Download: PostScript, BibTex-Entry.
Download PostScript, PDF
Download Extended version(.pdf)
Extends the following paper: "Locality and subsumption testing in EL and some of its extensions " Proceedings of the 21st International Workshop on Description Logics (DL2008). CEUR Workshop Proceedings series. Download(.pdf)
Download Preprint(.pdf).
Download Download(.pdf)
Download PostScript, PDF
Download PostScript, BibTex-Entry.
(with Harald Ganzinger and Uwe Waldmann)
Download Postscript (gzipped)
(with Harald Ganzinger and Uwe Waldmann)
Download PartialFun-bibl.html
(with Johannes Faber, Carsten Ihlemann and Swen Jacobs)
(with Carsten Ihlemann and Swen Jacobs)
Download PostScript, PDF
Extends the following paper:
Viorica Sofronie-Stokkermans, Carsten Ihlemann, and Swen Jacobs,
" Local Theory Extensions, Hierarchical Reasoning and Applications to Verification
" In Deduction and Decision Procedures, Dagstuhl Seminar Proceedings,
F. Baader, B. Cook, J. Giesl, R. Nieuwenhuis (Eds.) IBFI, Schloss Dagstuhl, Germany, December 2007. Download
(with Johannes Faber and Swen Jacobs)
Download PostScript, PDF
(with Andrey Rybalchenko)
Download PDF
(with Swen Jacobs)
Download PDF
This paper extends:
Download PostScript, PDF
Download PDF
This is the extended version of the following paper:
Download: PostScript, BibTex-Entry
Download: PostScript, BibTex-Entry
Download: BibTex-Entry, PostScript,
Download: BibTex-Entry
Download: preliminary version (PostScript); BibTex-Entry.
Abstract on the Kluwer Academic Publishers Home page (a .pdf file is also available from that page).
Download: preliminary version (PostScript); BibTex-Entry.
Abstract on the Kluwer Academic Publishers Home page (a .pdf file is also available on that page).
Download: preliminary version (PostScript file); BibTex-Entry.
Download: preliminary version PDF.
Download: preliminary version PDF.
Download PostScript (ACM TOCL website) PostScript (own version) BibTex-Entry.
Download: gzipped PostScript, BibTex-Entry
Download: gzipped .ps file, BibTex-Entry.
Download: Pdf file, BibTex-Entry.
(i) Structure-preserving translation to clause form. Testing the satisfiability of a unification problem $S$ is reduced to the problem of checking the satisfiability of a set $\Phi_S$ of clauses. Expressing $\Phi_S$ as a set of constrained clauses further simplifies the representation of the problem.
(ii) Ordered resolution with selection for (constrained) clauses is used for testing the satisfiability of $\Phi_S$.
Step 1 uses the description of the free bounded distributive lattice over $C$ as the lattice of all upwards-sets of (P(C), \subseteq), which is a consequence of the Priestley representation theorem. We also show that similar ideas can be used for unification with linear constant restrictions. The main advantage of our approach is that it makes it much easier to treat the unification problem for bounded distributive lattices, by using results in resolution theory. Using results of Baader and Schulz, our results also show that resolution can be used for deciding the positive theory of ${\sf D}_{01}$.
Download: PostScript, BibTex-Entry
Download: PostScript, BibTex-Entry
Download: PostScript, BibTex-Entry,
Download: PostScript, BibTex-Entry.
Download: PostScript, BibTex-Entry.
Download Pdf, BibTex-Entry.
Download: PostScript, BibTex-Entry.
Download: PostScript, BibTex-Entry.
Download: PostScript, BibTex-Entry.
Download: PDF Proceedings of UNIF 2007.
Download PostScript (ACM TOCL website) PostScript (own version) BibTex-Entry.
Download: gzipped PostScript, BibTex-Entry
(i) Structure-preserving translation to clause form. Testing the satisfiability of a unification problem $S$ is reduced to the problem of checking the satisfiability of a set $\Phi_S$ of clauses. Expressing $\Phi_S$ as a set of constrained clauses further simplifies the representation of the problem.
(ii) Ordered resolution with selection for (constrained) clauses is used for testing the satisfiability of $\Phi_S$.
Step 1 uses the description of the free bounded distributive lattice over $C$ as the lattice of all upwards-sets of (P(C), \subseteq), which is a consequence of the Priestley representation theorem. We also show that similar ideas can be used for unification with linear constant restrictions. The main advantage of our approach is that it makes it much easier to treat the unification problem for bounded distributive lattices, by using results in resolution theory. Using results of Baader and Schulz, our results also show that resolution can be used for deciding the positive theory of ${\sf D}_{01}$.
Download: PostScript, BibTex-Entry