Logic programming - Revision history

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	\| url =https://apps.dtic.mil/sti/pdfs/ADA052440.pdf		\| url =https://apps.dtic.mil/sti/pdfs/ADA052440.pdf
	}}		}}
	</ref> Popler,<ref>Davies, J.M., 1971. POPLER: a POP-2 planner. Edinburgh University, Department of Machine Intelligence and Perception.</ref> Conniver,<ref>{{cite tech report \|last1=McDermott \|first1=D.V. \|author-link1=Drew McDermott \|last2=Sussman \|first2=G.J. \|author-link2=Gerald Jay Sussman \|date=May 1972 \|title=The Conniver reference manual \|id=Artificial Intelligence Memo No. 259 \|url=https://www.researchgate.net/publication/37597046_The_Conniver_Reference_Manual}}</ref> QLISP,<ref>{{cite tech report \|last1=Reboh \|first1=R. \|last2=Sacerdoti \|first2=E.D. \|date=August 1973 \|title=A preliminary QLISP manual \|publisher=Artificial Intelligence Center, SRI International \|url=https://www.sri.com/publication/cyber-formal-methods-pubs/preliminary-qlisp-manual/}}</ref> and the concurrent language Ether.<ref>{{cite journal \|last1=Kornfeld \|first1=W.A. \|last2=Hewitt \|first2=C.E. \|author-link2=Carl Hewitt \|date=1981 \|title=The scientific community metaphor \|journal=IEEE Transactions on Systems, Man, and Cybernetics \|volume=11 \|issue=1 \|pages=24–33\|doi=10.1109/TSMC.1981.4308575 \|hdl=1721.1/5693 \|s2cid=1322857 \|hdl-access=free }}</ref>		</ref> Popler,<ref>Davies, J.M., 1971. POPLER: a POP-2 planner. Edinburgh University, Department of Machine Intelligence and Perception.</ref> Conniver,<ref>{{cite tech report \|last1=McDermott \|first1=D.V. \|author-link1=Drew McDermott \|last2=Sussman \|first2=G.J. \|author-link2=Gerald Jay Sussman \|date=May 1972 \|title=The Conniver reference manual \|id=Artificial Intelligence Memo No. 259 \|url=https://www.researchgate.net/publication/37597046_The_Conniver_Reference_Manual}}</ref> QLISP,<ref>{{cite tech report \|last1=Reboh \|first1=R. \|last2=Sacerdoti \|first2=E.D. \|date=August 1973 \|title=A preliminary QLISP manual \|publisher=Artificial Intelligence Center, SRI International \|url=https://www.sri.com/publication/cyber-formal-methods-pubs/preliminary-qlisp-manual/}}</ref> and the concurrent language Ether.<ref>{{cite journal \|last1=Kornfeld \|first1=W.A. \|last2=Hewitt \|first2=C.E. \|author-link2=Carl Hewitt \|date=1981 \|title=The scientific community metaphor \|journal=IEEE Transactions on Systems, Man, and Cybernetics \|volume=11 \|issue=1 \|pages=24–33\|doi=10.1109/TSMC.1981.4308575 \|bibcode=1981ITSMC..11...24K \|hdl=1721.1/5693 \|s2cid=1322857 \|hdl-access=free }}</ref>

	Hayes and Kowalski in Edinburgh tried to reconcile the logic-based declarative approach to knowledge representation with Planner's procedural approach. Hayes (1973) developed an equational language, Golux, in which different procedures could be obtained by altering the behavior of the theorem prover.<ref>{{cite conference\|first=Pat\|last=Hayes\|title=Computation and Deduction\|book-title=Proceedings of the 2nd MFCS Symposium\|publisher=[[Czechoslovak Academy of Sciences]]\|date=1973\|pages=105–118}}</ref>		Hayes and Kowalski in Edinburgh tried to reconcile the logic-based declarative approach to knowledge representation with Planner's procedural approach. Hayes (1973) developed an equational language, Golux, in which different procedures could be obtained by altering the behavior of the theorem prover.<ref>{{cite conference\|first=Pat\|last=Hayes\|title=Computation and Deduction\|book-title=Proceedings of the 2nd MFCS Symposium\|publisher=[[Czechoslovak Academy of Sciences]]\|date=1973\|pages=105–118}}</ref>
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	Relational databases use a relational calculus or relational algebra, with [[Relational database#Relational operations\|relational operations]], such as ''union'', ''intersection'', ''set difference'' and ''cartesian product'' to specify queries, which access a database. Datalog uses logical connectives, such as ''or'', ''and'' and ''not'' in the bodies of rules to define relations as part of the database itself.		Relational databases use a relational calculus or relational algebra, with [[Relational database#Relational operations\|relational operations]], such as ''union'', ''intersection'', ''set difference'' and ''cartesian product'' to specify queries, which access a database. Datalog uses logical connectives, such as ''or'', ''and'' and ''not'' in the bodies of rules to define relations as part of the database itself.

