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Lectures

Page history last edited by Michael 16 years, 7 months ago

Syllabus for the ESSLLI '07 Course

 


 

Day 1: Introducing Lambek-Grishin calculus

 

  • Limitations of the Lambek systems
  • Unary modalities and controlled structural rules
  • Lambek-Grishin calculus LG: symmetry and structure preserving interaction
  • Completeness for the relational semantics
  • Cut elimination and decidable proof search

 

Slides: print

 

Day 2: Derivational semantics

 

  • The Curry-Howard (CH) isomorphism
  • CH for LG
  • CPS (continuation-passing-style) interpretation: call-by-value vs call-by-name
  • Linguistic illustration: scope construal

 

Slides: print; a note on natural deduction versus sequent terms.

 

Day 3: Relating CPS and direct interpretation

 

  • Montague-style interpretation for Lambek derivations
  • Lifting the MG lexicon to CPS level
  • Linguistic illustrations:
  1. Quantifiers
  2. Bridge Predicates vs. Non-bridge predicates
  3. First-order versus higher order predicates
  4. Generalized coordination

 

Slides: print. Slides (covered on the first part of thursday): print

 

For a comparison between Hendriks' Flexible Montague Grammar and the Lambek-Grishin view on meaning composition, see Chapter 4 of Arno Bastenhof's BA thesis Quantifier Scope And Coordination in Flexible and Continuation-Based Approaches to NL Semantics. Utrecht, 2007.

 

Day 4: Type Similarity

 

  • Relations between types: derivability versus similarity
  • Characterizing LG type similarity
  • Linguistic applications
  1. Long distance dependencies
  2. Crossed dependencies

 

Slides: print

 

Day 5: Symmetry for unary modalities

 

  • (Dual) residuated pairs
  • (Dual) Galois connected pairs
  • Syntax and semantics
  • Linguistic application: islands

 

Slides: friday.pdf (updated with lexical solution for non-bridge predicate)

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