Fixpoint semantics for logic programming a survey

The variety of semantical approaches that have been invented for logic programs is quite broad, drawing on classical and many-valued logic, lattice theory, game theory, and topology. One source of this richness is the inherent non-monotonicity of its negation, something that does not have close para...

Full description

Saved in:
Bibliographic Details
Published in:Theoretical computer science Vol. 278; no. 1; pp. 25 - 51
Main Author: Fitting, Melvin
Format: Journal Article Conference Proceeding
Language:English
Published: Amsterdam Elsevier B.V 06.05.2002
Elsevier
Subjects:
Applied sciences
Computer science; control theory; systems
Exact sciences and technology
Programming theory
Theoretical computing
Fix point
Stability
Semantics
Belnap logic
Valuation
Apt-van Emden Kowalski semantics
Models
Logical programming
Syntax
Stable model semantics
Lattice
ISSN:0304-3975, 1879-2294
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Abstract The variety of semantical approaches that have been invented for logic programs is quite broad, drawing on classical and many-valued logic, lattice theory, game theory, and topology. One source of this richness is the inherent non-monotonicity of its negation, something that does not have close parallels with the machinery of other programming paradigms. Nonetheless, much of the work on logic programming semantics seems to exist side by side with similar work done for imperative and functional programming, with relatively minimal contact between communities. In this paper we summarize one variety of approaches to the semantics of logic programs: that based on fixpoint theory. We do not attempt to cover much beyond this single area, which is already remarkably fruitful. We hope readers will see parallels with, and the divergences from the better known fixpoint treatments developed for other programming methodologies.
AbstractList The variety of semantical approaches that have been invented for logic programs is quite broad, drawing on classical and many-valued logic, lattice theory, game theory, and topology. One source of this richness is the inherent non-monotonicity of its negation, something that does not have close parallels with the machinery of other programming paradigms. Nonetheless, much of the work on logic programming semantics seems to exist side by side with similar work done for imperative and functional programming, with relatively minimal contact between communities. In this paper we summarize one variety of approaches to the semantics of logic programs: that based on fixpoint theory. We do not attempt to cover much beyond this single area, which is already remarkably fruitful. We hope readers will see parallels with, and the divergences from the better known fixpoint treatments developed for other programming methodologies.
The variety of semantical approaches that have been invented for logic programs is quite broad, drawing on classical and many-valued logic, lattice theory, game theory, and topology. One source of this richness is the inherent non-monotonicity of its negation, something that does not have close parallels with the machinery of other programming paradigms. Nonetheless, much of the work on logic programming semantics seems to exist side by side with similar work done for imperative and functional programming, with relatively minimal contact between communities. In this paper we summarize one variety of approaches to the semantics of logic programs: that based on fixpoint theory. We do not attempt to cover much beyond this single area, which is already remarkably fruitful. We hope readers will see parallels with, and the divergences from the better known fixpoint treatments developed for other programming methodologies. copyright 2002 Elsevier Science B.V. All rights reserved.
Author Fitting, Melvin
Author_xml – sequence: 1
  givenname: Melvin
  surname: Fitting
  fullname: Fitting, Melvin
  email: fitting@alpha.lehman.cuny.edu
  organization: Department of Mathematics and Computer Science, Lehman College (CUNY), Bronx, NY 10468, USA
BackLink http://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=13661419$$DView record in Pascal Francis
BookMark eNqFkD1PwzAQhi0EEm3hJyBlAcEQOMeO04gBoYoCUiUGYLYc51wZJXax04r-e9IPdWDhllue973TMyTHzjsk5ILCLQUq7t6BAU9ZWeTXADcAjEHKjsiAjosyzbKSH5PBATklwxi_oJ-8EANCp_Zn4a3rkoitcp3VMTE-JI2fW50sgp8H1bbWzROVxGVY4fqMnBjVRDzf7xH5nD59TF7S2dvz6-RxlmrOeJdmtAJuCjbOjeBcVJVSwlDKcsNqIbIcMUPoUQN5BRmtNaUICmoGlcpMadiIXO16-ye-lxg72dqosWmUQ7-MMisoB-DjHrzcgypq1ZignLZRLoJtVVhLyoSgnJY9d7_jdPAxBjRS20511rsuKNtICnKjU251yo0rCSC3OiXr0_mf9OHAP7mHXQ57VyuLQUZt0WmsbUDdydrbfxp-AbnhjWo
CODEN TCSCDI
CitedBy_id crossref_primary_10_1016_j_artint_2018_03_008
