chomsky, Aspects of the Theory of Syntax, MIT Press, Cambridge, MA, USA, 1965. |
| [12] | H.B. Curry, Some logical aspects of grammatical structure, in: R. Jakobson (Ed.), The Structure of Language and its Mathematical Aspects, Amer. Math. Soc., Providence, RI, USA, 1961.; H.B. Curry, Some logical aspects of grammatical structure, in: R. Jakobson (Ed.), The Structure of Language and its Mathematical Aspects, Amer. Math. Soc., Providence, RI, USA, 1961. · Zbl 0111.16102 |
| [13] | Fenstad, J. E., Models for natural languages, (Hintikka, J.; Niiniluoto, I.; Saarinen, E., Essays on Mathematical and Philosophical Logic (1978), Reidel, Dordrecht: Reidel, Dordrecht Netherlands) · Zbl 0402.03010 |
| [14] | Fenstad, J. E., Remarks on the science and technology of language, European Rev., 4, 107-219 (1996) |
| [15] | Fenstad, J. E., Formal semantics, geometry and mind, (Arrazola, X.; etal., Discourse, Interaction and Communication (1998), Kluwer, Dordrecht: Kluwer, Dordrecht Netherlands), 85-103 |
| [16] | Fenstad, J. E.; Halvorsen, P. K.; Langholm, T.; van Benthem, J., Situations, Language and Logic (1987), Reidel, Dordrecht: Reidel, Dordrecht Netherlands · Zbl 0731.03002 |
| [17] | P. Gärdenfors, Conceptual Spaces: The Geometry of Thought, MIT Press, Cambridge, MA, USA, 2000.; P. Gärdenfors, Conceptual Spaces: The Geometry of Thought, MIT Press, Cambridge, MA, USA, 2000. |
| [18] | Z. Harris, Methods in Structural Linguistics, University of Chicago Press, Chicago, IL, USA, 1951.; Z. Harris, Methods in Structural Linguistics, University of Chicago Press, Chicago, IL, USA, 1951. |
| [19] | Kamp, H.; Reyle, U., From Discourse to Logic (1993), Kluwer, Dordrecht: Kluwer, Dordrecht Netherlands |
| [20] | R. Kaplan, J. Bresnan, Lexical-Functional Grammar, in: J. Bresnan (Ed.), [7], pp. 173-281.; R. Kaplan, J. Bresnan, Lexical-Functional Grammar, in: J. Bresnan (Ed.), [7], pp. 173-281. |
| [21] | J. Koster, How natural is natural language, in: J.E. Fenstad, I.T. Frolov, R. Hilpinen (Eds.), Studies in Logic, Vol. 126, North-Holland, Amsterdam, Netherlands, 1989, pp. 591-606.; J. Koster, How natural is natural language, in: J.E. Fenstad, I.T. Frolov, R. Hilpinen (Eds.), Studies in Logic, Vol. 126, North-Holland, Amsterdam, Netherlands, 1989, pp. 591-606. |
| [22] | R. Langacker, Foundation of Cognitive Grammar, Vols. I and II, Stanford University Press, Stanford, CA, USA, 1987 and 1991.; R. Langacker, Foundation of Cognitive Grammar, Vols. I and II, Stanford University Press, Stanford, CA, USA, 1987 and 1991. |
| [23] | Lesniewski, S., Grundzüge eines neuen Systems der Grundlagen der Mathematik, Fund. Math., 14, 1-81 (1929) · JFM 55.0626.03 |
| [24] | R. Montague, The Proper Treatment of Quantification in Ordinary English, in: R. Thomason (Ed.), [35], pp. 247-270.; R. Montague, The Proper Treatment of Quantification in Ordinary English, in: R. Thomason (Ed.), [35], pp. 247-270. |
| [25] | C.W. Morris, Foundation of the Theory of Signs, in: O. Neurath, et al. (Eds.), [27], pp. 77-137.; C.W. Morris, Foundation of the Theory of Signs, in: O. Neurath, et al. (Eds.), [27], pp. 77-137. |