	It was recognized early in the development of relational databases that recursive queries cannot be expressed in either relational algebra or relational calculus, and that this ~~defficiency~~ can be remedied by introducing a least-fixed-point operator.<ref>Aho, A.V. and Ullman, J.D., 1979, January. Universality of data retrieval languages. In Proceedings of the 6th ACM SIGACT-SIGPLAN symposium on Principles of programming languages (pp. 110-119).</ref><ref>Maier, D., Tekle, K.T., Kifer, M. and Warren, D.S., 2018. Datalog: concepts, history, and outlook. In Declarative Logic Programming: Theory, Systems, and Applications (pp. 3-100).</ref> In contrast, recursive relations can be defined naturally by rules in logic programs, without the need for any new logical connectives or operators.		It was recognized early in the development of relational databases that recursive queries cannot be expressed in either relational algebra or relational calculus, and that this deficiency can be remedied by introducing a least-fixed-point operator.<ref>Aho, A.V. and Ullman, J.D., 1979, January. Universality of data retrieval languages. In Proceedings of the 6th ACM SIGACT-SIGPLAN symposium on Principles of programming languages (pp. 110-119).</ref><ref>Maier, D., Tekle, K.T., Kifer, M. and Warren, D.S., 2018. Datalog: concepts, history, and outlook. In Declarative Logic Programming: Theory, Systems, and Applications (pp. 3-100).</ref> In contrast, recursive relations can be defined naturally by rules in logic programs, without the need for any new logical connectives or operators.

	Datalog differs from more general logic programming by having only constants and variables as terms. Moreover, all facts are variable-free, and rules are restricted, so that if they are executed bottom-up, then the derived facts are also variable-free.		Datalog differs from more general logic programming by having only constants and variables as terms. Moreover, all facts are variable-free, and rules are restricted, so that if they are executed bottom-up, then the derived facts are also variable-free.
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	* Ehud Shapiro (Editor). ''Concurrent Prolog''. MIT Press. 1987.		* Ehud Shapiro (Editor). ''Concurrent Prolog''. MIT Press. 1987.
	* James Slagle. [https://dl.acm.org/doi/abs/10.1145/365691.365960 "Experiments with a Deductive Question-Answering Program"]. CACM. December 1965.		* James Slagle. [https://dl.acm.org/doi/abs/10.1145/365691.365960 "Experiments with a Deductive Question-Answering Program"]. CACM. December 1965.
	* [[Dov Gabbay\|Gabbay, Dov M.]]; Hogger, Christopher John; Robinson, J.A., eds. (~~1993-1998~~). [https://www.worldcat.org/oclc/26300491 Handbook of Logic in Artificial Intelligence and Logic Programming].Vols. 1–5, Oxford University Press.		* [[Dov Gabbay\|Gabbay, Dov M.]]; Hogger, Christopher John; Robinson, J.A., eds. (1993–1998). [https://www.worldcat.org/oclc/26300491 Handbook of Logic in Artificial Intelligence and Logic Programming].Vols. 1–5, Oxford University Press.