crossref_primary_10_1016_j_artint_2017_11_003
crossref_primary_10_1016_j_artint_2015_03_006
crossref_primary_10_1145_2963096
crossref_primary_10_1145_383779_383789
crossref_primary_10_1007_s11225_014_9546_3
crossref_primary_10_1016_j_jal_2004_07_012
crossref_primary_10_1145_3428193
crossref_primary_10_1017_S1471068415000162
crossref_primary_10_1016_j_apal_2016_10_005
crossref_primary_10_1017_S1471068421000314
crossref_primary_10_1016_j_ic_2004_02_004
crossref_primary_10_1016_j_fss_2012_01_016
crossref_primary_10_1145_2980983_2908096
crossref_primary_10_1007_s00182_011_0314_6
crossref_primary_10_1017_S1471068413000069
crossref_primary_10_1109_TFUZZ_2011_2114669
crossref_primary_10_1007_s10472_008_9099_0
crossref_primary_10_1016_j_artint_2024_104112
crossref_primary_10_1093_logcom_exaa077
crossref_primary_10_1016_S0168_0072_98_00041_4
crossref_primary_10_1016_j_entcs_2008_12_071
crossref_primary_10_1016_j_entcs_2008_12_073
crossref_primary_10_1007_s11225_017_9721_4
crossref_primary_10_1016_j_ijar_2013_04_004
crossref_primary_10_3166_jancl_21_211_232
crossref_primary_10_1007_s13748_021_00240_8
crossref_primary_10_1145_1342991_1342998
crossref_primary_10_4018_jssci_2011010105
crossref_primary_10_1016_j_artint_2013_09_004
crossref_primary_10_1017_S147106840700302X
crossref_primary_10_1016_j_entcs_2006_04_028
crossref_primary_10_1016_j_artint_2020_103370
crossref_primary_10_1016_j_jlamp_2023_100870
crossref_primary_10_1016_S0004_3702_02_00184_4
crossref_primary_10_1016_j_artint_2024_104273
crossref_primary_10_1016_j_tcs_2015_01_032
crossref_primary_10_1017_S1471068422000308
crossref_primary_10_1016_j_ijar_2015_06_009
crossref_primary_10_1016_j_artint_2007_02_002
crossref_primary_10_1145_2480759_2480767
crossref_primary_10_1016_j_fss_2012_09_012
crossref_primary_10_1016_j_jlamp_2021_100679
crossref_primary_10_1007_s11229_011_9963_z
crossref_primary_10_1016_j_apal_2007_10_004
crossref_primary_10_1016_j_apal_2013_05_008
crossref_primary_10_1017_S1471068411000378
crossref_primary_10_1016_j_jlamp_2016_09_004
crossref_primary_10_1007_s00165_016_0404_0
crossref_primary_10_1007_s10472_012_9294_x
crossref_primary_10_1007_s11784_015_0232_5
crossref_primary_10_1017_S1471068418000108
crossref_primary_10_3390_math10173105
crossref_primary_10_2989_16073606_2020_1812757
crossref_primary_10_1007_s10472_007_9049_2
crossref_primary_10_1145_981009_981013
crossref_primary_10_1145_1055686_1055694
crossref_primary_10_1016_j_fss_2007_12_006
crossref_primary_10_1093_logcom_exaa056
crossref_primary_10_1016_j_fss_2003_10_019
crossref_primary_10_1016_S0004_3702_02_00293_X
crossref_primary_10_1016_j_jal_2004_03_002
crossref_primary_10_1016_j_tcs_2005_04_005
crossref_primary_10_1093_logcom_exac072
crossref_primary_10_1017_S1471068421000168
crossref_primary_10_1145_3643027
Cites_doi 10.1016/S0743-1066(85)80005-4
10.2307/2024634
10.1111/j.1467-8640.1988.tb00280.x
10.1016/0743-1066(86)90003-8
10.1016/0743-1066(89)90022-8
10.1016/0743-1066(88)90005-2
10.1016/0004-3702(91)90013-A
10.1007/978-1-4684-3384-5_11
10.7551/mitpress/3133.001.0001
10.1093/logcom/1.6.797
10.1017/S0960129500001018
10.1007/3-540-16492-8_94
10.1016/0743-1066(87)90007-0
10.1145/308386.308444
10.3233/FI-1994-201234
10.1145/322326.322339
10.1016/0743-1066(91)90014-G
10.1145/73721.73722
10.1016/0743-1066(88)90014-3
10.2140/pjm.1955.5.285
10.1007/978-94-009-5203-4_1
10.1016/0743-1066(93)90031-B
10.1109/ISMVL.1990.122627
10.1016/0304-3975(86)90096-4
10.1016/S0019-9958(82)91234-7
10.1145/321978.321991
ContentType Journal Article
Conference Proceeding
Copyright 2002 Elsevier Science B.V.
2002 INIST-CNRS
Copyright_xml – notice: 2002 Elsevier Science B.V.
– notice: 2002 INIST-CNRS
DBID 6I.
AAFTH
AAYXX
CITATION
IQODW
7SC
8FD
JQ2
L7M
L~C
L~D
DOI 10.1016/S0304-3975(00)00330-3
DatabaseName ScienceDirect Open Access Titles
Elsevier:ScienceDirect:Open Access
CrossRef
Pascal-Francis
Computer and Information Systems Abstracts
Technology Research Database
ProQuest Computer Science Collection
Advanced Technologies Database with Aerospace
Computer and Information Systems Abstracts – Academic
Computer and Information Systems Abstracts Professional
DatabaseTitle CrossRef
Computer and Information Systems Abstracts
Technology Research Database
Computer and Information Systems Abstracts – Academic
Advanced Technologies Database with Aerospace
ProQuest Computer Science Collection
Computer and Information Systems Abstracts Professional
DatabaseTitleList
Computer and Information Systems Abstracts
DeliveryMethod fulltext_linktorsrc
Discipline Mathematics
Computer Science
Applied Sciences
EISSN 1879-2294
EndPage 51
ExternalDocumentID 13661419
10_1016_S0304_3975_00_00330_3
S0304397500003303
GroupedDBID --K
--M
-~X
.DC
.~1
0R~
123
1B1
1RT
1~.
