The unifying topic of this thesis was the concept of discourse.
In the first part of the thesis we accounted for discourse related notions such as anaphora, quantifier scope, binding, singular and plural pronouns (conjunction and disjunction, distibutivity and maximality condition included) ellipsis, accommodation, quantifying over eventualities (Dinu 2011.a, Dinu 2011.b). All of these phenomena needed no extra stipulations to be accounted for in continuation semantics framework. This is due to the fact that the continuation based semantics provides a unified account of scope-taking. No other theory to our knowledge lets indefinites, other quantifiers, pronouns and other anaphors interact in a uniform system of scope taking, in which quantification and binding employ the same mechanism. We also proposed a mechanism (left underspecified in previous work on continuation semantics) which ensures that no lexical entry having the scope bounded to its minimal clause (such as not, no, every, each, any, etc) will ever take scope outside (Dinu 2011.c).
The second part of this thesis presented the work on creating and analyzing electronic resources for Romanian language: a Romanian Generative Lexicon (Dinu 2010.a, Dinu 2010.b) and a corpus for the study of differential object marking in Romanian (Dinu and Tigau 2010). RoGL contains a corpus, an ontology of types, a graphical interface and a database from which we generate data in XML format. The interface and the data base where the annotated lexical entries are stored and processed are hosted on the server of Faculty of Mathematics and Computer Science, University of Bucharest: http://ro-gl.fmi.unibuc.ro. To implement the generative structure and the composition rules, we have chosen the functional programming language Haskell. Our choice was determined by the fact that reducing expressions in lambda calculus (obviously needed in a GL implementation), evaluating a program (i.e. function) in Haskell, and composing the meaning of a natural language sentence are, in a way, all the same thing. The most important work which still needs to be done in RoGL framework is to annotate more lexical entries. The manual annotation, although standardized and mediated by the graphical interface is notoriously time consuming especially for complex information such as those required by a generative lexicon.
Building a Romanian corpus for the study of Differential Object Marking (DOM) was motivated by the fact that in Romanian the uses of the accusative marker “pe” with the direct object (in combination or not with clitics) involve mechanisms which are not fully understood and seeming messy for the non-native speaker: sometimes the accusative marker is obligatory, sometimes it is optional and even forbidden. This research provided a systematic account for these linguistic phenomena based on empirical evidence present in the corpora. Such an account may be used in subsequent studies to improve statistical methods with targeted linguistic knowledge.
The third part of the thesis comprised two experiments of classification by coherence/incoherence of short English and Romanian texts, respectively, using machine learning techniques (Dinu 2010.c, Dinu 2008). We proposed a quantitative approach that relies on the use of ratios between morphological categories from the texts as discriminant features, assuming that these ratios are not completely random in coherent text. We used a number of supervised machine learning techniques, letting the algorithms to extract important features from all the pos ratios.
In this thesis, we have analyzed the semantic content of distinct lexical entries, as well as of the discourse as a hole, using computer science tools and methods such as continuations and machine learning techniques.
We leave for future research challenging issues such as:
-
Completing an algorithm that generates all possible interpretations for a given piece of discourse in continuation semantics framework ;
-
The possibility to express situation semantics in continuation framework;
-
A complete specification of event semantics, that is obviously not possible without taking into consideration thematic roles, aspect, modality and tense.
-
A way of representing the imprecision of the restriction RelevEvent, needed to implement the event semantics presented in this work.
-
The comparison of our approach to anaphora to anaphora in algebraic linguistics.
References:
-
Aissen, Judith. 2003. Differential Object Marking: Iconicity vs. Economy. Natural Language and Linguistic Theory 21: 435-483.
-
Ajdukiewicz, Kazimierz. 1935. Die syntaktische Konnexitat. In Polish Logic 1920-1939, ed. StorrsMcCall.
-
Asher, Nicholas and Alex Lascarides. 2003. Logics of Conversation, Cambridge University Press.
-
Asher, Nicholas and Sylvain Pogodalla. 2010. SDRT and continuation semantics. In Proceedings of the Seventh International Workshop on Logic and Engineering of Natural Language Semantics (LENLS 7), ISBN: 978-4-915905-41-4 C3004(JSAI), JSAI International Symposia on AI 2010, Campus Innovation Center, Tokyo, Japan.
-
Bach, Emmon. 1981. On Time, Tense, and Aspect: An Essay in English Metaphysics. In P. Cole (ed.). Radical Pragmatics, pp. 63-81.
