A graphical representation of relational formulae with complementation

Cantone, Domenico; Formisano, Andrea; Asmundo, Marianna Nicolosi; Omodeo, Eugenio Giovanni

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 46 (2012) no. 2, pp. 261-289.

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.

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