1~5
29Q
4.4
457
4G.
5VS
6I.
7-5
71M
8P~
9JN
AABNK
AACTN
AAEDT
AAEDW
AAFTH
AAIAV
AAIKJ
AAKOC
AALRI
AAOAW
AAQFI
AAQXK
AAXUO
AAYFN
ABAOU
ABBOA
ABEFU
ABFNM
ABJNI
ABMAC
ABTAH
ABVKL
ABXDB
ABYKQ
ACAZW
ACDAQ
ACGFS
ACNNM
ACRLP
ACZNC
ADBBV
ADEZE
ADMUD
AEBSH
AEKER
AENEX
AEXQZ
AFKWA
AFTJW
AGHFR
AGUBO
AGYEJ
AHHHB
AHZHX
AIALX
AIEXJ
AIKHN
AITUG
AJBFU
AJOXV
ALMA_UNASSIGNED_HOLDINGS
AMFUW
AMRAJ
AOUOD
ARUGR
ASPBG
AVWKF
AXJTR
AZFZN
BKOJK
BLXMC
CS3
DU5
EBS
EFJIC
EFLBG
EJD
EO8
EO9
EP2
EP3
F5P
FDB
FEDTE
FGOYB
FIRID
FNPLU
FYGXN
G-2
G-Q
G8K
GBLVA
GBOLZ
HVGLF
HZ~
IHE
IXB
J1W
KOM
LG9
M26
M41
MHUIS
MO0
N9A
NCXOZ
O-L
O9-
OAUVE
OK1
OZT
P-8
P-9
P2P
PC.
Q38
R2-
RIG
ROL
RPZ
SCC
SDF
SDG
SES
SEW
SPC
SPCBC
SSV
SSW
SSZ
T5K
TAE
TN5
WH7
WUQ
XJT
YNT
ZMT
ZY4
~G-
9DU
AATTM
AAXKI
AAYWO
AAYXX
ABDPE
ABWVN
ACLOT
ACRPL
ACVFH
ADCNI
ADNMO
ADVLN
AEIPS
AEUPX
AFJKZ
AFPUW
AGQPQ
AIGII
AIIUN
AKBMS
AKRWK
AKYEP
ANKPU
APXCP
CITATION
EFKBS
~HD
ABPIF
ABPTK
IQODW
7SC
8FD
JQ2
L7M
L~C
L~D
ID FETCH-LOGICAL-c434t-21b04f7385f6446bbaa6f1135f3d6625ee2e0c43f05b021dc11e0a0d30ba2f9f3
ISICitedReferencesCount 132
ISICitedReferencesURI http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000175733600003&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN 0304-3975
IngestDate Sat Sep 27 19:41:36 EDT 2025
Sun Oct 22 16:08:00 EDT 2023
Tue Nov 18 22:10:14 EST 2025
Sat Nov 29 06:16:35 EST 2025
Fri Feb 23 02:33:38 EST 2024
IsDoiOpenAccess true
IsOpenAccess true
IsPeerReviewed true
IsScholarly true
Issue 1
Keywords Fix point
Stability
Semantics
Belnap logic
Valuation
Apt-van Emden Kowalski semantics
Models
Logical programming
Syntax
Stable model semantics
Lattice
Language English
License http://www.elsevier.com/open-access/userlicense/1.0
https://www.elsevier.com/tdm/userlicense/1.0
https://www.elsevier.com/open-access/userlicense/1.0
CC BY 4.0
LinkModel OpenURL
MeetingName Mathematical Foundations of Programming Semantics
MergedId FETCHMERGED-LOGICAL-c434t-21b04f7385f6446bbaa6f1135f3d6625ee2e0c43f05b021dc11e0a0d30ba2f9f3
Notes ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
OpenAccessLink https://dx.doi.org/10.1016/S0304-3975(00)00330-3
PQID 27140048
PQPubID 23500
PageCount 27
ParticipantIDs proquest_miscellaneous_27140048
pascalfrancis_primary_13661419
crossref_citationtrail_10_1016_S0304_3975_00_00330_3
crossref_primary_10_1016_S0304_3975_00_00330_3
elsevier_sciencedirect_doi_10_1016_S0304_3975_00_00330_3
PublicationCentury 2000
PublicationDate 2002-05-06
PublicationDateYYYYMMDD 2002-05-06
PublicationDate_xml – month: 05
  year: 2002
  text: 2002-05-06
  day: 06
PublicationDecade 2000
PublicationPlace Amsterdam
PublicationPlace_xml – name: Amsterdam
PublicationTitle Theoretical computer science
PublicationYear 2002
Publisher Elsevier B.V
Elsevier
Publisher_xml – name: Elsevier B.V
– name: Elsevier
References Fitting (BIB11) 1987; 48
M. Gelfond, V. Lifschitz, The stable model semantics for logic programming, in: R. Kowalski, K. Bowen (Eds.), Proc. of the 5th Logic Programming Symp., MIT Press, Cambridge, MA, 1988, pp. 1070–1080.
Fitting (BIB10) 1985; 2
L. Giordano, N. Olivetti, Negation as failure in intuitionistic logic programming, Logic Programming, Proc. Joint Internat. Conf. and Symp. MIT Press, Cambridge, MA, 1992, pp. 430–445.