	==Further reading==		==Further reading==

~2025-31865-54: /* Negation as failure */ Fix inconsistency in rule names

2025-11-07T10:36:08Z

Negation as failure: Fix inconsistency in rule names

← Previous revision		Revision as of 10:36, 7 November 2025
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	This focus on the logical, declarative reading of logic programs was given further impetus by the development of [[constraint logic programming]] in the 1980s and [[Answer set programming\|Answer Set Programming]] in the 1990s. It is also receiving renewed emphasis in recent applications of Prolog<ref name="Prolog Book">{{cite book \|last1=Warren \|first1=D.S. \|editor-last1=Warren \|editor-first1=D.S. \|editor-last2=Dahl \|editor-first2=V. \|editor-last3=Eiter \|editor-first3=T. \|editor-last4=Hermenegildo \|editor-first4=M.V. \|editor-last5=Kowalski \|editor-first5=R. \|editor-last6=Rossi \|editor-first6=F. \|chapter=Introduction to Prolog \|title=Prolog: The Next 50 Years \|series=Lecture Notes in Computer Science() \|date=2023 \|volume=13900 \|publisher=Springer, Cham. \|doi=10.1007/978-3-031-35254-6_1 \|pages=3–19\|isbn=978-3-031-35253-9 }}</ref>		This focus on the logical, declarative reading of logic programs was given further impetus by the development of [[constraint logic programming]] in the 1980s and [[Answer set programming\|Answer Set Programming]] in the 1990s. It is also receiving renewed emphasis in recent applications of Prolog<ref name="Prolog Book">{{cite book \|last1=Warren \|first1=D.S. \|editor-last1=Warren \|editor-first1=D.S. \|editor-last2=Dahl \|editor-first2=V. \|editor-last3=Eiter \|editor-first3=T. \|editor-last4=Hermenegildo \|editor-first4=M.V. \|editor-last5=Kowalski \|editor-first5=R. \|editor-last6=Rossi \|editor-first6=F. \|chapter=Introduction to Prolog \|title=Prolog: The Next 50 Years \|series=Lecture Notes in Computer Science() \|date=2023 \|volume=13900 \|publisher=Springer, Cham. \|doi=10.1007/978-3-031-35254-6_1 \|pages=3–19\|isbn=978-3-031-35253-9 }}</ref>

	The [[Association for Logic Programming]] (ALP) was founded in 1986 to promote Logic Programming. Its official journal until 2000, was ''[[The Journal of Logic Programming]]''. Its founding [[editor-in-chief]] was [[J. Alan Robinson]].<ref>{{cite journal \|first=J. Alan \|last=Robinson \|year=2001 \|title=Invited Editorial \|journal=Theory and Practice of Logic Programming \|volume=1 \|issue=1 \|pages=1 \|publisher=[[Cambridge University Press]] \|doi=10.1017/s1471068400000028~~\|doi-broken-date=1 November 2024~~ \|doi-access=free }}</ref> In 2001, the journal was renamed ''The Journal of Logic and Algebraic Programming'', and the official journal of ALP became ''[[Theory and Practice of Logic Programming]]'', published by [[Cambridge University Press]].		The [[Association for Logic Programming]] (ALP) was founded in 1986 to promote Logic Programming. Its official journal until 2000, was ''[[The Journal of Logic Programming]]''. Its founding [[editor-in-chief]] was [[J. Alan Robinson]].<ref>{{cite journal \|first=J. Alan \|last=Robinson \|year=2001 \|title=Invited Editorial \|journal=Theory and Practice of Logic Programming \|volume=1 \|issue=1 \|pages=1 \|publisher=[[Cambridge University Press]] \|doi=10.1017/s1471068400000028\|doi-access=free }}</ref> In 2001, the journal was renamed ''The Journal of Logic and Algebraic Programming'', and the official journal of ALP became ''[[Theory and Practice of Logic Programming]]'', published by [[Cambridge University Press]].

	==Concepts==		==Concepts==
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	relational expression, which is similar to an expression in first-order predicate logic.		relational expression, which is similar to an expression in first-order predicate logic.

