Natural Language Processing with Python

Summary

• First-order logic is a suitable language for representing natural language meaning in a computational setting since it is flexible enough to represent many useful aspects of natural meaning, and there are efficient theorem provers for reasoning with first-order logic. (Equally, there are a variety of phenomena in natural language semantics which are believed to require more powerful logical mechanisms.)

• As well as translating natural language sentences into first-order logic, we can state the truth conditions of these sentences by examining models of first-order formulas.

• In order to build meaning representations compositionally, we supplement first-order logic with the λ-calculus.

• β-reduction in the λ-calculus corresponds semantically to application of a function to an argument. Syntactically, it involves replacing a variable bound by λ in the function expression with the expression that provides the argument in the function application.

• A key part of constructing a model lies in building a valuation which assigns interpretations to non-logical constants. These are interpreted as either n-ary predicates or as individual constants.

• An open expression is an expression containing one or more free variables. Open expressions receive an interpretation only when their free variables receive values from a variable assignment.

• Quantifiers are interpreted by constructing, for a formula φ[x] open in variable x, the set of individuals which make φ[x] true when an assignment g assigns them ...