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9 votes
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What explanatory advantages does so-called "type theory" have?

I can't see the sense in reducing everything in a language to either an "e" or a "t". Maybe this is a good place to start. Type theory (more accurately: so-called simple type ...
Natalie Clarius's user avatar
6 votes
Accepted

Intuitionistic type theory in linguistics

It's really nice to know that there are some other guys who are interested in type-theoretical semantics. I will give you some advice and references that might be interesting. First, there is a ...
Fred's user avatar
  • 99
4 votes

What explanatory advantages does so-called "type theory" have?

Type theory avoids the paradoxes in set theory that were discovered early in the last century, e.g. Russell's paradox. It is not the only way to avoid the paradoxes. It is often used in the formal ...
Greg Lee's user avatar
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2 votes

Is type theory compatible with n-ary branching?

Church's original formulation of type theory (based on λ-calculus) suggests binary branching. One way of dealing with this limitation is the use of linear logic, whose connective for tensor ...
Atamiri's user avatar
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2 votes

What explanatory advantages does so-called "type theory" have?

There are many “type theories.” In mathematics, Russell used a simple one to resolve paradoxes in set theory, but there are now other ways to get rid of them. Relevant to linguistics is Church’s “...
Atamiri's user avatar
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2 votes
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If adjectives denote functions of type <<e,t>,<e,t>>, then what denotation of *be* will allow adjectives to appear in predicative position?

Note 1: this sounds like a homework problem, so I'm going to try to give guidance toward the answer instead of just giving an answer outright. Note 2: writing out the types of all the variables gets ...
Draconis's user avatar
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1 vote
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Does simple type theory distinguish between those common nouns that are used as arguments and those that are used as predicates?

For general use as an argument: You need EITHER a silent determiner (or another head) that converts <e,t> to either <<e,t>,t> or e OR a theory of coercion that performs its function ...
Viridianus's user avatar
1 vote

Is type theory compatible with n-ary branching?

As I understand type theory and as described by lemontree, type theory necessarily construes syntactic structures as being generated in terms of one input and one output. This is a misunderstanding. "...
varkor's user avatar
  • 119
1 vote

Is type theory compatible with n-ary branching?

My answer is no, not n-ary branching, but rather binary branching. As Atamiri's answer might suggest, the basic notion of type theory is that of a function -- the types are just means to that end. ...
Greg Lee's user avatar
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1 vote
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Compositional Semantics of relative clauses

This is a good start and your calculation works out, but the standard literature wouldn't agree on your suggestion that Tom destroyed is of type t. The crucial point is that that the moved-away ...
Natalie Clarius's user avatar
1 vote

Compositional Semantics of relative clauses

The view which emerged from Lauri Karttunen's classic paper "Migs and Pilots" is that a relative pronoun is coreferential with the NP relative clause construction it occurs in. See Pauline Jacobson. ...
Greg Lee's user avatar
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1 vote

Compositional semantic: Type of conjunctions

There are numerous kinds of coordinate structures that challenge such an approach to coordination in terms of types. The main difficulty concerns the fact that the strings that can be coordinated need ...
Tim Osborne's user avatar
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1 vote

Converting types into lambda notation and set notation

As for and: You got your lambda term for and wrong. Either you mean coordination between subject DPs ("Mary and John sneeze") then your lambda term is λP[λx[λy[P(x)^P(y)]]], with just one ...
Natalie Clarius's user avatar
1 vote

Solving type mismatch

As a little intellectual exercise, I looked around a little and found an online PDF using your notation - "Elements of Formal Semantics" (http://www.phil.uu.nl/~yoad/efs/EFS-ch3-online.pdf). ...
Carl Dombrowski's user avatar
1 vote

The semantic type of and?

I will first present a simple solution where "and" conjoins the respective NPs/VPs in such a way that the resulting conjoined elements combine with the VP/subject NP in such as if there was just a ...
Natalie Clarius's user avatar

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