Mirqāt The Ascent of Logic

Foundation · a field of logic

Propositional Logic

Truth tables, the connectives, and rules of inference: the algebra of whole statements, and the natural first system to master.

An entry point for computer science

The problem
How do the truth values of compound statements depend, mechanically, on the truth of their parts?
The turning point
Truth-functionality: every connective is fixed by a finite table, and the system is complete for tautologies.
An open question
Which non-classical readings of the connectives (relevant, intuitionistic) best capture real inference?

The Canon

  • Kleene Mathematical Logic

To study it

  • Goldrei Propositional and Predicate Calculus
  • Grassmann Logic & Discrete Mathematics
  • Ben-Ari Mathematical Logic for Computer Science