Unfounded Sets and Well-Founded Semantics for General Logic Programs

Summary: Introduce unfounded sets and the well‑founded partial model as a canonical semantics for general logic programs with negation; 'well‑behaved' programs have a total well‑founded model. Prove this strictly generalizes stratified/local stratified programs and that a well‑founded model yields a unique (coinciding) stable model, though the converse may fail. (summarized by gpt-5-mini on Feb 09 2026)

Paper ID: 831
Venue: PODS
Year: 1988
Pagerank: 0.00010502706
Overall Rank: 1,522 | 89.56%
DOI: 10.1145/308386.308444

Incoming Non-self Citations Over Time

Authors

1. Allen Van Gelder (University of California Santa Cruz)
2. Kenneth Ross (Stanford University)
3. John S. Schlipf (University of Cincinnati)

BibTeX Citation

@inproceedings{gelder_pods88,
        address = {New York, NY, USA},
        series = {{PODS} '88},
        title = {{Unfounded Sets and Well-Founded Semantics for General Logic Programs}},
        url = {https://dl.acm.org/doi/10.1145/308386.308444},
        doi = {10.1145/308386.308444},
        booktitle = {Proceedings of the {ACM} {SIGMOD} Symposium on {Principles} of {Database} {Systems}},
        publisher = {Association for Computing Machinery},
        author = {Van Gelder, Allen and Ross, Kenneth and Schlipf, John S.},
        year = {1988}
}

Incoming Citations (Sorted by Pagerank)

Showing 16 of 16 citing papers.

Rank	Citing Paper	Year	Venue	Pagerank
1,297	The Alternating Fixpoint of Logic Programs with Negation (Extended Abstract)	1989	PODS	0.0001126031
1,419	Every Logic Program Has a Natural Stratification And an Iterated Least Fixed Point Model	1989	PODS	0.00010830412
1,714	Modular Stratification and Magic Sets for DATALOG Programs with Negation	1990	PODS	9.9404301e-05
1,891	A Logic for Object-Oriented Logic Programming (Maier's O-Logic Revisited)	1989	PODS	9.5298123e-05
2,028	A Procedural Semantics for Well Founded Negation in Logic Programs	1989	PODS	9.285972e-05
4,831	Stable Models and Non-Determinism in Logic Programs with Negation	1990	PODS	6.4877275e-05
4,943	Datalog Unchained	2021	PODS	6.4332239e-05
5,532	Qualified Answers That Reflect User Needs and Preferences	1994	VLDB	6.1835054e-05
6,620	An alternating fixpoint tailored to magic programs	1993	PODS	5.8212982e-05
7,260	On the Power of Algebras with Recursion	1993	SIGMOD	5.6612789e-05
7,885	IDLOG: Extending the Expressive Power of Deductive Database Languages	1990	SIGMOD	5.5228272e-05
8,295	The Expressive Powers of the Logic Programming Semantics	1990	PODS	5.4574671e-05
8,621	Three-Valued Formalization of Logic Programming: Is It Needed?	1990	PODS	5.3986999e-05
9,326	Extending Logic Programming	1990	SIGMOD	5.289545e-05
13,105	A Non-deterministic Deductive Database Language	1991	SIGMOD	5.093636e-05
14,396	On Negation in HiLog	1991	PODS	-

Outgoing Citations (Sorted by Pagerank)

Showing 0 of 0 cited papers.

Citations counted here include only citations to other VLDB/SIGMOD/CIDR/PODS papers in this database.

Rank	Cited Paper	Year	Venue	Pagerank

Semantically Similar Papers

#	Overall Rank	Paper	Year	Venue
1	1,297	The Alternating Fixpoint of Logic Programs with Negation (Extended Abstract)	1989	PODS
2	6,221	Well-Founded Semantics for Extended Datalog and Ontological Reasoning	2013	PODS
3	8,621	Three-Valued Formalization of Logic Programming: Is It Needed?	1990	PODS
4	2,474	Logic Programming as Constructivism: A Formalization and its Application to Databases	1989	PODS
5	2,028	A Procedural Semantics for Well Founded Negation in Logic Programs	1989	PODS
6	5,111	The Well-Founded Semantics of Aggregation (Extended Abstract)	1992	PODS
7	4,831	Stable Models and Non-Determinism in Logic Programs with Negation	1990	PODS
8	1,419	Every Logic Program Has a Natural Stratification And an Iterated Least Fixed Point Model	1989	PODS
9	8,083	The Valid Model Semantics for Logic Programs	1992	PODS
10	8,295	The Expressive Powers of the Logic Programming Semantics	1990	PODS