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  Hierarchical and modular reasoning in complex theories: The case of local theory extensions

Sofronie-Stokkermans, V. (2007). Hierarchical and modular reasoning in complex theories: The case of local theory extensions. In B. Konev, & F. Wolter (Eds.), Frontiers of Combining Systems: 6th International Symposium, FroCos 2007 (pp. 47-71). Berlin, Germany: Springer.

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Datensatz-Permalink: https://hdl.handle.net/11858/00-001M-0000-000F-1F65-6 Versions-Permalink: https://hdl.handle.net/11858/00-001M-0000-002D-7C54-C
Genre: Konferenzbeitrag

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Urheber

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 Urheber:
Sofronie-Stokkermans, Viorica1, Autor           
Affiliations:
1Automation of Logic, MPI for Informatics, Max Planck Society, ou_1116545              

Inhalt

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Schlagwörter: -
 Zusammenfassung: Many problems in computer science can be reduced to proving the satisfiability of conjunctions of literals w.r.t. a background theory. This theory can be a concrete theory (e.g. the theory of real or rational numbers), the extension of a theory with additional functions (free, monotone, or recursively defined) or a combination of theories. It is therefore very important to have efficient procedures for checking the satisfiability of conjunctions of ground literals in such theories. We here give an overview of results on hierarchical and modular reasoning in complex theories. We show that for a special type of extensions of a base theory, which we call local, hierarchic reasoning is possible (i.e. proof tasks in the extension can be hierarchically reduced to proof tasks w.r.t. the base theory). Many theories important for computer science or mathematics fall into this class (typical examples are theories of data structures, theories of free or monotone functions, but also functions occurring in mathematical analysis). In fact, it is often necessary to consider complex extensions, in which various types of functions or data structures need to be taken into account at the same time. We show how such local theory extensions can be identified and under which conditions locality is preserved when combining theories, and we investigate possibilities of efficient modular reasoning in such theory combinations. We present several examples of application domains where such theories occur in a natural way. We show, in particular, that various phenomena analyzed in the verification literature can be explained in a unified way using the notion of locality.

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Sprache(n): eng - English
 Datum: 2008-03-252007
 Publikationsstatus: Erschienen
 Seiten: -
 Ort, Verlag, Ausgabe: -
 Inhaltsverzeichnis: -
 Art der Begutachtung: -
 Identifikatoren: eDoc: 356417
DOI: 10.1007/978-3-540-74621-8_3
Anderer: Local-ID: C12573CC004A8E26-C9A94C9D14B155F1C1257322003877B1-Sofronie-Stokkermans-frocos-07
 Art des Abschluß: -

Veranstaltung

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Titel: Untitled Event
Veranstaltungsort: Liverpool, UK
Start-/Enddatum: 2007-09-10 - 2007-09-12

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Quelle 1

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Titel: Frontiers of Combining Systems : 6th International Symposium, FroCos 2007
Genre der Quelle: Konferenzband
 Urheber:
Konev, Boris, Herausgeber
Wolter, Frank, Herausgeber
Affiliations:
-
Ort, Verlag, Ausgabe: Berlin, Germany : Springer
Seiten: - Band / Heft: - Artikelnummer: - Start- / Endseite: 47 - 71 Identifikator: ISBN: 978-3-540-74620-1

Quelle 2

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Titel: Lecture Notes in Artificial Intelligence
Genre der Quelle: Reihe
 Urheber:
Affiliations:
Ort, Verlag, Ausgabe: -
Seiten: - Band / Heft: - Artikelnummer: - Start- / Endseite: - Identifikator: -