Introduction to Semantics
2015 Linguistic Summer Institute
University of Chicago
M/Th 8.30-10.20
SS 302

Chris Kennedy (instructor)
Rosenwald 205E
Office hours W 10-12 or by appointment



Julian Grove (TA)
Social Science 010B
Office hours Th 10.30-12 or by appointment

Homework 1: Ambiguity

Today in class we developed a syntax and semantics for a toy language of numerical expressions that has the following features:

  • There are two types of meanings:
    1. the set of rational numbers Q
    2. the set of truth values {TRUE, FALSE}
  • The vocabulary consists of the ten expressions {'0','1','2','3','4','5','6','7','8','9'} (part of the object language); these items are all of syntactic category D, and their meanings are the corresponding numbers: {0,1,2,3,4,5,6,7,8,9} (part of the metalanguage for representing meanings).
  • The grammar of the language (syntax and semantics) consists of the following principles:
    1. If 'x' is a D with meaning [[x]], then 'x' is a N with meaning [[x]].
    2. If 'x' is a N with meaning [[x]] and 'y' is a D with meaning [[y]], then 'xy' is a N with meaning [[x]] x 10 + [[y]].
    3. If 'x', 'y' are Ns with meanings [[x]], [[y]], then:
      1. 'x+y' is a N with meaning [[x]]+[[y]]
      2. 'x*y' is a N with meaning [[x]] x [[y]]
      3. 'x-y' is a N with meaning [[x]]-[[y]]
      4. 'x ÷ y' is a N with meaning [[x]] ÷ [[y]]
    4. If 'x', 'y' are Ns with meanings [[x]], [[y]], then 'x = y' is a S with meaning TRUE if [[x]] = [[y]], otherwise FALSE.

    QUESTION: Consider the complex expression '2*3+10 = 26.' This expression is predicted to be ambiguous, according to the syntax and semantics for the toy numerical language we invented: it can be associated with two different semantic values. Explain why it is predicted to be ambiguous, and say what its two possible semantic values are.