-
Bach, Emmon. 1986. The Algebra of Events. Linguistics and Philosophy 9, 5-16.
-
Barbu, Ana Maria. 2008. Romanian Lexical Data Bases: Inflected and Syllabic Forms Dictionaries. Proceedings of LREC 2008, May, 28-30, Marrakech, Marocco.
-
Bar-Hillel, Yehoshua. 1953. A Quasi-arithmetical Notation for Syntactic Description. Language 29:47–58.
-
Barker, Chris and Shan Chung-chieh. 2008. Donkey anaphora is in-scope binding. In Semantics & Pragmatics Volume 1, pages 1–46.
-
Barker, Chris and Shan Chung-chieh. 2006. Types as graphs: Continuations in Type-Logical Grammar. Journal of Logic, Language, and Information 15.4: 331–370.
-
Barker, Chris. 2002. Continuations and the nature of quantification. Natural Language Semantics 10(3). 211–242.
-
Barker, Chris. 2004. Continuations in natural language. In Hayo Thielecke, editor, Proceedings of the fourth ACM SIGPLAN workshop on continuations, pages 55–64.
-
Barwise, Jon and Robin Cooper. 1981. Generalized quantifiers and natural language. Linguistics and philosophy 4: 159–219.
-
Bird, Richard. 1998. Introduction to Functional Programming Using Haskell. Prentice Hall.
-
Brasoveanu, Adrian. 2007. Structured nominal and modal reference. Ph.D. thesis, Rutgers University.
-
Federica Busa, Nicoletta Calzolari, Alessandro Lenci 2001. Generative Lexicon and the SIMPLE Model; Developing Semantic Resources for NLP, in Bouillon P. and Busa F. (eds.), The Language of Word Meaning, Cambridge University Press, pp. 333-349.
-
Carlson, Lauri 1981. Aspect and Quantification. P. Tedeschi & A. Zaenen (eds.), 31-64.
-
Champollion, Lucas. 2010. Quantification in event semantics. Presented at the 6th International Symposium of Cognition, Logic and Communication. Formal Semantics and Pragmatics: Discourse, Context, and Models. November 19-21. Riga, Latvia.
-
Chen, Xiao, Philip Ender, Michael Mitchell and Christine Wells. (2003). Regression with SPSS http://www.ats.ucla.edu/stat/ spss/webbooks/reg/default.htm .
-
Chierchia, Gennaro. 1995. Dynamics of meaning: Anaphora, presupposition, and the theory of grammar. University of Chicago Press.
-
Chih-Chung Chang and Chih-Jen Lin (2001) LIBSVM: a library for support vector machines. Software avalable at http://ww.csie.ntu.edu.tw/ cjlin/libsvm.
-
Condoravdi Cleo and David Beaver. 2007. On the Logic of Verbal Modification. In Proceedings of the Amsterdam Colloquium.
-
Copestake, Ann and Ted Briscoe 1992. Lexical Operations in a Unificationbased Framework. In J.Pustejovsky and S. Bergler, eds., Lexical Semantics and Knowledge Reperesentation, Springer Verlag, Berlin.
-
Cornilescu, Alexandra. 2011. Nominal ellipsis as definiteness and anaphoricity: the case of Romanian. (to appear).
-
Cornilescu, Alexandra. 2002. At the Romanian Left Periphery. Bucharest Working Papers in Linguistics 4: 88-106.
-
Cristea, Dan 2003. The relationship between discourse structure and referentiality in Veins Theory, in W. Menzel and C. Vertan (eds.) Natural Language Processing between Linguistic Inquiry and System Engineering, „Al.I.Cuza” University Publishing House, Iaşi.
-
Cristianini Nelo and John Shawe-Taylor. 2000. An Introduction to Support Vector Machines. Cambridge University Press, Cambridge, UK.
-
Beaver, David. 2004. The Optimization of Discourse Anaphora. Linguistics and Philosophy 27(1), pp. 3-56.
-
Davidson, Donald. 1967. The logical form of action sentences, in Rescher, N. (ed.), The Logic of Decision and Action, Pittsburgh, University of Pittsburgh Press: 81-95.
-
de Groote, Philippe. 2006. Towards a montagovian account of dynamics. In Semantics and Linguistic Theory XVI.
