TY - JOUR
T1 - Reasoning with minimal models
T2 - Efficient algorithms and applications
AU - Ben-Eliyahu-Zohary, Rachel
AU - Palopoli, Luigi
N1 - Funding Information:
The work of the first author was supportedi n part by grants NSF IRI-88-21444 and AFOSR 90-0136, and in part by an infrastructureg rant for data-mining technology from the Israeli Ministry of Science. The second author is supportedi n part by the ECC under the EU-US project “DEUS EX MACHINA: Non-determinism for deductived atabases” and by a MURST grant (40% share) under the project “Sistemi formali e strumentip er basi di dati evolute”.
PY - 1997/1/1
Y1 - 1997/1/1
N2 - Reasoning with minimal models is at the heart of many knowledge-representation systems. Yet it turns out that this task is formidable, even when very simple theories are considered. In this paper, we introduce the elimination algorithm, which performs, in linear time, minimal model finding and minimal model checking for a significant subclass of positive CNF theories which we call positive head-cycle-free (HCF) theories. We also prove that the task of minimal entailment is easier for positive HCF theories than it is for the class of all positive CNF theories. Finally, we show how variations of the elimination algorithm can be applied to allow queries posed on disjunctive deductive databases and disjunctive default theories to be answered in an efficient way.
AB - Reasoning with minimal models is at the heart of many knowledge-representation systems. Yet it turns out that this task is formidable, even when very simple theories are considered. In this paper, we introduce the elimination algorithm, which performs, in linear time, minimal model finding and minimal model checking for a significant subclass of positive CNF theories which we call positive head-cycle-free (HCF) theories. We also prove that the task of minimal entailment is easier for positive HCF theories than it is for the class of all positive CNF theories. Finally, we show how variations of the elimination algorithm can be applied to allow queries posed on disjunctive deductive databases and disjunctive default theories to be answered in an efficient way.
KW - Disjunctive databases
KW - Disjunctive default logic
KW - Disjunctive logic programs
KW - Linear time algorithms
KW - Minimal models
KW - Stable model semantics
UR - http://www.scopus.com/inward/record.url?scp=0031272679&partnerID=8YFLogxK
U2 - 10.1016/S0004-3702(97)00060-X
DO - 10.1016/S0004-3702(97)00060-X
M3 - Article
AN - SCOPUS:0031272679
SN - 0004-3702
VL - 96
SP - 421
EP - 449
JO - Artificial Intelligence
JF - Artificial Intelligence
IS - 2
ER -