M.A. Khamsi, V. Kreinovich, D. Misane, A new method of proving the existence of answer sets for disjunctive logic programs: a metric fixed point theorem for multi-valued mappings, J. Logic Programming, forthcoming.
Fine (BIB9) 1989
Smullyan (BIB38) 1956; 62
Van Gelder, Ross, Schlipf (BIB44) 1991; 38
A. Van Gelder, K.A. Ross, J.S. Schlipf, Unfounded sets and well-founded semantics for general logic programs, Proc. 7th Symp. on Principles of Database Systems, 1988, pp. 221–230.
K.L. Clark, Negation as failure. In Logic and Databases, H. Gallaire and J. Minker, Eds. Plenum, 1978, pp. 55–76.
A.K. Seda, Quasi-metrics and the semantics of logic programs 1996.
M.C. Fitting, Bilattices in logic programming, in: G. Epstein (Ed.), The Twentieth Internat. Symp. on Multiple-Valued Logic, IEEE, New York, 1990, pp. 238–246.
Fitting (BIB13) 1991; 11
Kleene (BIB22) 1950
McCarty (BIB30) 1988; 5
McCarty (BIB29) 1988; 5
van Emden (BIB40) 1986; 3
Lloyd (BIB28) 1987
Przymusinski (BIB32) 1990
Kunen (BIB26) 1988
T.C. Przymusinski, Three-valued non-monotonic formalisms and semantics of logic programs, J. Artificial Intelligence (1991).
E. Shapiro, Logic programs with uncertainties: a tool for implementing rule-based systems, in: A. Bundy (Ed.), Proc. 8th IJCAI, Kaufmann, 1983, pp. 529–532.
S. Blamey, Handbook of Philosophical Logic, Vol. 3, D. Reidel, Dordrecht, 1985, pp. 1–70 (Chapter-Partial Logic).
Ginsberg (BIB19) 1988; 4
Belnap (BIB4) 1977
K. Kunen, Answer sets and negation-as-failure, in: J.-L. Lassez (Ed.), Logic Programming, Proc. 4th Internat Conf. MIT Press, Cambridge, MA, 1987, pp. 219–228.
D. Miller, A theory of modules for logic programming, IEEE Symp. on Logic Programming, 1986, pp. 106–114.
Przymusinski (BIB33) 1990; 13
S. Kripke, Outline of a theory of truth, J. Philos. 72 (1975) 690–716. (Reprinted in New Essays on Truth and the Liar Paradox, R. L. Martin (Ed.), Oxford, 1983).
A. Van Gelder, The alternating fixpoint of logic programs with negation, Proc. 8th ACM Symp. on Principles of Database Systems, ACM, Philadelphia, 1989, pp. 1–10.
Apt, van Emden (BIB2) 1982; 29
Fitting (BIB16) 1994; 20
Kunen (BIB25) 1987; 4
van Emden, Kowalski (BIB41) 1976; 23
A. Avron, The structure of interlaced bilattices. Math. Struct. Comput. Sci., forthcoming.
Fitting (BIB14) 1992; 1
Smullyan (BIB37) 1956; 62
K. Doets, From Logic to Logic Programming. MIT Press, Cambridge, MA, 1994.
Kunen (BIB27) 1989; 7
Blair (BIB5) 1982; 54
Fitting (BIB15) 1993; 17
Tarski (BIB39) 1955; 5
K. Apt, Handbook of Theoretical Computer Science, Vol. B. Elsevier and MIT Press, 1990.
M.C. Fitting, On prudent bravery and other abstractions, 1994.
10.1016/S0304-3975(00)00330-3_BIB31
Apt (10.1016/S0304-3975(00)00330-3_BIB2) 1982; 29
Smullyan (10.1016/S0304-3975(00)00330-3_BIB38) 1956; 62
10.1016/S0304-3975(00)00330-3_BIB12
10.1016/S0304-3975(00)00330-3_BIB34
Tarski (10.1016/S0304-3975(00)00330-3_BIB39) 1955; 5
Fitting (10.1016/S0304-3975(00)00330-3_BIB10) 1985; 2
Fitting (10.1016/S0304-3975(00)00330-3_BIB15) 1993; 17
Van Gelder (10.1016/S0304-3975(00)00330-3_BIB44) 1991; 38
Przymusinski (10.1016/S0304-3975(00)00330-3_BIB32) 1990
10.1016/S0304-3975(00)00330-3_BIB8
10.1016/S0304-3975(00)00330-3_BIB6
10.1016/S0304-3975(00)00330-3_BIB7
Belnap (10.1016/S0304-3975(00)00330-3_BIB4) 1977
Fine (10.1016/S0304-3975(00)00330-3_BIB9) 1989
Fitting (10.1016/S0304-3975(00)00330-3_BIB11) 1987; 48
10.1016/S0304-3975(00)00330-3_BIB1
10.1016/S0304-3975(00)00330-3_BIB24
10.1016/S0304-3975(00)00330-3_BIB3
10.1016/S0304-3975(00)00330-3_BIB20
10.1016/S0304-3975(00)00330-3_BIB42
10.1016/S0304-3975(00)00330-3_BIB21
10.1016/S0304-3975(00)00330-3_BIB43
10.1016/S0304-3975(00)00330-3_BIB23
Ginsberg (10.1016/S0304-3975(00)00330-3_BIB19) 1988; 4
Blair (10.1016/S0304-3975(00)00330-3_BIB5) 1982; 54
Lloyd (10.1016/S0304-3975(00)00330-3_BIB28) 1987
van Emden (10.1016/S0304-3975(00)00330-3_BIB40) 1986; 3
Kunen (10.1016/S0304-3975(00)00330-3_BIB25) 1987; 4
Fitting (10.1016/S0304-3975(00)00330-3_BIB16) 1994; 20
Kleene (10.1016/S0304-3975(00)00330-3_BIB22) 1950
10.1016/S0304-3975(00)00330-3_BIB17