-
de Groote, Philippe and Ekaterina Lebedeva. 2010. Presupposition Accommodation as Exception Handling, Proceedings of SIGDIAL 2010: the 11th Annual Meeting of the Special Interest Group on Discourse and Dialogue, pages 71–74, September 24-25, 2010, Association for Computational Linguistics.
-
de Swart, Henriette. 1993. Adverbs of Quantification: A Generalized Quantifier Approach, New York, Garland.
-
Dinu, Anca. 2008. On classifying coherent/incoherent Romanian short texts. In Proceedings 6-th international conference on Language Resources and Evaluation (LREC) 2008, Marakech, Morocco, pp. 2871-2874.
-
Dinu, Anca. 2010.a. Annotating a Romanian lexicon in a generative framework. Bucharest working papers in linguistics,Vol XII no. 2, pp. 83-93.
-
Dinu, Anca. 2010.b. Building a generative lexicon for Romanian. In Proceedings of The seventh international conference on Language Resources and Evaluation (LREC), Valletta, Malta, pp. 315-319.
-
Dinu, Anca. 2010.c. On classifying short texts. In Proceedings of International Conference on Stochastic Modeling Techniques and Data Analysis, Chania, Crete, Greece, 5 pp.
-
Dinu, Anca and Alina Tigau. 2010. Building and exploiting Romanian corpora for the study of Differential Object Marking. In Proceedings of Exploitation of multilingual resources and tools for Central and (South) Eastern European Languages(workshop at LREC 2010 conference), Valletta, Malta, pp. 9-14.
-
Dinu, Anca and Liviu Dinu. 2005. On the syllabic similarities of Romance languages. Lecture Notes in Computer Science, vol. 3406, pp. 785-788, Springer.
-
Dinu, Anca and Liviu Dinu. 2006. Total rank distance and scaled total rank distance: two alternative metrics in computational linguistics. In J. Nerbonne & E.Hinrichs (eds.) Proceedings Linguistic Distances. Workshop at the joint conference of International Committee on Computational Linguistics and the Association for Computational Linguistics (ACL-COLING 2006), Sydney, pp.109-117.
-
Dinu, Anca. 2011a. Versatility of ’continuations’ in discourse semantics. Fundamenta Informaticae, 18 pp. (accepted).
-
Dinu, Anca. 2011b. Quantifying over eventualities in continuation semantics. In Journal of Multiple-Valued Logic and Soft Computing, 19 pp. (accepted).
-
Dinu, Anca. 2011.c. A mechanism to restrict the scope of clause-bounded quantifiers in 'continuation' semantics. In Proceedings of ACL Conference Recent Advances in Natural Language Processing, RANLP 2011, September, 8 pp. (accepted).
-
Dinu Anca, Liviu P. Dinu, Marius Popescu. 2008. Authorship identification of Romanian texts with controversial paternity. In Proceedings 6-th LREC 2008, Marrakech, Maroc, 3392-3397.
-
Dobrovie-Sorin, Carmen.1994. The Syntax of Romanian. Berlin: Mouton de Gruyter.
-
Dowty, David. 2007. Compositionality as an empirical problem. In Chris Barker & Pauline Jacobson (eds.), Direct compositionality. Oxford University Press.
-
Duda, Richard, Peter Hart, David Stork. 2001. Pattern Classification (2nd ed.). Wiley-Interscience Publication.
-
Dumais, Susan , George W. Furnas, Thomas K. Landauer, Scott Deerwester, and Richard Harshman. 1988. Using Latent Semantic Analysis to improve access to textual information. In Human Factors in Computing Systems, in CHI'88 Conference Proceedings (Washington, D.C.), pages 281- 285, New York, May. ACM.
-
Efron, Bradley and Robert John Tibshirani 1997. Improvements on cross-validation: the bootstrap method. J. Amer. Statist. Assoc, 92:548–560.
-
Egli, U. and K. Heusinger (eds.). 1995. Choice functions in Natural Language Semantics, Arbeitspapier Nr. 71, Fachgruppe Sprachwisenschaft, Universitat Konstanz.
-
Enç, Mürvet .1991. The Semantics of Specificity. Linguistic Inquiry 22: 1-25.
-
Evans, Gareth. 1977. Pronouns, Quantifiers and Relative Clauses I & II. Canadian Journal of Philosophy 7. (Reprinted in The Collected Papers. 1985. Oxford University Press. 76-175).
