Welcome To Math Notes
Math Notes is my journey through Cal State San Bernardino's math coursework using generalized truth functions. The first two sections, herein, explain what I mean by generalized truth functions and some algebraic tools I've developed. While the rest of the sections are applications derived from textbooks.
The concept of a generalized truth function rests on the output conditions of a truth function being represented by variables. That is, for a given input condition the function returns an unspecified value. As you will see, this variable output goes a long way to overcome the limitations of propositional calculus' fixed connectives.
My aim here is to develop a method for addressing problems that works algebraically. That being said, I really don't know if this method will be practical or practicable. Let's see together.
Generalized Truth Functions
Logic is all about choices. An idea is true or false, a student is present or absent, a switch is on or off. All the truth tables and specialized language of propositional calculus is geared to exploring these choices and their consequences.
Truth Function Algebra
Algebra is all about keeping a predicate true while rearranging the variables that define its shape. Identities introduce new or repeats of existing variables, commutativity switches the location of variables, and associativity changes what functions variables are in.
Introduction To Mathematical Logic
By Elliot Mendelson