We improve existing techniques for graphical representation of relational expressions and for exploitation of this representation in the translation of (hybrid) dyadic first-order sentences into equalities between relational expressions. The enhanced technique can cope with the relational complement construct and the negation connective. Complementation is handled by adopting a Smullyan-like uniform notation to classify and decompose map expressions, whereas negation is treated by generalizing the notion of graph for a formula in ${\cal L}^{+}$ and by introducing a series of graph transformation rules which reflect the meaning of the connectives and quantifiers occurring in the formula.

### A graphical representation of relational formulae with complementation

#### Abstract

We improve existing techniques for graphical representation of relational expressions and for exploitation of this representation in the translation of (hybrid) dyadic first-order sentences into equalities between relational expressions. The enhanced technique can cope with the relational complement construct and the negation connective. Complementation is handled by adopting a Smullyan-like uniform notation to classify and decompose map expressions, whereas negation is treated by generalizing the notion of graph for a formula in ${\cal L}^{+}$ and by introducing a series of graph transformation rules which reflect the meaning of the connectives and quantifiers occurring in the formula.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11391/173358
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