Przymusinski (10.1016/S0304-3975(00)00330-3_BIB33) 1990; 13
van Emden (10.1016/S0304-3975(00)00330-3_BIB41) 1976; 23
10.1016/S0304-3975(00)00330-3_BIB18
McCarty (10.1016/S0304-3975(00)00330-3_BIB30) 1988; 5
Fitting (10.1016/S0304-3975(00)00330-3_BIB13) 1991; 11
Kunen (10.1016/S0304-3975(00)00330-3_BIB27) 1989; 7
Smullyan (10.1016/S0304-3975(00)00330-3_BIB37) 1956; 62
10.1016/S0304-3975(00)00330-3_BIB35
10.1016/S0304-3975(00)00330-3_BIB36
Fitting (10.1016/S0304-3975(00)00330-3_BIB14) 1992; 1
Kunen (10.1016/S0304-3975(00)00330-3_BIB26) 1988
McCarty (10.1016/S0304-3975(00)00330-3_BIB29) 1988; 5
References_xml – volume: 62
  start-page: 601
  year: 1956
  ident: BIB38
  article-title: On definability by recursion (abstract)
  publication-title: Bull. Amer. Math. Soc.
– reference: K. Apt, Handbook of Theoretical Computer Science, Vol. B. Elsevier and MIT Press, 1990.
– volume: 23
  start-page: 733
  year: 1976
  end-page: 742
  ident: BIB41
  article-title: The semantics of predicate logic as a programming language
  publication-title: J. Assoc. Comput. Mach.
– volume: 54
  start-page: 25
  year: 1982
  end-page: 47
  ident: BIB5
  article-title: The recursion-theoretic complexity of the semantics of predicate logic as a programming language
  publication-title: Inform. and Control
– reference: A. Van Gelder, K.A. Ross, J.S. Schlipf, Unfounded sets and well-founded semantics for general logic programs, Proc. 7th Symp. on Principles of Database Systems, 1988, pp. 221–230.
– reference: A. Van Gelder, The alternating fixpoint of logic programs with negation, Proc. 8th ACM Symp. on Principles of Database Systems, ACM, Philadelphia, 1989, pp. 1–10.
– volume: 48
  start-page: 229
  year: 1987
  end-page: 255
  ident: BIB11
  article-title: Partial models and logic programming
  publication-title: Theoret. Comput. Sci.
– volume: 17
  start-page: 197
  year: 1993
  end-page: 225
  ident: BIB15
  article-title: The family of stable models
  publication-title: J. Logic Programming
– reference: K. Kunen, Answer sets and negation-as-failure, in: J.-L. Lassez (Ed.), Logic Programming, Proc. 4th Internat Conf. MIT Press, Cambridge, MA, 1987, pp. 219–228.
– reference: M.C. Fitting, Bilattices in logic programming, in: G. Epstein (Ed.), The Twentieth Internat. Symp. on Multiple-Valued Logic, IEEE, New York, 1990, pp. 238–246.
– reference: A.K. Seda, Quasi-metrics and the semantics of logic programs 1996.
– volume: 4
  start-page: 289
  year: 1987
  end-page: 308
  ident: BIB25
  article-title: Negation in logic programming
  publication-title: J. Logic Programming
– volume: 2
  start-page: 295
  year: 1985
  end-page: 312
  ident: BIB10
  article-title: A Kripke/Kleene semantics for logic programs
  publication-title: J. Logic Programming
– volume: 29
  start-page: 841
  year: 1982
  end-page: 862
  ident: BIB2
  article-title: Contributions to the theory of logic programming
  publication-title: J. Assoc. Comput. Mach.
– year: 1977
  ident: BIB4
  article-title: A useful four-valued logic
  publication-title: Modern Uses of Multiple-Valued Logic
– volume: 4
  start-page: 265
  year: 1988
  end-page: 316
  ident: BIB19
  article-title: Multivalued logics: a uniform approach to reasoning in artificial intelligence
  publication-title: Comput. Intelligence
– reference: A. Avron, The structure of interlaced bilattices. Math. Struct. Comput. Sci., forthcoming.
– volume: 5
  start-page: 93
  year: 1988
  end-page: 132
  ident: BIB30
  article-title: Clausal intuitionistic logic II, tableau proof procedures
  publication-title: J. Logic Programming
– start-page: 40
  year: 1990
  end-page: 59
  ident: BIB32
  article-title: Stationary semantics for disjunctive logic programs and deductive databases
  publication-title: Logic Programming, Proc. 1990 North American Conf.
– reference: M.C. Fitting, On prudent bravery and other abstractions, 1994.
– reference: M.A. Khamsi, V. Kreinovich, D. Misane, A new method of proving the existence of answer sets for disjunctive logic programs: a metric fixed point theorem for multi-valued mappings, J. Logic Programming, forthcoming.
