19 Summary (Ad)

Introduction

Peirce's rules of inference form a system of logic that is equivalent to First Order Predicate Logic. They can be used to reason using conceptual graphs.

Negative contexts

A context is negative if it has the "not" symbol () in front of it.

Evenly enclosed, oddly enclosed

A graph is said to be evenly enclosed if, going from the graph outwards to the outermost level, we encounter an even number of negative contexts. The term "oddly enclosed" is defined analogously.

Dominating context

A context x is said to dominate a context y if y is nested somewhere inside x.

The five rules

The five rules are:

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.


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