# 16 Peirce's rules of inference (Ad)

## Introduction

Peirce's rules of inference can be used to reason with conceptual graphs. Here, we formulate the rules for conceptual graphs using the definitions we have just given.

## The rules

Erasure:
Any evenly enclosed graph may be erased.
Insertion:
Any graph may be inserted in any oddly enclosed context.
Iteration:
A copy of any graph u may be inserted into the same context in which u occurs or into any context dominated by a concept in u.
Deiteration:
Any graph whose occurrence could be the result of iteration may be erased (i.e., if it is identical to another graph in the same context or in a dominating context).
Double negation:
A double negation may be drawn around or removed from any graph or set of graphs in any context.

## An axiom: The empty graph

The only axiom for Peirce's rules of inference is the empty graph. The empty graph says nothing about anything, and by convention is assumed to be true.

## Applying the rules

When one starts with a collection of conceptual graphs S and then applies the rules to form another collection of conceptual graphs V, we say that we have proved V from S.

If we start with the empty graph and prove a collection of conceptual graphs V, V is said to be a theorem.

## Next

Next, we give an example of how to use the rules.