Logic in linguistics: some issues in the philosophy of language
	Università degli studi di VERONA Facoltà di Lettere e Filosofia

Syllabus

This lecture can be viewed as a course in mathematical logic for linguists and philosophers — and for computer scientists interested in the modelling of human language. We will therefore focus on the logical methods and structures that have already been successful in linguistics as well as on the ones that are presently considered to be promising. The accent will be on formal semantics (words, sentences, sequences of sentences) and on some issues in the philosophy of language. Although parts of the lecture are advanced, we do not assume any background: prerequisites will be reminded on demand. If the program is too technical and lengthy, some paragraph might be skipped, except from the part on lexical semantics, and the notions it requires, since lexical semantics in a compositonal setting is the main objective of the lecture.

• Basics on first order classical logic and its interpretation
  • Basics of philosophy of language and its relation to logic, following Recanati.
  • Basic of first order classical logic: proofs, models and completeness.
  • A word on Discourse Representation Theory and FOL
• Refinements: possible worlds and topological models
  • Modal and intuitionnistic variations: proofs, a word on Kripke semantics.
  • A bit of topology, category theory and categorical logic.
  • Sheaf semantics for intuitionnistic logic.
  • Classical and intuitionistic higher order logic
  • Petitot on predicates applied to spatial entities.
• Proofs, lambda terms and compositional semantics
  • Proofs, lambda-terms and the Curry-Howard isomorphism
  • Linear logic and Lambek calculus
  • Categorial grammar and Montague semantics
• Categories, types and terms for lexical semantics
  • On the semantics of proofs and lambda terms.
  • A concrete example: coherence spaces.
  • Abrusci and Fouqueré on applications of coherence spaces to ontologies.
  • Asher on types systems for lexical semantics in a compositional framework
  • Bassac, Mery and Retoré on the same issue.

Some on line specific documents
(in addition to the bibliography below):

• Introduction to the Verona lecture (slides)
• A memento on first order logic (in French)
• A talk on logic and linguistics then focussing on lexical semantics (slides)

Bibliography:

• Nicholas ASHER Lexical Meaning in Context: A Web of Words. Manuscript. http://timeml.org/jamesp/lexsemastypes-9.pdf
• Christian BASSAC, Bruno MERY, Christian RETORE Towards a Type-Theoretical Account of Lexical Semantics Journal of Logic Language and Information 19(2) 2010.
• René CORI & Daniel LASCAR, Mathematical Logic : A course with exercises -- Part I -- Propositional Calculus, Boolean Algebras, Predicate Calculus, Completeness Theorems, Oxford University Press, 2000.
• Francis CORBLIN Théorie des représentations discursives, PUF, 2004.
• L. T. F. GAMUT Logic, Language, and Meaning, Volume 2: Intensional Logic and Logical Grammar, Chicago University Press, 1991.
• Jean-Yves GIRARD Le point aveugle — cours de logique. Vol I & II. Hermann 2006. English version: The blind spot
• Joachim LAMBEK & Phil SCOTT Introduction to Higher-Order Categorical Logic Cambridge studies in advanced mathematics Cambridge University Press, 1988
• Saunders MAC LANE & Ieke MOERDIJK Sheaves in geometry and logic: a first introduction to topos theory Springer University Texts, 1993
• Jean PETITOT, La neige est blanche ssi... Prédication et perception Mathématiques et Sciences Humaines, 140, pp. 35-50, 1997
• James PUSTEJOVSKY The generative lexicon. MIT Press 1995.
• François RECANATI Philosophie du langage (et de l'esprit) Folio essais, Gallimard, 2008.
• Anne Sjerp TROELSTRA & Dirk VAN DALEN Constructivism in mathematics, Vol I & II, North-Holland, 1988.
• Jan VAN EIJCK &Hans KAMP, Representing Discourse in Context, Chapter 3 - Pages 179-237. In Handbook of Logic and Language edited by J. van Benthem and A. ter Meulen. Elsevier and MIT Press 1996.

Lundi 10 Mai, 2010 12:55

Backgound picture: (pale version of) an illustration by Max Ernst of some selected logical and poetic writtings of Lewis Carroll ("Wunderhorn").