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A graphical representation of relational formulae with complementation

Published online by Cambridge University Press:  27 February 2012

Domenico Cantone
Affiliation:
Dipartimento di Matematica e Informatica, Università di Catania, Viale Andrea Doria 6, 95125 Catania, Italy. cantone@dmi.unict.it; nicolosi@dmi.unict.it
Andrea Formisano
Affiliation:
Dipartimento di Matematica e Informatica, Università di Perugia, Via Vanvitelli 1, 06123 Perugia, Italy; formis@dmi.unipg.it
Marianna Nicolosi Asmundo
Affiliation:
Dipartimento di Matematica e Informatica, Università di Catania, Viale Andrea Doria 6, 95125 Catania, Italy. cantone@dmi.unict.it; nicolosi@dmi.unict.it
Eugenio Giovanni Omodeo
Affiliation:
Dipartimento di Matematica e Informatica, Università di Trieste, Via Valerio 12/1, 34127 Trieste, Italy; eomodeo@units.it
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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
Copyright
© EDP Sciences 2012

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