	Other relational programming languages are based on the relational calculus<ref>{{cite journal \|last1=MacLennan \|first1=Bruce James \|editor1-last=Wexelblat \|editor1-first=Richard L. \|editor1-link=Richard Wexelblat \|title=Overview of relational programming \|journal=ACM SIGPLAN Notices \|date=March 1983 \|volume=18 \|issue=3 \|pages=~~36-45~~ \|doi=10.1145/988209.988213 \|url=https://dl.acm.org/doi/10.1145/988209.988213 \|access-date=8 May 2025 \|publisher=Association for Computing Machinery \|location=New York, NY \|issn=0362-1340 \|oclc=25073822\|hdl=10945/29034 \|hdl-access=free \|url-access=subscription }}</ref> or relational algebra.<ref>Behnke, R., Berghammer, R., Meyer, E. and Schneider, P., 1998. RELVIEW—A system for calculating with relations and relational programming. In Fundamental Approaches to Software Engineering: First International Conference, FASE'98 Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS'98 Lisbon, Portugal, March 28–April 4, 1998 Proceedings 1 (pp. 318-321). Springer Berlin Heidelberg.</ref>		Other relational programming languages are based on the relational calculus<ref>{{cite journal \|last1=MacLennan \|first1=Bruce James \|editor1-last=Wexelblat \|editor1-first=Richard L. \|editor1-link=Richard Wexelblat \|title=Overview of relational programming \|journal=ACM SIGPLAN Notices \|date=March 1983 \|volume=18 \|issue=3 \|pages=36–45 \|doi=10.1145/988209.988213 \|url=https://dl.acm.org/doi/10.1145/988209.988213 \|access-date=8 May 2025 \|publisher=Association for Computing Machinery \|location=New York, NY \|issn=0362-1340 \|oclc=25073822\|hdl=10945/29034 \|hdl-access=free \|url-access=subscription }}</ref> or relational algebra.<ref>Behnke, R., Berghammer, R., Meyer, E. and Schneider, P., 1998. RELVIEW—A system for calculating with relations and relational programming. In Fundamental Approaches to Software Engineering: First International Conference, FASE'98 Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS'98 Lisbon, Portugal, March 28–April 4, 1998 Proceedings 1 (pp. 318-321). Springer Berlin Heidelberg.</ref>

	=== Semantics of Horn clause programs ===		=== Semantics of Horn clause programs ===
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	<syntaxhighlight lang="prolog">		<syntaxhighlight lang="prolog">
	~~minor~~(tom).		is_a_minor(tom).

	?- should_receive_sanction(tom, Sanction).		?- should_receive_sanction(tom, Sanction).
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	<syntaxhighlight lang="prolog">		<syntaxhighlight lang="prolog">
	~~violent~~(tom).		is_violent(tom).

	?- should_receive_sanction(tom, Sanction).		?- should_receive_sanction(tom, Sanction).
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	===Constraint logic programming===		===Constraint logic programming===
	{{Main\|Constraint logic programming}}		{{Main\|Constraint logic programming}}

	[[Constraint logic programming]] (CLP) combines Horn clause logic programming with [[constraint solving]]. It extends Horn clauses by allowing some predicates, declared as constraint predicates, to occur as literals in the body of a clause. Constraint predicates are not defined by the facts and rules in the program, but are predefined by some domain-specific model-theoretic structure or theory.		[[Constraint logic programming]] (CLP) combines Horn clause logic programming with [[constraint solving]]. It extends Horn clauses by allowing some predicates, declared as constraint predicates, to occur as literals in the body of a clause. Constraint predicates are not defined by the facts and rules in the program, but are predefined by some domain-specific model-theoretic structure or theory.

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	=== Datalog ===		=== Datalog ===
	{{Main\|Datalog}}		{{Main\|Datalog}}

	Datalog is a database definition language, which combines a relational view of data, as in [[relational database]]s, with a logical view, as in logic programming.		Datalog is a database definition language, which combines a relational view of data, as in [[relational database]]s, with a logical view, as in logic programming.

