16 Peirce's rules of inference (Ad)


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

Any evenly enclosed graph may be erased.
Any graph may be inserted in any oddly enclosed context.
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.
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, we give an example of how to use the rules.

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