-
Farkas, Donka and Heusinger, von Fintel. 2003. Stability of reference and object marking in Romanian. Ms. Workshop on Direct reference and Specificity ESSLLI Vienna.
-
Farkas, Donka and Henriette de Swart. 2001. The Semantics of Incorporation. Stanford, California: CSLI.
-
Farkas, Donka. 2002a. Specificity Distinction. Journal of Semantics 19: 213-243.
-
Felleisen, M Matthias. 1988. The theory and practice of first-class prompts. In J. Ferrante and P. Mager, editors, Proceedings of the Fifteenth Annual ACM Symposium on Principles of Programming Languages, pages 180-190, San Diego, California, ACM Press.
-
Franco, J. 2000. Agreement as a Continuum. In Beukema Frits, den Dikken Marcel (eds), Clitic Phenomena in European Languages, 146-189. Amsterdam: Benjamins.
-
Groenendijk, Jeroen A. G. and Martin B. J. Stokhof. 1990. Dynamic Montague Grammar, in Papers from the Second Symposium on Logic and Language, Laszlo Kalman and Laszlo Polos, eds. Budapest: Akadémiai Kiadó.
-
Groenendijk, Jeroen and Martin Stokhof. 1991. Dynamic predicate logic. Linguistics and Philosophy 14(1). 39–100.
-
Heim, Irene. 1983. File change semantics and the familiarity theory of definiteness. In Rainer Bauerle, Cristoph Schwarze, and Arnim von Stechow, editors, Meaning, Use and the Interpretation of Language. Walter de Gruyter and Co.
-
Heim, Irene. 1990. E-Type Pronouns and Donkey Anaphora. Linguistics and Philosophy 13. 137-177.
-
Hirst, Graeme and David St.-Onge 1997. Lexical chains as representation of context for the detection and correction of malapropisms. In Christiane Fellbaum, editor, Wordnet: An electronic lexical database and some of its applications. MIT Press, Cambridge, pages 305-332.
-
Hristea, Florentina, Marius Popescu. 2003. A Dependency Grammar Approach to Syntactic Analysis with Special Reference to Romanian. In Building Awareness in Language Technology (editori Florentina Hristea si Marius Popescu). Bucuresti, Editura Universitatii din Bucuresti, p. 9-34.
-
Hutton, Graham. 2007. Programming in Haskell. Cambridge University Press,.
-
Jackendoff, Ray. 2002. Foundations of language: Brain, meaning, grammar, evolution. Oxford, UK: Oxford University Press.
-
Jackendoff, Ray. 1972. Semantic Interpretation in Generative Grammar. MIT Press, Cambridge, MA.
-
Jacobson, Pauline. 1999. Towards a variable-free semantics. Linguistics and Philosophy 22(2). 117–185.
-
John S. Taylor and Nello Cristianini. 2004. Kernel Methods for Pattern Analysis. Cambridge University Press, New York, NY, USA.
-
Müller, Klaus-Robert, Sebastian Mika, Gunnar Rätsch, Koji Tsuda, and Bernhard Schölkopf. 2001. An introduction to kernel-based learning algorithms. IEEE Transactions on Neural Networks, 12 (2):181–201.
-
Kamp, Hans and Uwe Reyle. 1993. From Discourse to Logic. An Introduction to Modeltheoretic Semantics of Natural Language, Formal Logic and Discourse Representation Theory, Kluwer Academic Publishers, Dordrecht Netherlands.
-
Keenan, Edward 2002. Some Properties of Natural Language Quantifiers: Generalized Quantifier Theory. Linguistics and Philosophy 25 (5-6):627-654.
-
Keenan, Edward. 2002. Some Properties of Natural Language Quantifiers: Generalized Quantifier Theory. Linguistics and Philosophy 25 (5-6):627-654.
-
Kehler, Andrew. 2002. Coherence, Reference, and the Theory of Grammar. Stanford, CA: CSLI Publications.
-
Kenny, Anthony. 1963. Action, Emotion and Will. London: Routledge and Kegan Paul.
-
Lambek, Joachim. 1958. The mathematics of sentence structure, Amer. Math. Monthly 65, 3 pp 154--170
-
Landman, Fred. 2000. Events and Plurality. Dordrecht: Kluwer.
-
Larson, Richard and Gabriel Segal. 1995. Knowledge of Meaning: An Introduction to Semantic Theory. The MIT Press, Cambridge.
