semantics of first-order logic

(1.4 hours to learn)

Summary

The semantics of a first-order language is defined in terms of mathematical structures which give the meanings of all the constants, functions, and predicates in the language. In particular, one can recursively define a function which evaluates, given a structure and a first-order sentence, whether the structure satisfies the sentence. If all structures satisfying a set A of sentences also satisfy another set B of sentences, then A logically implies B.

Context

This concept has the prerequisites:

Goals

  • define what it means for a mathematical structure to satisfy (or be a model of) a set of first-order sentences
  • define what it means for one set of first-order sentences to logically entail another

Core resources (read/watch one of the following)

-Free-

Notes on Logic (2013)
Lecture notes for a course on first order logic.
Author: Henry Cohn

-Paid-

See also

-No Additional Notes-