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Proof-theoretic semantics for a natural language fragment

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Abstract

The paper presents a proof-theoretic semantics (PTS) for a fragment of natural language, providing an alternative to the traditional model-theoretic (Montagovian) semantics (MTS), whereby meanings are truth-condition (in arbitrary models). Instead, meanings are taken as derivability-conditions in a “dedicated” natural-deduction (ND) proof-system. This semantics is effective (algorithmically decidable), adhering to the “meaning as use” paradigm, not suffering from several of the criticisms formulated by philosophers of language against MTS as a theory of meaning. In particular, Dummett’s manifestation argument does not obtain, and assertions are always warranted, having grounds of assertion. The proof system is shown to satisfy Dummett’s harmony property, justifying the ND rules as meaning conferring. The semantics is suitable for incorporation into computational linguistics grammars, formulated in type-logical grammar.

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References

  • Barwise J., Cooper R. (1981) Generalized quantifiers and natural language. Linguistics and Philosophy 4(2): 159–219

    Article  Google Scholar 

  • Belnap N. (1962) Tonk, Plonk and Plink. Analysis 22: 130–134

    Article  Google Scholar 

  • Ben-Avi, G., & Francez, N. (2004). Categorial grammar with ontology-refined types. In Categorial Grammars 2004: An efficient tool for Natural Language Processing, Montpellier, France, June 2004.

  • Ben-Avi, G., & Francez, N. (2005). A proof-theoretic semantics for the syllogistic fragment. In Proceedings of the Amsterdam Colloquium, Amsterdam, The Netherlands, December.

  • Ben-Avi, G., & Francez, N. (2011). A proof-theoretic reconstruction of generalized quantifiers. In preparation.

  • Boulter S. (2001) Whose challenge. Which semantics. Synthese 126: 325–337

    Google Scholar 

  • Brandom R.B. (2000) Articulating reasons. MA: Harvard University Press, Cambridge

    Google Scholar 

  • de Groote, P., & Retoré, C. (1996). On the semantic readings of proof-nets. In G.-J. Kruijff & D. Oehrle (Eds.), Formal grammar (pp. 57–70). Prague: FOLLI.

  • Dummett M. (1991) The logical basis of metaphysics. MA: Harvard University Press, Cambridge

    Google Scholar 

  • Fernando, T. (2001). Conservative generalized quantifiers and presupposition. In Semantics and linguistic Theory XI (pp. 172–191). Cornell: CLC Publications.

  • Fitch F.B. (1973) Natural deduction rules for English. Philosophical Studies 24: 89–104

    Article  Google Scholar 

  • Forbes G. (2000) Attitude problems. Oxford University Press, Oxford

    Google Scholar 

  • Francez, N., & Ben-Avi, G. (2011). Proof-theoretic semantic values for logical operators. Review of Symbolic Logic. Under refereeing.

  • Francez N., & Dyckhoff, R. (2010). A note on harmony. Journal of Philosophical Logic, accepted.

  • Francez N., Dyckhoff R., Ben-Avi G. (2010) Proof-theoretic semantics for subsentential phrases. Studia Logica 94: 381–401

    Article  Google Scholar 

  • Gentzen, G. (1935). Investigations into logical deduction. In M. E. Szabo (Ed.), The collected papers of Gerhard Gentzen (pp. 68–131). Amsterdam: North-Holland. (English translation of the 1935 paper in German.)

  • Hinzen W. (2000) Anti-realist semantics. Erkenntnis 52: 281–311

    Article  Google Scholar 

  • Lappin, S. (eds) (1997) The handbook of contemporary semantic theory. Blackwell, Oxford

    Google Scholar 

  • Larson R.K. (2001) The grammar of intensionality. In: Preyer G., Peter G. (eds) Logical form and natural language.. Oxford University Press, Oxford, pp 228–262

    Google Scholar 

  • Moltmann F. (1997) Intensional verbs and quantifiers. Natural Language Semantics 5(1): 1–52

    Article  Google Scholar 

  • Moltmann F. (2008) Intensional verbs and their intentional objects. Natural Language Semantics 16(3): 239–270

    Article  Google Scholar 

  • Moltmann, F. (to appear). Abstract objects and the semantics of natural language. Oxford: Oxford University Press.

  • Moortgat M. (1997) Categorial type logics. In: Benthem J., ter Meulen A. (eds) Handbook of logic and language.. North Holland, Amsterdam, pp 93–178

    Chapter  Google Scholar 

  • Montague, R. (1973). The proper treatment of quantification in ordinary English. In J. Hintikka, J. Moravcsik, & P. Suppes (Eds.), Approaches to natural language. Proceedings of the 1970 Stanford workshop on grammar and semantics. Dordrecht: Reidel.