-
Lascarides, Alex and Nicholas Asher. 2007. Segmented Discourse Representation Theory: Dynamic Semantics with Discourse Structure, in H. Bunt and R. Muskens (eds.) Computing Meaning: Volume 3, pp87--124, Springer.
-
Lenci Alessandro, Bel N., Busa F., Calzolari N., Gola E., Monachini M., Ogonowsky A., Peters I., Peters W., Ruimy N., Villegas M., Zampolli A. 2000. SIMPLE: A General Framework for the Development of Multilingual Lexicons. International Journal of Lexicography, XIII (4): 249-263.
-
Levin, Beth. and Malka Rappaport Hovav. 2005. Argument Realization, Cambridge University Press, Cambridge, UK.
-
Link, Godehard. 1983. The logical analysis of plurals and mass terms: A lattice-theoretical approach. In Meaning, use and the interpretation of language, eds. R. Bäuerle, C. Schwarze and A. von Stechow, 303-323. Berlin, New York: Walter de Gruyter. Reprinted in Link, Godehard. 1998. Algebraic Semantics in Language and Philosophy: CSLI lecture notes No. 74. Stanford, Calif.:CSLI Publications. pp.11-34. Reprinted in Portner and Partee, eds., 2002, 127-146.
-
Link, Godehard. 1998. Algebraic Semantics in Language and Philosophy: CSLI lecture notes No. 74. Stanford, Calif.: CSLI Publications.
-
Mann, William C. & Thompson, Sandra A. 1986. ‘Relational Propositions in Discourse’, Discourse Processes, vol. 9, no. 1, pp. 57–90.
-
Marcus, Solomon. 1967. Algebraic linguistics; analytical models. Academic Press, New York .
-
Marcus, Solomon. 1980. Textual cohesion and textual coherence. In Revue roumaine de linguistique, vol. 25, nr. 2, p. 101-112.
-
May, Robert. 1977. The grammar of quantification. Diss, MIT, Cambridge, MA.
-
Mika, A.J. Smola, and B. Schölkopf. 2001. An improved training algorithm for kernel Fisher discriminants. In T. Jaakkola and T. Richardson, editors, Proceedings AISTATS 2001, pages 98–104, San Francisco, CA.
-
Mika, Sebastian, Gunnar Rätsch, Jason Weston, Bernhard Schölkopf, and Klaus-Robert Müller. 1999. Fisher discriminant analysis with kernels. In Y.-H. Hu, J. Larsen, E. Wilson, and S. Douglas, editors, Neural Networks for Signal Processing IX, pages 41–48. IEEE.
-
Miller, Tristan. 2004. Essay Assessment with Latent Semantic Analysis. Journal of Educational Computing Research 28.
-
Montague, Richard. 1970. The Proper Treatment of Quantification in English. InR. Thomason (ed). Formal Philosophy: Selected Papers of Richard Montague, 247-270. New Haven:Yale.
-
Morrill, Glyn 2010. Categorial Grammar: Logical Syntax, Semantics, and Processing. Oxford University Press.
-
Mourelatos, Alexander P. D. 1978. Events, Processes and States. Linguistics and Philosophy 2:415-434. [Reprinted in P. Tedeschi & A. Zaenen (eds.) 1981, 191-212.] Oxford University Press, 207-231. translated from Studia Philosophica, 1, 1-27.
-
Parsons, Terence. 1990. Events in the Semantics of English. Cambridge, MA: MIT.
-
Partee, Barbara H. & Mats Rooth. 1983. Generalized conjunction and type ambiguity. In Rainer Buerle, Christoph Schwarze & Arnim von Stechow. (eds.), Meaning, use, and interpretation of language, 361-383.Walter de Gruyter and Co.
-
Peyton, Jones S., editor. 2003. Haskell 98 Language and Libraries. Cambridge, University Press.
-
Polanyi, Livia. 1995. The Linguistic Structure of Discourse, Technical Report no. CSLI-96-200, Stanford University, Center for the Study of Language and Information.
-
Pustejovsky, James. 1995. The Generative Lexicon, Cambridge, MA: MIT Press.
-
Pustejovsky, James. 2006. Type Theory and Lexical Decomposition, Journal of Cognitive Science.
-
Pustejovsky, James. 2007. Type Theory and Lexical Decomposition. In P. Bouillon and C. Lee, editors, Trends in Generative Lexicon Theory. Kluwer Publishers.
