Deriving focused lattice calculi
- We derive rewrite-based ordered resolution calculi for semilattices, distributive lattices and boolean lattices. Using ordered resolution as a metaprocedure, theory axioms are first transformed into independent bases. Focused inference rules are then extracted from inference patterns in refutations. The derivation is guided by mathematical and procedural background knowledge, in particular by ordered chaining calculi for quasiorderings (forgetting the lattice structure), by ordered resolution (forgetting the clause structure) and by Knuth-Bendix completion for non-symmetric transitive relations (forgetting both structures). Conversely, all three calculi are derived and proven complete in a transparent and generic way as special cases of the lattice calculi.
| Author: | Georg StruthGND |
|---|---|
| URN: | urn:nbn:de:bvb:384-opus4-1816 |
| Frontdoor URL | https://opus.bibliothek.uni-augsburg.de/opus4/230 |
| Series (Serial Number): | Reports / Technische Berichte der Fakultät für Angewandte Informatik der Universität Augsburg (2002-08) |
| Publisher: | Institut für Informatik, Universität Augsburg |
| Place of publication: | Augsburg |
| Type: | Report |
| Language: | English |
| Year of first Publication: | 2002 |
| Publishing Institution: | Universität Augsburg |
| Release Date: | 2006/06/13 |
| Tag: | automated deduction; lattice theory; ordered resolution; term rewriting; ordered chaining |
| Institutes: | Fakultät für Angewandte Informatik |
| Fakultät für Angewandte Informatik / Institut für Informatik | |
| Fakultät für Angewandte Informatik / Institut für Informatik / Professur für Programmiermethodik und Multimediale Informationssysteme | |
| Dewey Decimal Classification: | 0 Informatik, Informationswissenschaft, allgemeine Werke / 00 Informatik, Wissen, Systeme / 004 Datenverarbeitung; Informatik |