  • Moss L. (2010) Syllogistic logics with verbs. Journal of Logic and Computation 20(4): 947–967

    Article  Google Scholar 

  • Nishihara N., Morita K., Iwata S. (1990) An extended syllogistic system with verbs and proper nouns, and its completeness proof. Systems and Computers in Japan 21(1): 96–111

    Article  Google Scholar 

  • Peregrin J. (1997) Language and models: Is model theory a theory of semantics?. Nordic Journal of Philosophical Logic 2(1): 1–23

    Google Scholar 

  • Pfenning F., Davies R. (2001) A judgmental reconstruction of modal logic. Mathematical Structures in Computer Science 11: 511–540

    Article  Google Scholar 

  • Prawitz, D. (1965). Natural deduction: A proof-theoretical study. Stockholm: Almqvist and Wicksell. (Soft cover edition by Dover, 2006.)

  • Prawitz, D. (1978). Proofs and the meaning and completeness of logical constants. In J. Hintikka, I. Niiniluoto, & E. Saarinen (Eds.), Essays in mathematical and philosophical logic (pp. 25–40). Dordrecht: Reidel.

  • Prior A.N. (1960) The runabout inference-ticket. Analysis 21: 38–39

    Article  Google Scholar 

  • Quine W.v.O. (1969) Ontological relativity and other essays. Columbia University Press, New York

    Google Scholar 

  • Ranta A. (1994) Type-theoretical grammar. Oxford University Press, Oxford

    Google Scholar 

  • Ranta A. (2004a) Computational semantics in type theory. Mathematics and Social Sciences 165: 31–57

    Google Scholar 

  • Ranta A. (2004) Grammatical frameworks: A type-theoretical grammar formalism. The Journal of Functional Programming 14(2): 145–189

    Article  Google Scholar 

  • Rayo, A., Uzquiano, G. (eds) (1997) Absolute generality. Oxford University Press, Oxford

    Google Scholar 

  • Read S. (2000) Harmony and autonomy in classical logic. Journal of Philosophical Logic 29: 123–154

    Article  Google Scholar 

  • Read, S. (2004). Identity and harmony. Analysis, 64(2), 113–119. See correction in Kremer, M., 2007, Read on identity and harmony—A friendly correction and simplification. Analysis, 67(2), 157–159.

  • Read, S. (2008). Harmony and modality. In C. Dégremont, L. Keiff, & H. Rückert (Eds.), On dialogues, logics and other strange things: Essays in honour of Shahid Rahman (pp. 285–303). London: College Publication.

  • Restall, G. (2010). Proof theory and meaning: on the context of deducibility. In Delon, F., Kohlenbach, U., Maddy, P., & Sephan, F. (Eds.), Proceedings of Logica 07, Hejnice, Czech Republic (pp. 204–219). Cambridge: Cambridge University Press.

  • Richard, R. (2001). Seeking a centaur, Adoring Adonis: Intensional transitives and empty terms. In P. French & H. Wettstein (Eds.), Midwest studies in philosophy, Vol. 25: Figurative language (pp. 103–127). Oxford: Blackwell.

  • Schroeder-Heister, P. (2006). Validity concepts in proof-theoretic semantics. In R. Kahle & P. Schroeder- Heister (Eds.), Proof-theoretic semantics, Special issue of Synthese (Vol. 148, pp. 525–571).

  • Tennant N. (1987) Anti-realism and logic Clarendon Library of Logic and Philosophy. Oxford University Press, Oxford

    Google Scholar 

  • van Dalen, D. (1986). Intuitionistic logic. In D. Gabbay & F. Günthner (Eds.), Handbook of philosophical logic (Vol. III, pp. 225–339). Dordrecht: Reidel.

  • von Plato J. (2001) Natural deduction with general elimination rules. Archive for Mathematical Logic 40: 541–567

    Article  Google Scholar 

  • Wieckowski, B. (2011). Rules for subatomic derivation. Review of Symbolic Logic, to appear.

  • Zimmermann T.E. (1993) On the proper treatment of opacity in certain verbs. Natural Language Semantics 1: 149–179

    Article  Google Scholar 

  • Zimmermann, T. E. (2006). Monotonicity in opaque verbs. Linguistics and Philosophy, 29, 715–761. doi:https://doi.org/10.1007/s10988-006-9009-z.

    Article  Google Scholar 

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Authors and Affiliations

  1. Computer Science Department, the Technion-IIT, Haifa, Israel

    Nissim Francez

  2. School of Computer Science, University of St Andrews, St Andrews, Scotland, UK

    Roy Dyckhoff

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  1. Nissim Francez
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  2. Roy Dyckhoff
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Correspondence to Nissim Francez.

Additional information

A preliminary version of the paper was presented at MOL10, Los-Angeles, July 2007.

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Francez, N., Dyckhoff, R. Proof-theoretic semantics for a natural language fragment. Linguist and Philos 33, 447–477 (2010). https://doi.org/10.1007/s10988-011-9088-3

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