– volume: 62
  start-page: 600
  year: 1956
  ident: BIB37
  article-title: Elementary formal systems (abstract)
  publication-title: Bull. Amer. Math. Soc.
– volume: 5
  start-page: 285
  year: 1955
  end-page: 309
  ident: BIB39
  article-title: A lattice-theoretical theorem and its applications
  publication-title: Pacific J. Math.
– reference: K. Doets, From Logic to Logic Programming. MIT Press, Cambridge, MA, 1994.
– volume: 3
  start-page: 37
  year: 1986
  end-page: 53
  ident: BIB40
  article-title: Quantitative deduction and its fixpoint theory
  publication-title: J. Logic Programming
– volume: 38
  start-page: 620
  year: 1991
  end-page: 650
  ident: BIB44
  article-title: The well-founded semantics for general logic programs
  publication-title: J. Appl. Comput. Math.
– reference: D. Miller, A theory of modules for logic programming, IEEE Symp. on Logic Programming, 1986, pp. 106–114.
– volume: 13
  start-page: 445
  year: 1990
  end-page: 463
  ident: BIB33
  article-title: Well-founded semantics coincides with three-valued stable-semantics
  publication-title: Fund. Inform.
– reference: L. Giordano, N. Olivetti, Negation as failure in intuitionistic logic programming, Logic Programming, Proc. Joint Internat. Conf. and Symp. MIT Press, Cambridge, MA, 1992, pp. 430–445.
– volume: 1
  start-page: 797
  year: 1992
  end-page: 810
  ident: BIB14
  article-title: Kleene's logic, generalized
  publication-title: J. Logic Comput.
– volume: 5
  start-page: 1
  year: 1988
  end-page: 31
  ident: BIB29
  article-title: Clausal intuitionistic logic I. fixed point semantics
  publication-title: J. Logic Programming
– reference: S. Blamey, Handbook of Philosophical Logic, Vol. 3, D. Reidel, Dordrecht, 1985, pp. 1–70 (Chapter-Partial Logic).
– reference: E. Shapiro, Logic programs with uncertainties: a tool for implementing rule-based systems, in: A. Bundy (Ed.), Proc. 8th IJCAI, Kaufmann, 1983, pp. 529–532.
– reference: S. Kripke, Outline of a theory of truth, J. Philos. 72 (1975) 690–716. (Reprinted in New Essays on Truth and the Liar Paradox, R. L. Martin (Ed.), Oxford, 1983).
– year: 1950
  ident: BIB22
  publication-title: Introduction to Metamathematics
– year: 1987
  ident: BIB28
  publication-title: Foundations of Logic Programming
– reference: T.C. Przymusinski, Three-valued non-monotonic formalisms and semantics of logic programs, J. Artificial Intelligence (1991).
– volume: 11
  start-page: 91
  year: 1991
  end-page: 116
  ident: BIB13
  article-title: Bilattices and the semantics of logic programming
  publication-title: J. Logic Programming
– volume: 20
  start-page: 113
  year: 1994
  end-page: 131
  ident: BIB16
  article-title: Kleene's three-valued logics and their children
  publication-title: Fund. Inform.
– reference: M. Gelfond, V. Lifschitz, The stable model semantics for logic programming, in: R. Kowalski, K. Bowen (Eds.), Proc. of the 5th Logic Programming Symp., MIT Press, Cambridge, MA, 1988, pp. 1070–1080.
– reference: K.L. Clark, Negation as failure. In Logic and Databases, H. Gallaire and J. Minker, Eds. Plenum, 1978, pp. 55–76.
– start-page: 978
  year: 1988
  end-page: 992
  ident: BIB26
  article-title: Some remarks on the completed database
  publication-title: Logic Programming, Proc. 5th Internat. Conf. Symp.
– start-page: 263
  year: 1989
  end-page: 301
  ident: BIB9
  article-title: The justification of negation as failure
  publication-title: Logic, Methodology and Philosophy of Science VIII
– volume: 7
  start-page: 231
  year: 1989
  end-page: 245
  ident: BIB27
  article-title: Signed data dependencies in logic programming
  publication-title: J. Logic Programming
– volume: 2
  start-page: 295
  year: 1985
  ident: 10.1016/S0304-3975(00)00330-3_BIB10
  article-title: A Kripke/Kleene semantics for logic programs
  publication-title: J. Logic Programming
  doi: 10.1016/S0743-1066(85)80005-4
– ident: 10.1016/S0304-3975(00)00330-3_BIB23
  doi: 10.2307/2024634
– volume: 4
  start-page: 265
  year: 1988
  ident: 10.1016/S0304-3975(00)00330-3_BIB19
  article-title: Multivalued logics: a uniform approach to reasoning in artificial intelligence
  publication-title: Comput. Intelligence
  doi: 10.1111/j.1467-8640.1988.tb00280.x
– volume: 3
  start-page: 37
  year: 1986
  ident: 10.1016/S0304-3975(00)00330-3_BIB40
  article-title: Quantitative deduction and its fixpoint theory
  publication-title: J. Logic Programming
  doi: 10.1016/0743-1066(86)90003-8
– volume: 7
  start-page: 231
  year: 1989
  ident: 10.1016/S0304-3975(00)00330-3_BIB27
  article-title: Signed data dependencies in logic programming
  publication-title: J. Logic Programming
  doi: 10.1016/0743-1066(89)90022-8
– ident: 10.1016/S0304-3975(00)00330-3_BIB1
– volume: 5
  start-page: 1
  year: 1988
  ident: 10.1016/S0304-3975(00)00330-3_BIB29
  article-title: Clausal intuitionistic logic I. fixed point semantics
  publication-title: J. Logic Programming
  doi: 10.1016/0743-1066(88)90005-2
– ident: 10.1016/S0304-3975(00)00330-3_BIB34
  doi: 10.1016/0004-3702(91)90013-A
– ident: 10.1016/S0304-3975(00)00330-3_BIB7
  doi: 10.1007/978-1-4684-3384-5_11
– year: 1977
  ident: 10.1016/S0304-3975(00)00330-3_BIB4
  article-title: A useful four-valued logic
– ident: 10.1016/S0304-3975(00)00330-3_BIB18
– ident: 10.1016/S0304-3975(00)00330-3_BIB35
– ident: 10.1016/S0304-3975(00)00330-3_BIB8
  doi: 10.7551/mitpress/3133.001.0001
– volume: 1
  start-page: 797
  year: 1992
  ident: 10.1016/S0304-3975(00)00330-3_BIB14
  article-title: Kleene's logic, generalized
  publication-title: J. Logic Comput.
