| 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
cantone@dmi.unict.it; nicolosi@dmi.unict.it
2
Dipartimento di Matematica e Informatica, Università di
Perugia, Via Vanvitelli
1, 06123
Perugia,
Italy
formis@dmi.unipg.it
3
Dipartimento di Matematica e Informatica, Università di
Trieste, Via Valerio
12/1, 34127
Trieste,
Italy
eomodeo@units.it
Received:
21
December
2010
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
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.