Abstract
In the formal semantics based on modern type theories, common nouns are interpreted as types, rather than as predicates of entities as in Montague’s semantics. This brings about important advantages in linguistic interpretations but also leads to a limitation of expressive power because there are fewer operations on types as compared with those on predicates. The theory of coercive subtyping adequately extends the modern type theories and, as shown in this paper, plays a very useful role in making type theories more expressive for formal semantics. It not only gives a satisfactory solution to the basic problem of ‘multiple categorisation’ caused by interpreting common nouns as types, but provides a powerful formal framework to model interesting linguistic phenomena such as copredication, whose formal treatment has been found difficult in a Montagovian setting. In particular, we show how to formally introduce dot-types in a type theory with coercive subtyping and study some type-theoretic constructs that provide useful representational tools for reference transfers and multiple word meanings in formal lexical semantics.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Agda proof assistant (version 2). (2008). Available from the web page: http://appserv.cs.chalmers.se/users/ulfn/wiki/agda.php.
Asher N. (2008) A type driven theory of predication with complex types. Fundamenta Informaticae 84(2): 151–183
Asher, N. (2011). Lexical meaning in context: A web of words. Cambridge: Cambridge University Press.
Asher, N., & Pustejovsky, J. (2005). Word meaning and commonsense metaphysics.
Bailey, A. (1999). The machine-checked literate formalisation of algebra in type theory. PhD thesis, University of Manchester.
Callaghan P., Luo Z. (2001) An implementation of LF with coercive subtyping and universes. Journal of Automated Reasoning 27(1): 3–27
Church A. (1940) A formulation of the simple theory of types. Journal of Symbolic Logic 5(1): 56–68
Cooper, R. (2007). Copredication, dynamic generalized quantification and lexical innovation by coercion. In Proceedings of GL2007, the fourth international workshop on generative approaches to the lexicon.
Cooper, R. (2011). Copredication, quantification and frames. In Logical aspects of computational linguistics (LACL’2011). LNAI 6736.
Coq Development Team. (2007). The Coq proof assistant reference manual (Version 8.1). Orsay: INRIA.
Coquand T., Huet G. (1988) The calculus of constructions. Information and Computation 76(2–3): 95–120
Curry, H. B., & Feys, R. (1958). Combinatory logic (Vol. 1). Amsterdam: North Holland.
Dummett, M. (1975). The philosophical basis of intuitionistic logic. In H. Rose & J. Shepherdson (Eds.), Proceedings of the logic colloquium, 1973. Amsterdam: North Holland. (Reprinted in P. Benacerraf & H. Putnam (Eds.), Philosophy of mathematics: Selected readings. Cambridge: Cambridge University Press.)
Dummett, M. (1991). The logical basis of metaphysics. London: Duckworth.
Feferman, S. (2005). Predicativity. In S. Shapiro (Ed.), The Oxford handbook of philosophy of mathematics and logic. Oxford: Oxford University Press.
Geach, P. (1962). Reference and generality. Ithaca, NY: Cornell University Press.
Howard, W. A. (1980). The formulae-as-types notion of construction. In J. Hindley & J. Seldin (Eds.), To H. B. Curry: Essays on combinatory logic. New York: Academic Press.
Luo, Y. (2005). Coherence and transitivity in coercive subtyping. PhD thesis, University of Durham.
Luo, Z. (1994). Computation and reasoning: A type theory for computer science. Oxford: Oxford University Press.
Luo, Z. (1997). Coercive subtyping in type theory. In Computer science logic 1996. Lecture notes in computer science 1258. New York: Springer.
Luo Z. (1999) Coercive subtyping. Journal of Logic and Computation 9(1): 105–130
Luo, Z. (2010). Type-theoretical semantics with coercive subtyping. In Semantics and linguistic theory 20 (SALT20), Vancouver.
Luo, Z. (2011a). Adjectives and adverbs in type-theoretical semantics. Notes.