  doi: 10.1093/logcom/1.6.797
– start-page: 40
  year: 1990
  ident: 10.1016/S0304-3975(00)00330-3_BIB32
  article-title: Stationary semantics for disjunctive logic programs and deductive databases
– ident: 10.1016/S0304-3975(00)00330-3_BIB21
– ident: 10.1016/S0304-3975(00)00330-3_BIB3
  doi: 10.1017/S0960129500001018
– ident: 10.1016/S0304-3975(00)00330-3_BIB31
  doi: 10.1007/3-540-16492-8_94
– start-page: 978
  year: 1988
  ident: 10.1016/S0304-3975(00)00330-3_BIB26
  article-title: Some remarks on the completed database
– volume: 38
  start-page: 620
  year: 1991
  ident: 10.1016/S0304-3975(00)00330-3_BIB44
  article-title: The well-founded semantics for general logic programs
  publication-title: J. Appl. Comput. Math.
– ident: 10.1016/S0304-3975(00)00330-3_BIB24
  doi: 10.1016/0743-1066(87)90007-0
– ident: 10.1016/S0304-3975(00)00330-3_BIB43
  doi: 10.1145/308386.308444
– volume: 62
  start-page: 601
  year: 1956
  ident: 10.1016/S0304-3975(00)00330-3_BIB38
  article-title: On definability by recursion (abstract)
  publication-title: Bull. Amer. Math. Soc.
– volume: 20
  start-page: 113
  year: 1994
  ident: 10.1016/S0304-3975(00)00330-3_BIB16
  article-title: Kleene's three-valued logics and their children
  publication-title: Fund. Inform.
  doi: 10.3233/FI-1994-201234
– volume: 4
  start-page: 289
  year: 1987
  ident: 10.1016/S0304-3975(00)00330-3_BIB25
  article-title: Negation in logic programming
  publication-title: J. Logic Programming
  doi: 10.1016/0743-1066(87)90007-0
– volume: 29
  start-page: 841
  year: 1982
  ident: 10.1016/S0304-3975(00)00330-3_BIB2
  article-title: Contributions to the theory of logic programming
  publication-title: J. Assoc. Comput. Mach.
  doi: 10.1145/322326.322339
– volume: 11
  start-page: 91
  year: 1991
  ident: 10.1016/S0304-3975(00)00330-3_BIB13
  article-title: Bilattices and the semantics of logic programming
  publication-title: J. Logic Programming
  doi: 10.1016/0743-1066(91)90014-G
– ident: 10.1016/S0304-3975(00)00330-3_BIB42
  doi: 10.1145/73721.73722
– volume: 5
  start-page: 93
  year: 1988
  ident: 10.1016/S0304-3975(00)00330-3_BIB30
  article-title: Clausal intuitionistic logic II, tableau proof procedures
  publication-title: J. Logic Programming
  doi: 10.1016/0743-1066(88)90014-3
– volume: 5
  start-page: 285
  year: 1955
  ident: 10.1016/S0304-3975(00)00330-3_BIB39
  article-title: A lattice-theoretical theorem and its applications
  publication-title: Pacific J. Math.
  doi: 10.2140/pjm.1955.5.285
– ident: 10.1016/S0304-3975(00)00330-3_BIB6
  doi: 10.1007/978-94-009-5203-4_1
– start-page: 263
  year: 1989
  ident: 10.1016/S0304-3975(00)00330-3_BIB9
  article-title: The justification of negation as failure
– volume: 17
  start-page: 197
  year: 1993
  ident: 10.1016/S0304-3975(00)00330-3_BIB15
  article-title: The family of stable models
  publication-title: J. Logic Programming
  doi: 10.1016/0743-1066(93)90031-B
– volume: 13
  start-page: 445
  year: 1990
  ident: 10.1016/S0304-3975(00)00330-3_BIB33
  article-title: Well-founded semantics coincides with three-valued stable-semantics
  publication-title: Fund. Inform.
