We began talking about Barker and Shan's version of categorial grammar, which makes scope taking particularly natural.

Reading

In the CNL book

• chapter 1

No class (because I was sick)

We presented the natural deduction rules (introduction and elimination) for the 'double up-arrow' scoping constructor.

We investigated type constructors for medial extraction, and for 'covert movement.'

We discussed Glyn Morrill's work on complexity metrics for type logical grammar.

Reading

• Morrill on Aphasic comprehension and working memory load
• Morrill on Incremental processing and acceptability

We discussed reflexives, investigating the types needed to account for their distribution in simple transitive sentences (O but not S), and their semantics (turning a relation into a property by giving it the same argument twice).

We saw that the proof structures in more complex examples look as though (from a transformational perspective) the reflexive has raised to a position adjoined to the VP.

We also mentioned briefly the problem of peripheral extraction.

We introduced hypothetical reasoning. It was observed that hypothetical reasoning looks somewhat like movement.

We used extraction from the O position of a transitive verb as an example (as in, relativization).

We continued reviewing applicative categorial grammar, covering

• (nominal) PP attachment ambiguity
• verbal PP adjuncts (different syntactic type from nominals, but same semantic type)
• subject relative clauses

We saw that the lack of a Sub + Verb constituent made it difficult to deal with object relatives, and with certain kinds of coordinations

Reading

In the TLS book

• try exercises 1, 5, 8 and 9
• we will be starting next time on chapter 5

We reviewed applicative categorial grammar, and explored how to assign syntactic types to expressions based on their distribution, and then how their semantic types constrained the choice of the function representing their meaning (qua contribution to truth conditions). We looked at

• nominal modification (adjectives and PPs)
• transitive verbs
• In the TLS book
  • catch up on previous readings (we are currently working on chapter four)

(Exceptional time and date due to Reformationstag.)

We discussed higher order logic, and how λ terms are useful in representing functions. We then discussed how to use the typing system of function application to account for syntactic combination.

1. with syntactic types equal to semantic types, we couldn't account for word order (that determiners are to the left of their arguments, and predicates to the right of theirs)
2. refining the 'arrow' type constructor to allow for directionality (using the forward '/' and backward '\' slashes) made this possible, but nouns and predicates had the same (or similar) types, but only predicates allow for syntactic arguments
3. refining atomic types, so that syntactic types are different from semantic ones, allowed us to assign type n to nouns, and np\s to predicates. Syntactic types are no longer isomorphic to semantic types, but are related to them via a type homomorphism.
4. In the TLS book
   • Chapter four (up to section 4.6)

We discussed using λ notation to represent complicated tree parts. We talked about types, saw how to write a type as a tree, where its order was a measure of its depth. We also saw how the types involved in function application behaved like the logic rule of modus ponens.

Reading

In the TLS book

• Chapter two (up to section 2.3)
• optional Chapter three (up to section 3.6)

We discussed the empirical base of semantics, and began talking about parts of trees.

Reading

• Chapter one