Proof Theory for Reasoning with Euler Diagrams: A Logic Translation and Normalization

@article{Takemura2013ProofTF,
title={Proof Theory for Reasoning with Euler Diagrams: A Logic Translation and Normalization},
author={Ryo Takemura},
journal={Studia Logica},
year={2013},
volume={101},
pages={157-191}
}

Proof-theoretical notions and techniques, which are developed based on sentential/symbolic representations of formal proofs, are applied to Euler diagrams. A translation of an Euler diagrammatic system into a natural deduction system is given, and the soundness and faithfulness of the translation are proved. Some consequences of the translation are discussed in view of the notion of free ride, which is one of the most basic properties of diagrams that is mainly discussed in the literature of… CONTINUE READING