semantics of first-order logic

(1.4 hours to learn)


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.


This concept has the prerequisites:


  • 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)


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


See also

-No Additional Notes-