Logic in linguistics:
some issues in the philosophy of language 


Calendario Lezioni di Linguistica Generale per la specialistica in Linguistica (interfacoltà)
Responsabile: prof. Denis Delfitto (Università degli studi di Verona Facoltà di Lettere e Filosofia)
Docente: prof. Christian Retoré (Université Bordeaux 1, LaBRICNRS & INRIA) – incentivazione insegnamento in lingua inglese.
Tutte le lezioni si svolgeranno nella Sala Riunioni del dip.to di Filologia, Lett. e Linguistica, Polo Zanotto, III piano.
Martedi: 27 aprile — 4 maggio — 11 maggio: 10:00 / 12:40
Venerdi: 30 aprile — 7 maggio — 14 maggio: 11:50 / 14:30
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, lambdaterms and the CurryHoward 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):
Bibliography:
 Nicholas ASHER Lexical Meaning in Context: A Web of Words. Manuscript. http://timeml.org/jamesp/lexsemastypes9.pdf
 Christian BASSAC, Bruno MERY, Christian RETORE Towards a TypeTheoretical 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.
 JeanYves GIRARD Le point aveugle — cours de logique. Vol I & II. Hermann 2006. English version: The blind spot
 Joachim LAMBEK & Phil SCOTT Introduction to HigherOrder 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. 3550, 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, NorthHolland, 1988.
 Jan VAN EIJCK &Hans KAMP, Representing Discourse in Context, Chapter 3  Pages 179237. 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").