-
Pustejovsky, James, Anna. Rumshisky, Jessica L. Moszkowicz, and Olga Batiukova. 2009. GLML: Annotating argument selection and coercion. IWCS-8: Eighth International Conference on Computational Semantics.
-
Ratnaparkhi, Adwait 1996. A Maximum Entropy Part- Of-Speach Tagger. In Proceedings of the Empirical Methods in NLP Conference, University of PennsylvaniaA.J.F.
-
Roberts, Craige. 1987. Modal subordination, anaphora and distributivity. PhD dissertation, UMass. Amherst.
-
Ruimy Nilda., Pierrette Bouillon and Bruno Cartoni. 2004. Semi-automatic Derivation of a French Lexicon from CLIPS, in: Proceedings of LREC04, Lisbon.
-
Ruimy Nilda., Pierrette Bouillon and Bruno Cartoni. 2005. Inferring a semantically annotated generative French lexicon from an Italian lexical resource. In: Third International Workshop on Generative Approaches to the Lexicon, Geneva, Switzerland. 218-226.
-
Saunders, C., Mark O. Stitson, Jason Weston, Leon Bottou, Bernhard Schölkopf, and Alex J. Smola 1998. Support vector machine reference manual. Technical Report CSD-TR-98-03, Royal Holloway University, London.
-
Scha, Remko. 1981. Distributive, collective and cumulative quantification. In Groenendijk, J., Stokhof, M., and Janssen, T. M. V., editors, Formal Methods in the Study of Language. Mathematisch Centrum, Amsterdam.
-
Schölkopf, Bernhard and Alex J. Smola. 2002. Learning with Kernels. MIT Press, Cambridge, MA.
-
Schroeder, Larry D., David L. Sjoquist, and Paula E. Stephan. 1986. Understanding regression analysis: An introductory guide. Thousand Oaks, CA: Sage Publications. Series: Quantitative Applications in the Social Sciences, No. 57.
-
Shan, Chung-chieh and Chris Barker. 2006. Explaining crossover and superiority as left-to-right evaluation. Linguistics and Philosophy 29.1:91–134.
-
Shan, Chung-chieh. 2005. Linguistic side effects. Ph.D. thesis, Harvard University.
-
Stan, Cornelia. 2007. Complementul direct. unpublished ms.
-
Steedman, Mark. 2000. The syntactic process. MIT Press.
-
Tigau, Alina. 2010. The Syntax of the direct object in Romanian. Unpublished PhD thesis.
-
Tsuda, Koji, Gunnar Rätsch, Sebastian Mika, and Klaus-Robert Müller. 2001. Learning to predict the leave-oneout error of kernel based classifiers. In G. Dorffner, H. Bischof, and K. Hornik, editors, Artificial Neural Networks — ICANN’01, pages 331–338. Springer Lecture Notes in Computer Science, Vol. 2130.
-
van den Berg, Martin. 1996. Dynamic Generalized Quantifiers. In van der Does, J. and van J. Eijck, (eds.), Quantifiers, Logic, and Language, CSLI Lecture Notes No.54, Stanford, California.
-
Vendler, Zeno. 1957. Verbs and Times. Philosophical Review 66:143-160. Reprinted in Z. Vendler (1967), Linguistics in Philosophy, Ithaca: Cornell University Press, 97-121.
-
Vertan, Cristina, Walter von Hahn and Monica Gavrila. 2005. Designing a parole/simple german-english-romanian lexicon. In Language and Speech Infrastructure for Information Access in the Balkan Countries Workshop Proceedings - RANLP 2005, Borovets, Bulgaria.
-
von Fintel, Kai. 1994. Restrictions on quantifier domains. Ph.D. Dissertation. University of Massachusetts at Amherst.
-
von Heusinger, Klaus and Onea, Edgar. 2008. Triggering and blocking effects in the diachronic development of DOM in Romanian, Probus 20:71-116.
Share with your friends: |
and the relation := is the lexicon which relates categories to symbols 
. (Cat) is the least set such that 
and if 
then
. A/B and B\A represent functions from into , where the slash determines that the argument is applied to the right (/) or to the left (\) of the functor, respectively. There are two rules: application A/B + B = A or B + A\B = A and composition A/B + B/C = A/C. For a recent survey of Categorial Grammars we refer the reader to Morrill (2010).