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A graphical representation of relational formulae with complementation∗
Published online by Cambridge University Press: 27 February 2012
Abstract
We study translations of dyadic first-order sentences into equalities between relational expressions. The proposed translation techniques (which work also in the converse direction) exploit a graphical representation of formulae in a hybrid of the two formalisms. A major enhancement relative to previous work is that we can cope with the relational complement construct and with the negation connective. Complementation is handled by adopting a Smullyan-like uniform notation to classify and decompose relational expressions; negation is treated by means of a generalized graph-representation of formulae in ℒ+, and through a series of graph-transformation rules which reflect the meaning of connectives and quantifiers.
- Type
- Research Article
- Information
- RAIRO - Theoretical Informatics and Applications , Volume 46 , Issue 2: 12th Italian Conference on Theoretical Computer Science (ICTCS) , April 2012 , pp. 261 - 289
- Copyright
- © EDP Sciences 2012
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