| Issue |
RAIRO-Theor. Inf. Appl.
Volume 46, Number 2, April-June 2012
12th Italian Conference on Theoretical Computer Science (ICTCS)
|
|
|---|---|---|
| Page(s) | 261 - 289 | |
| DOI | https://doi.org/10.1051/ita/2012003 | |
| Published online | 27 February 2012 | |
A graphical representation of relational formulae with complementation∗
1
Dipartimento di Matematica e Informatica, Università di
Catania, Viale Andrea Doria
6, 95125
Catania,
Italy
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2
Dipartimento di Matematica e Informatica, Università di
Perugia, Via Vanvitelli
1, 06123
Perugia,
Italy
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3
Dipartimento di Matematica e Informatica, Università di
Trieste, Via Valerio
12/1, 34127
Trieste,
Italy
This email address is being protected from spambots. You need JavaScript enabled to view it.
Received:
21
December
2010
Accepted:
17
January
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.
Mathematics Subject Classification: 68Q40 / 68T15 / 03C10
Key words: Algebra of binary relations / quantifier elimination / graph transformation
This research is partially supported by GNCS-10, GNCS-11, and PRIN-08 projects, and by grants 2009.010.0336 and 2010.011.0403. We would like to thank the anonymous referees for their useful suggestions.
© EDP Sciences 2012
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