The well-founded semantics for general logic programs
Abstract
A general logic program (abbreviated to "program" hereafter) is a set of rules that have both positive and negative subgoals. It is common to view a deductive database as a general logic program consisting of rules (IDB) sitting above elementary relations (EDB, facts). It is desirable to associate one Herbrand model with a program and think of that model as the "meaning of the program," or its "declarative semantics." Ideally, queries directed to the program would be answered in accordance with this model. Recent research indicates that some programs do not have a "satisfactory" total model; for such programs, the question of an appropriate partial model arises. We introduce unfounded sets and well-founded partial models, and define the well-founded semantics of a program to be its well-founded partial model. If the well-founded partial model is in fact a total model, we call it the well-founded model. We show that the class of programs possessing a total well-founded model properly in...
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ILP approaches that learn normal logic programs can be characterised by their semantics, such as completion, well-founded, or stable model semantics.
“ILP approaches that learn normal logic programs can further be characterised by their semantics, such as whether they are based on completion (Clark, 1977), well-founded (Gelder et al., 1991), or stable model (answer set) (Gelfond & Lifschitz, 1988) semantics.”
From Inductive Logic Programming At 30: A New Introduction (2022) · cites this paper as Gelder et al., 1991
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Inductive Logic Programming At 30: A New Introduction
Cropper, A., & Dumančić, S. (2022) · Journal of Artificial Intelligence Research · doi:10.1613/jair.1.13507 · Cited by 83 · see citing works
“There are many different semantics ascribed to non-monotonic programs, including completion (Clark, 1977), well-founded (Gelder et al., 1991), and stable model (answer set) (Gelfond & Lifschitz, 1988) semantics.”
BackgroundFifty Years of Prolog and Beyond
KÖRNER, P., LEUSCHEL, M., BARBOSA, J., COSTA, V. S., DAHL, V., HERMENEGILDO, M. V., MORALES, J. F., WIELEMAKER, J., DIAZ, D., ABREU, S., et al. (2022) · Theory and Practice of Logic Programming · doi:10.1017/s1471068422000102 · Cited by 40 · see citing works
Prolog and ASP Inference under One Roof
Balduccini, M., Lierler, Y., & Schüller, P. (2013) · Lecture Notes in Computer Science · doi:10.1007/978-3-642-40564-8_15 · Cited by 8 · see citing works
- Authors
- Van Gelder, A., Ross, K. A., & Schlipf, J. S.
- Affiliations
- Univ. of California at Santa Cruz, Santa Cruz
- Stanford University (US)
- University of Cincinnati (US)
- ORCID
- Ross, Kenneth A.
- Venue
- Journal of the ACM
- Published
- 1991-07
- Volume
- 38
- Issue
- 3
- Pages
- 619-649
- ISSN
- 0004-5411 (ISSN-L)
- 1557-735X
- OpenAlex
- W1968513265
- Cited by
- 1,652
- References
- 0
- Citations by year
- 2026: 8 · 2025: 12 · 2024: 24 · 2023: 19 · 2022: 23 · 2021: 34 · 2020: 40 · 2019: 26 · 2018: 27 · 2017: 46 · 2016: 42 · 2015: 57 · 2014: 52 · 2013: 70 · 2012: 39
- FWCI
- 53.09
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Journal of the ACM (publishedVersion)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Logic, Reasoning, and Knowledge
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Advanced Algebra and Logic
- Physical Sciences › Computer Science › Artificial Intelligence › Logic, programming, and type systems
- Keywords
- well-founded semantics, Herbrand models, deductive databases, declarative semantics, partial models
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