MODAL TABLEAUX FOR REASONING ABOUT DIAGRAMS

Luis Fariñas del Cerro; Olivier Gasquet

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MODAL TABLEAUX FOR REASONING ABOUT DIAGRAMS

In: Essays in Logic and Ontology

Authors:

Luis Fariñas del Cerro

Luis Fariñas del Cerro
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Olivier Gasquet

Olivier Gasquet
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Type:: Chapter

Pages:: 169–184

DOI:: https://doi.org/10.1163/9789004332966_012

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Abstract

This paper, we propose a modal logic satisfying minimal requirements for reasoning about diagrams via collection of sets and relations between them, following Harel’s proposal. We first give an axiomatics of such a theory and then provide its Kripke semantics. Then we extend previous works of ours in order to obtain a decision procedure based on tableaux for this logic. Beside soundness and completeness of our tableaux, we manage to define a strategy of rule application ensuring termination by extending the usual loop test of modal logic S4 to whole sub-structures of the model being computed.

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Essays in Logic and Ontology

Series: Poznań Studies in the Philosophy of the Sciences and the Humanities, Volume: 91 and Poznań Studies in the Philosophy of the Sciences and the Humanities Online, Volume: 91

E-Book ISBN:: 9789004332966

Publisher:: Brill

Print Publication Date:: 01 Jan 2007

Subjects
- Philosophy
  - Philosophy of Science
  - Philosophy of Mind

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MODAL TABLEAUX FOR REASONING ABOUT DIAGRAMS

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Essays in Logic and Ontology

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