Dynamic semantics (Brian Morris & Mr. Rose, 4/13 & 4/27)

Semantics is the study of “what does that sentence even mean actually?”. Human languages aren’t great at being specific, so linguistics try to write the meaning of sentences in precise first order logic. But when those darn donkey sentences start messing everything up, we need something more…dynamic. Read lecture notes below or the slides for details (part 1 and part 2).

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Dynamic semantics

  • Semantics
    • It’s the study of meaning
    • Truth conditional semantics
      • Meaning is truth conditions
      • When da sentence true: “Anna’s dog is tired”
        • Anna has a dog
        • And that dog is tired
      • The meaning of a sentence is its truth conditions
      • It isn’t perfect. It doesn’t provide for questions, just declarative factual statements
      • Theory associated with Donald Davidson published in 1967 trying to go from formal logic to natural language
      • Can use first order logic to show meaning
    • FOL: an intro bullet
      • For all X P(X)
        • Where P(X) is the property “x is pretty”
        • true in the universe that is like that…
      • Domain of Discourse is the set of things you are talk
      • Want: convert natural language to FOL
    • FOL: no longer completely an intro bullet
      • Object language that is doing the actual meaning
      • Meta-language describes this stuff and all
      • Fancy bracket notation
        • [[snow]] = snow
          • This is an Object
          • First one is the word in the object language
          • Second is thing in meta language
        • [[is white]] = {things that are white}
          • This is a Predicate
          • It is also a set
          • Predicates give whether something is in the set
      • Time for some crazy FOL
        • “Anna’s dog is tired”
        • “Anna” refers to Anna: [[Anna]] = Anna
        • “Anna’s dog” is not very specific
        • ⱻx[Dog(x) ^ Owns(a, x) ^Tired(x)]
    • FOL: next level
      • Things it has
        • Quantifiers (ⱻ  (there exists a(n) ,Ɐ (for all), )
        • Variable symbols (x, y, z)
        • Predicate symbols (P, Q)
        • Individual constant symbols (a, b, c…)
      • A Model M = <D, I> connects language of FOL to reality
        • D is the domain of discourse (the universe)
        • I is the interpretation function
          • It maps from constant symbols to objects in D and predicate symbols to the sets of objects satisfying them
      • You have a s which is a chunk of FOL language like Ɐx
        • [[s]] gets the meaning of it
        • [[s]] = I(s) or a truth value
      • Variables
        • If x is referring to some b, [[x]] = I(b)
        • You need to know what was assigned to x before we can evaluate
        • A variable assignment g is a function from a variable symbol to an object in the domain D
        • Meaning relative to the assignment.
          • [[x]]g = g(x)
          • Can do things like
            • Let g = f[x/Anna]
              • which assigns the value Anna to x
              • g(x) = Anna
        • Quantification
          • Taking an existing variable assignment and temporarily reassigning the quantified-over variable in order to make the statement inside the quantifier true
          • Version of the above that makes sense: just keep swapping around the variable for all of the things in a particular set that you specified.
          • For any object a in D
          • Bluh just look at the pictures and delete that bullet
      • Flaws/examples
        • “Aaron has children. Aaron’s son is 5 and his daughter is 3”
          • Reversing the order makes it redundant
        • “Jessica left the room. Jessica started to cry”
          • Reversing the order of the sentences changes the meaning.
        • Basically, order matters

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