## Archive for the ‘**Formal Logic**’ Category

## Propositional Logic and some Tautologies

In the quest for the ultimate chatbot one may be well advised to take a diversion into formal logic. There are several types of logics but the simplest is usually known as “Propositional Logic”. I have a recommended book I am looking at called “Logic” by Wilfred Hodges.

At one point in the book the author gives a list of tautologies. I am interested by these because they encapsulate some of the self evident facts of reasoning. Any statement can be proved if it can be reduced to a tautology. Before I show the list to you we need to decide on notation. I have stuck with the basic options that html gives you for these. You could use LaTeX but it is more work.

The symbols are as follows

implication -> | → |

equivalence <-> | ↔ |

not ~ | ˜ |

and & | ∧ |

or + | ∨ |

grouping ‘(‘,’)’ | (,) |

If you are used to writing code then most of this is common sense, since it is the hidden process behond Boolean variables and and, or, not, True, False etc in Python or any language. Still fun though !