Introduction
We propose a Proof − Theoretic Semantics (PTS) for a (positive) fragment \(E^{+}_{0}\) of Natural Language (NL) (English in this case). The semantics is intended [7] to be incorporated into actual grammars, within the framework of Type − Logical Grammar (TLG) [12]. Thereby, this semantics constitutes an alternative to the traditional model − theoretic semantics (MTS), originating in Montague’s seminal work [11], used in TLG.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Ben-Avi, G., Francez, N.: A proof-theoretic reconstruction of generalized quantifiers (2009) (submitted for publication)
Brandom, R.B.: Articulating Reasons. Harvard University Press, Cambridge (2000)
Dummett, M.: The Logical Basis of Metaphysics. Harvard University Press, Cambridge (1991)
Francez, N., Ben-Avi, G.: Proof-theoretic semantic values for logical operator. Synthese (2009) (under refereeing)
Francez, N., Dyckhoff, R.: A note on proof-theoretic validity (2007) (in preparation)
Francez, N., Dyckhoff, R.: A note on harmony. Journal of Philosophical Logic (2007) (submitted)
Francez, N., Dyckhoff, R., Ben-Avi, G.: Proof-theoretic semantics for subsentential phrases. Studia Logica 94, 381–401 (2010), doi:10.1007/s11225-010-9241-y
Gentzen, G.: Investigations into logical deduction. In: Szabo, M. (ed.) The collected papers of Gerhard Gentzen, pp. 68–131. North-Holland, Amsterdam (1935) (english translation of the 1935 paper in German)
de Groote, P., Retore, C.: On the semantic readings of proof-nets. In: Kruijf, G.J., Oehrle, D. (eds.) Formal Grammar, pp. 57–70. FOLLI (1996)
Kremer, M.: Read on identity and harmony – a friendly correction and simplification. Analysis 67(2), 157–159 (2007)
Montague, R.: The proper treatment of quantification in ordinary english. In: Hintikka, J., Moravcsik, J., Suppes, P. (eds.) Approaches to natural language, Reidl, Dordrecht (1973); proceedings of the 1970 Stanford workshop on grammar and semantics
Moortgat, M.: Categorial type logics. In: van Benthem, J., ter Meulen, A. (eds.) Handbook of Logic and Language, pp. 93–178. North-Holland, Amsterdam (1997)
Moss, L.: Syllogistic logics with verbs. Journal of Logic and Information (to appear 2010)
Pfenning, F., Davies, R.: A judgmental reconstruction of modal logic. Mathematical Structures in Computer Science 11, 511–540 (2001)
Plato, J.V.: Natural deduction with general elimination rules. Archive Mathematical Logic 40, 541–567 (2001)
Prawitz, D.: Natural Deduction: Proof-Theoretical Study. Almqvist and Wicksell, Stockholm (1965)
Prior, A.N.: The roundabout inference-ticket. Analysis 21, 38–39 (1960)
Read, S.: Harmony and autonomy in classical logic. Journal of Philosophical Logic 29, 123–154 (2000)
Read, S.: Identity and harmony. Analysis 64(2), 113–119 (2004); see correction in [10]
Read, S.: Harmony and modality. In: Dégremont, C., Kieff, L., Rückert, H. (eds.) Dialogues, Logics and Other Strong Things: Essays in Honour of Shahid Rahman, pp. 285–303. College Publications (2008)
Restall, G.: Proof theory and meaning: on the context of deducibility. In: Proceedings of Logica 2007, Hejnice, Czech Republic (2007)
Schroeder-Heister, P.: Validity concepts in proof-theoretic semantics. In: Kale, R., Schroeder-Heister, P. (eds.) Proof-Theoretic Semantics, vol. 148, pp. 525–571 (February 2006), special issue of Synthese
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Francez, N., Dyckhoff, R. (2010). Proof-Theoretic Semantics for a Natural Language Fragment. In: Ebert, C., Jäger, G., Michaelis, J. (eds) The Mathematics of Language. MOL MOL 2009 2007. Lecture Notes in Computer Science(), vol 6149. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14322-9_6
Download citation
DOI: https://doi.org/10.1007/978-3-642-14322-9_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-14321-2
Online ISBN: 978-3-642-14322-9
eBook Packages: Computer ScienceComputer Science (R0)