In this most recent foray into formal semantics, I started doing something on the handout that I had not been doing before, which is using these “fat brackets.” “What are they?”, you may be asking yourself.

Basically, in places where I “ought to” have written fat brackets, in the earlier handouts in the semester I’d simply written regular brackets because it was just easier to typeset.

The fat brackets represent the semantic evaluation function—when you put fat brackets around something, you are referring to the “semantic value” of that thing within the brackets.

Of course, since I started using fat brackets on the handout, and there’s no easy way to type them on the blog, I’ve started using “[[” to represent the fat left bracket and “]]” to represent the fat right bracket.

So, for example, the semantic value of the word hungry would be written something like this:

[[ hungry ]]^M,g,w,t = λx [ x ∈ F^w,t(hungry) ]

(This makes use of the lexical interpretation rule that says that if F provides a set of individuals, then the form of the semantic value is λx [ x ∈ the set of individuals F provides ]. See the handout.)

In case you were worried about all of these seemingly superfluous brackets, this is the explanation of why they’re there.