RAIRO-Theor. Inf. Appl.
Volume 46, Number 2, April-June 201212th Italian Conference on Theoretical Computer Science (ICTCS)
|Page(s)||261 - 289|
|Published online||27 February 2012|
A graphical representation of relational formulae with complementation∗
Dipartimento di Matematica e Informatica, Università di
Catania, Viale Andrea Doria
2 Dipartimento di Matematica e Informatica, Università di Perugia, Via Vanvitelli 1, 06123 Perugia, Italy
3 Dipartimento di Matematica e Informatica, Università di Trieste, Via Valerio 12/1, 34127 Trieste, Italy
Accepted: 17 January 2012
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.
Mathematics Subject Classification: 68Q40 / 68T15 / 03C10
Key words: Algebra of binary relations / quantifier elimination / graph transformation
© EDP Sciences 2012
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