| [26] | O. Neurath, Encyclopedia and Unified Science, in: O. Neurath, et al. (Eds.), [27], pp. 1-27.; O. Neurath, Encyclopedia and Unified Science, in: O. Neurath, et al. (Eds.), [27], pp. 1-27. |
| [27] | O. Neurath, R. Carnap, C. Morris (Eds.), International Encyclopedia of Unified Science, Vol. I, University of Chicago Press, Chicago, IL, USA, 1955.; O. Neurath, R. Carnap, C. Morris (Eds.), International Encyclopedia of Unified Science, Vol. I, University of Chicago Press, Chicago, IL, USA, 1955. |
| [28] | C. Pollard, I. Sag, Information-Based Syntax and Semantics, Vol. 1, CSLI, Stanford, CA, USA, 1987.; C. Pollard, I. Sag, Information-Based Syntax and Semantics, Vol. 1, CSLI, Stanford, CA, USA, 1987. |
| [29] | J. Pustejovsky, The Generative Lexicon, MIT Press, Cambridge, MA, USA, 1995.; J. Pustejovsky, The Generative Lexicon, MIT Press, Cambridge, MA, USA, 1995. |
| [30] | H. Reichenbach, Elements of Symbolic Logic, Macmillan, London, UK, 1947.; H. Reichenbach, Elements of Symbolic Logic, Macmillan, London, UK, 1947. · Zbl 0034.00301 |
| [31] | M. Rosner, R. Johnson (Eds.), Computational Linguistics and Formal Semantics, Cambridge University Press, Cambridge, UK, 1992.; M. Rosner, R. Johnson (Eds.), Computational Linguistics and Formal Semantics, Cambridge University Press, Cambridge, UK, 1992. |
| [32] | K. Skrindo, Leksikalsk Semantikk, Matematisk Institutt, Oslo, Norway, 2001 (in Norwegian).; K. Skrindo, Leksikalsk Semantikk, Matematisk Institutt, Oslo, Norway, 2001 (in Norwegian). |
| [33] | K.I.B. Spärck Jones, G.J.M. Gazdar, R.M. Needham (Eds.), Computers, Language and Speech: Formal Theories and Statistical Data, The Royal Society, London, UK, 2000.; K.I.B. Spärck Jones, G.J.M. Gazdar, R.M. Needham (Eds.), Computers, Language and Speech: Formal Theories and Statistical Data, The Royal Society, London, UK, 2000. · Zbl 0964.68542 |
| [34] | A. Tarski, The concept of truth in formalized languages, in: A. Tarski (Ed.), Logic, Semantics, Metamathematics, Oxford University Press, Oxford, UK, 1956. (This paper is a translation of the original article Der Wahrheitsbegriff in den formalisierten Sprachen from 1936.); A. Tarski, The concept of truth in formalized languages, in: A. Tarski (Ed.), Logic, Semantics, Metamathematics, Oxford University Press, Oxford, UK, 1956. (This paper is a translation of the original article Der Wahrheitsbegriff in den formalisierten Sprachen from 1936.) · JFM 62.1051.05 |
| [35] | R. Thomason, Formal Philosophy, Selected Papers of Richard Montague, Yale University Press, New Haven, CT, USA, 1974.; R. Thomason, Formal Philosophy, Selected Papers of Richard Montague, Yale University Press, New Haven, CT, USA, 1974. |
| [36] | Thomas of Erfurt, Grammatica Speculativa (Edition and translation by G.L. Bursill-Hall), Longman, London, UK, 1972.; Thomas of Erfurt, Grammatica Speculativa (Edition and translation by G.L. Bursill-Hall), Longman, London, UK, 1972. |
| [37] | E. Vestre, Representasjon av Direkte Sp \(ø\); E. Vestre, Representasjon av Direkte Sp \(ø\) |
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