Luo, Z. (2011b). Contextual analysis of word meanings in type-theoretical semantics. In Logical aspects of computational linguistics (LACL’2011). LNAI 6736.
Luo, Z. (2011c). Type-theoretical semantics with coercive subtyping. Lecture notes at ESSLLI 2011 (for the course on Lexical Semantics, taught together with Nicholas Asher), Ljubljana, Slovenia.
Luo, Z. (2012). Common nouns as types. In Logical aspects of computational linguistics(LACL’2012). LNAI 7351.
Luo, Z., & Callaghan, P. (1998). Coercive subtyping and lexical semantics (extended abstract). In Logical aspects of computational linguistics (LACL’98).
Luo, Z., & Pollack, R. (1992). LEGO proof development system: User’s manual. LFCS report ECS-LFCS-92-211, Department of Computer Science, University of Edinburgh.
Luo, Z., Soloviev, S., & Xue, T. (2012). Coercive subtyping: Theory and implementation. Information and Computation, 223(2013), 18–42.
Marlet, R. (2007). When the generative lexicon meets computational semantics. In Proceedings of the 4th international workshop on generative approaches to the lexicon (GL 2007).
Martin-Löf, P. (1984). Intuitionistic type theory. Napoli: Bibliopolis.
Martin-Löf, P. (1996). On the meanings of the logical constants and the justifications of the logical laws. Nordic Journal of Philosophical Logic, 1(1), 11–60.
Matita proof assistant. (2008). http://matita.cs.unibo.it/.
Moens M., Steedman M. (1988) Temporal ontology and temporal reference. Computational Linguistics 14: 15–28
Montague, R. (1974). Formal philosophy. New Haven, CT: Yale University Press. (Collection edited by R. Thomason).
Nordström, B., Petersson, K., & Smith, J. (1990). Programming in Martin-Löf’s type theory. Oxford: Oxford University Press.
Nunberg G. (1995) Transfers of meaning. Journal of Semantics 12(2): 109–132
Partee, B. (1986). Noun phrase interpretations and type-shifting principles. In J. Groenendijk, D. de Jongh, & M. Stokhof (Eds.), Studies in discourse representation theory and the theory of generalised quantifiers. Dordrecht: Foris.
Partee, B. (2010). Privative adjectives: Subsective plus coercion. In R. Bauerle, U. Reyle, & T. Zimmermann (Eds.), Presuppositions and discourse: Essays offered to Hans Kamp, volume 21 of Current research in semantics/pragmatics interface. Cambridge, MA: Emerald Group Publishing.
Partee, B., & Rooth, M. (1983). Generalised conjunction and type ambiguity. In R. Bauerle, C. Schwarze, & A. von Stechow (Eds.), Meaning, use, and interpretation of language. Berlin: De Gruyter.
Prawitz, D. (1974). On the idea of a general proof theory. Synthese, 27, 63–77.
Pustejovsky, J. (1995). The generative lexicon. Cambridge, MA: MIT Press.
Pustejovsky, J. (2005). A survey of dot objects. Manuscript.
Pustejovsky, J. (2011). Mechanisms of coercion in a general theory of selection.
Ranta, A. (1994). Type-theoretical grammar. Oxford: Oxford University Press.
Saïbi, A. (1997). Typing algorithm in type theory with inheritance. In Proceedings of principles of programming languages 1997.
Soloviev S., Luo Z. (2002) Coercion completion and conservativity in coercive subtyping. Annals of Pure and Applied Logic 113(1–3): 297–322
Xue, T., & Luo, Z. (2012). Dot-types and their implementation. In Logical aspects of computational linguistics (LACL’2012). LNAI 7351.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Luo, Z. Formal semantics in modern type theories with coercive subtyping. Linguist and Philos 35, 491–513 (2012). https://doi.org/10.1007/s10988-013-9126-4
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10988-013-9126-4