3 Lambda Calculus

Now that we've learned something about first-order logic and know how to work with it in Prolog, it is time to have a look at the first major issue of this course, which is:

How can we automate the process of associating semantic representations with natural language expressions?

In the following lecture we'll explore this issue concretely: first we'll try to write a simple Prolog program that will be able to perform the task we've requested - in a limited way, though. We'll observe where it commits errors, and why. This experiment will seamlessly lead us to formulating a version of -calculus. -Calculus is a tool that allows us to control the process of making substitutions. With its help, we will be able to describe concisely how semantic representations should be built. It is one of the main tools used in this course, and by the end of the lecture we will have seen why it is so useful to computational semantics.

• 3.1 Building Meaning Representations
  • 3.1.1 Being Systematic
  • 3.1.2 Being Systematic (II)
  • 3.1.3 [Sidetrack] Compositional Semantics
  • 3.1.4 Summing Up

• 3.2 Syntactic Analysis
  • 3.2.1 A Simple Solution: CFG
  • 3.2.2 Using DCGs

• 3.3 Semantics Construction
  • 3.3.1 A First Attempt
  • 3.3.2 Putting Things in the Right Place I
  • 3.3.3 Putting Things in the Right Place II

• 3.4 The Lambda Calculus
  • 3.4.1 Lambda-Abstraction
  • 3.4.2 Reducing Complex Expressions
  • 3.4.3 Using Lambdas
  • 3.4.4 [Sidetrack] Simply Typed Lambda-Calculus
  • 3.4.5 Advanced Topics: Proper Names and Transitive Verbs
  • 3.4.6 The Moral
  • 3.4.7 Accidental Bindings
  • 3.4.8 Alpha-Conversion
  • 3.4.9 Summing Up

• 3.5 Implementing Lambda Calculus
  • 3.5.1 Representations
  • 3.5.2 Extending the DCG
  • 3.5.3 The Lexicon
  • 3.5.4 A First Run
  • 3.5.5 Beta-Conversion
  • 3.5.6 Beta-Conversion Continued
  • 3.5.7 An Afterthought on Alpha-Conversion

• 3.6 Running the Program

• 3.7 Exercises