– ident: 10.1016/S0304-3975(00)00330-3_BIB12
  doi: 10.1109/ISMVL.1990.122627
– volume: 48
  start-page: 229
  year: 1987
  ident: 10.1016/S0304-3975(00)00330-3_BIB11
  article-title: Partial models and logic programming
  publication-title: Theoret. Comput. Sci.
  doi: 10.1016/0304-3975(86)90096-4
– ident: 10.1016/S0304-3975(00)00330-3_BIB17
– ident: 10.1016/S0304-3975(00)00330-3_BIB36
– ident: 10.1016/S0304-3975(00)00330-3_BIB20
– volume: 62
  start-page: 600
  year: 1956
  ident: 10.1016/S0304-3975(00)00330-3_BIB37
  article-title: Elementary formal systems (abstract)
  publication-title: Bull. Amer. Math. Soc.
– year: 1987
  ident: 10.1016/S0304-3975(00)00330-3_BIB28
– volume: 54
  start-page: 25
  issue: 1/2
  year: 1982
  ident: 10.1016/S0304-3975(00)00330-3_BIB5
  article-title: The recursion-theoretic complexity of the semantics of predicate logic as a programming language
  publication-title: Inform. and Control
  doi: 10.1016/S0019-9958(82)91234-7
– volume: 23
  start-page: 733
  year: 1976
  ident: 10.1016/S0304-3975(00)00330-3_BIB41
  article-title: The semantics of predicate logic as a programming language
  publication-title: J. Assoc. Comput. Mach.
  doi: 10.1145/321978.321991
– year: 1950
  ident: 10.1016/S0304-3975(00)00330-3_BIB22
SSID ssj0000576
Score 2.1224937
Snippet The variety of semantical approaches that have been invented for logic programs is quite broad, drawing on classical and many-valued logic, lattice theory,...
SourceID proquest
pascalfrancis
crossref
elsevier
SourceType Aggregation Database
Index Database
Enrichment Source
Publisher
StartPage 25
SubjectTerms Applied sciences
Computer science; control theory; systems
Exact sciences and technology
Programming theory
Theoretical computing
Title Fixpoint semantics for logic programming a survey
URI https://dx.doi.org/10.1016/S0304-3975(00)00330-3
https://www.proquest.com/docview/27140048
Volume 278
WOSCitedRecordID wos000175733600003&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
journalDatabaseRights – providerCode: PRVESC
  databaseName: Elsevier SD Freedom Collection Journals 2021
  customDbUrl:
  eissn: 1879-2294
  dateEnd: 20180131
  omitProxy: false
  ssIdentifier: ssj0000576
  issn: 0304-3975
  databaseCode: AIEXJ
  dateStart: 19950109
  isFulltext: true
  titleUrlDefault: https://www.sciencedirect.com
  providerName: Elsevier
link http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV3Pb9MwFLbQxgGEBIyhlR_DBw6gKsOx88M5IrSKITbtUKTeIie2pUpbWtVt1T-f59hOAgVVHLhEkRXHkt-X915sv-9D6L3kIo1rmUWsimmUCMKjSisZMQUOU0I-koiWMv97fnPDZ7Pi1uvdm1ZOIG8avtsVy_9qamgDY9vS2X8wd_dSaIB7MDpcwexw3Tf8n-PPoDix9qoNYx_qhhCZzHfLxbxZj426hwm2fM320GHrDcPBrfu2iHFsNqut6lbfJ1fTqS92ulZ3W0_eHdYOaHtSL-sXtHz0HfgcZjdKCidmcqGcT-R5EVHqtIiD06Q5H6LDlzB6J5gOwqmjk91z1G7NwHTjQTptVantuiqDwNBHp7Aj_1vQ6o4SxsxmGJb49ZiyjIOTO_58dTn71ofjNHcb1n6kvozrUz_8B0I--qH_lqA8WQoDdtNO72QvdLf5yPQZOu0rNfFth4Hn6IFqTtBT_2uBveM20BTUO0LbCXp83TH2mhcoDmDAHRgwgAG3YMADMGCBHRhO0Y_J5fTL18jLaUR1wpJ1ROOKJNqyF2lIgrOqEiLTccxSzWQGv8FKUUXgUU3SCjI_WcexIoJIRipBdaHZS3TULBp1hrDMtRa8KpTUwqqYiaIQmRXV1LkghcxHKAlzWNaea95KntyV_aFCmPrSTn1JWoJaRko2Qhddt6UjWznUgQcDlf4zcplgCTg71PX8F4P2A3pAjdC7YOESXK7dRxONWmxMSS3JJUS-V4de8Ro96r-6N-hovdqot-hhvV3PzercA_UnS1OZMw
linkProvider Elsevier
openUrl ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=proceeding&rft.title=Theoretical+computer+science&rft.atitle=Fixpoint+semantics+for+logic+programming+a+survey&rft.au=FITTING%2C+Melvin&rft.date=2002-05-06&rft.pub=Elsevier&rft.issn=0304-3975&rft.eissn=1879-2294&rft.volume=278&rft.issue=1-2&rft.spage=25&rft.epage=51&rft_id=info:doi/10.1016%2Fs0304-3975%2800%2900330-3&rft.externalDBID=n%2Fa&rft.externalDocID=13661419
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0304-3975&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0304-3975&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0304-3975&client=summon