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Unfounded sets and well-founded semantics for general logic programs

Authors:

Allen Van Gelder,

John S. SchlipfAuthors Info & Claims

PODS '88: Proceedings of the seventh ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems

Pages 221 - 230

https://doi.org/10.1145/308386.308444

Published: 01 March 1988 Publication History

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. 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 model, we call it the well-founded model, and say the program is “well-behaved”. We show that the class of well-behaved programs properly includes previously studied classes of “stratified” and “locally stratified” programs Gelfand and Lifschits have proposed a definition of “unique stable model” for general logic programs. We show that a program has a unique stable model if it has a well-founded model, in which case they are the same. We discuss why the converse is not true.

References

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Cited By

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cover image ACM Conferences

PODS '88: Proceedings of the seventh ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems

March 1988

352 pages

ISBN:0897912632

DOI:10.1145/308386

Chairmen:
Chris Edmondson-Yurkanan
Univ. of Texas at Austin, Austin
,
Mihalis Yannakakis
AT&T Bell Labs

Copyright © 1988 ACM.

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Published: 01 March 1988

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Overall Acceptance Rate 642 of 2,707 submissions, 24%

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Cited By

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Fitting M(2024)Modal, Fuzzy, ..., Vanilla Fixpoint Theories of Truth: A Uniform ApproachSaul Kripke on Modal Logic10.1007/978-3-031-57635-5_7(151-192)Online publication date: 2-Oct-2024
Azzolini D(2023)A Constrained Optimization Approach to Set the Parameters of Probabilistic Answer Set ProgramsInductive Logic Programming10.1007/978-3-031-49299-0_1(1-15)Online publication date: 13-Nov-2023
Liu YStoller S(2022)Recursive rules with aggregation: a simple unified semanticsJournal of Logic and Computation10.1093/logcom/exac07232:8(1659-1693)Online publication date: 14-Nov-2022
Azzolini DBellodi EFerilli SRiguzzi FZese R(2022)Abduction with probabilistic logic programming under the distribution semanticsInternational Journal of Approximate Reasoning10.1016/j.ijar.2021.11.003142:C(41-63)Online publication date: 1-Mar-2022
Liu YStoller S(2022)Recursive Rules with Aggregation: A Simple Unified SemanticsLogical Foundations of Computer Science10.1007/978-3-030-93100-1_11(156-179)Online publication date: 10-Jan-2022
Greco SMolinaro C(2022)Datalog and Logic DatabasesundefinedOnline publication date: 25-Feb-2022
VAN DESSEL KDEVRIENDT JVENNEKENS J(2021) FOLASP : FO(·) as Input Language for Answer Set Solvers Theory and Practice of Logic Programming10.1017/S147106842100035121:6(785-801)Online publication date: 19-Nov-2021
Brass S(2021)Event-Based Microcontroller Programming in DatalogRules and Reasoning10.1007/978-3-030-91167-6_6(80-94)Online publication date: 8-Sep-2021
Liu YStoller S(2020)Knowledge of uncertain worlds: programming with logical constraintsJournal of Logic and Computation10.1093/logcom/exaa07731:1(193-212)Online publication date: 23-Dec-2020
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