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	===Abductive logic programming===		===Abductive logic programming===
	{{Main\|Abductive logic programming}}		{{Main\|Abductive logic programming}}

	[[Abductive logic programming]]<ref>{{cite journal \|first1=M. \|last1=Denecker \|first2=A.C. \|last2=Kakas \|title=Special issue: abductive logic programming \|journal=Journal of Logic Programming \|volume=44 \|issue=1–3 \|pages=1–4 \|date=July 2000 \|doi=10.1016/S0743-1066(99)00078-3 \|doi-access=free }}</ref> (ALP), like CLP, extends normal logic programming by allowing the bodies of clauses to contain literals whose predicates are not defined by clauses. In ALP, these predicates are declared as ''abducible'' (or ''assumable''), and are used as in [[Abductive reasoning#Formalizations of abduction#Logic-based abduction\|abductive reasoning]] to explain observations, or more generally to add new facts to the program (as assumptions) to solve goals.		[[Abductive logic programming]]<ref>{{cite journal \|first1=M. \|last1=Denecker \|first2=A.C. \|last2=Kakas \|title=Special issue: abductive logic programming \|journal=Journal of Logic Programming \|volume=44 \|issue=1–3 \|pages=1–4 \|date=July 2000 \|doi=10.1016/S0743-1066(99)00078-3 \|doi-access=free }}</ref> (ALP), like CLP, extends normal logic programming by allowing the bodies of clauses to contain literals whose predicates are not defined by clauses. In ALP, these predicates are declared as ''abducible'' (or ''assumable''), and are used as in [[Abductive reasoning#Formalizations of abduction#Logic-based abduction\|abductive reasoning]] to explain observations, or more generally to add new facts to the program (as assumptions) to solve goals.

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	===Concurrent logic programming===		===Concurrent logic programming===
	{{Main\|Concurrent logic programming}}		{{Main\|Concurrent logic programming}}

	Concurrent logic programming integrates concepts of logic programming with [[concurrent programming]]. Its development was given a big impetus in the 1980s by its choice for the systems programming language of the [[Fifth generation computer\|Japanese Fifth Generation Project (FGCS)]].<ref>Shunichi Uchida and Kazuhiro Fuchi. ''Proceedings of the FGCS Project Evaluation Workshop''. Institute for New Generation Computer Technology (ICOT). 1992.</ref>		Concurrent logic programming integrates concepts of logic programming with [[concurrent programming]]. Its development was given a big impetus in the 1980s by its choice for the systems programming language of the [[Fifth generation computer\|Japanese Fifth Generation Project (FGCS)]].<ref>Shunichi Uchida and Kazuhiro Fuchi. ''Proceedings of the FGCS Project Evaluation Workshop''. Institute for New Generation Computer Technology (ICOT). 1992.</ref>

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	relational expression, which is similar to an expression in first-order predicate logic.		relational expression, which is similar to an expression in first-order predicate logic.

	Other relational programming languages are based on the relational calculus<ref>{{cite journal \|last1=MacLennan \|first1=Bruce James \|editor1-last=Wexelblat \|editor1-first=Richard L. \|editor1-link=Richard Wexelblat \|title=Overview of relational programming \|journal=ACM SIGPLAN Notices \|date=March 1983 \|volume=18 \|issue=3 \|pages=36-45 \|doi=10.1145/988209.988213 \|url=https://dl.acm.org/doi/10.1145/988209.988213 \|access-date=8 May 2025 \|publisher=Association for Computing Machinery \|location=New York, NY \|issn=0362-1340 \|oclc=25073822\|hdl=10945/29034 \|hdl-access=free }}</ref> or relational algebra.<ref>Behnke, R., Berghammer, R., Meyer, E. and Schneider, P., 1998. RELVIEW—A system for calculating with relations and relational programming. In Fundamental Approaches to Software Engineering: First International Conference, FASE'98 Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS'98 Lisbon, Portugal, March 28–April 4, 1998 Proceedings 1 (pp. 318-321). Springer Berlin Heidelberg.</ref>		Other relational programming languages are based on the relational calculus<ref>{{cite journal \|last1=MacLennan \|first1=Bruce James \|editor1-last=Wexelblat \|editor1-first=Richard L. \|editor1-link=Richard Wexelblat \|title=Overview of relational programming \|journal=ACM SIGPLAN Notices \|date=March 1983 \|volume=18 \|issue=3 \|pages=36-45 \|doi=10.1145/988209.988213 \|url=https://dl.acm.org/doi/10.1145/988209.988213 \|access-date=8 May 2025 \|publisher=Association for Computing Machinery \|location=New York, NY \|issn=0362-1340 \|oclc=25073822\|hdl=10945/29034 \|hdl-access=free \|url-access=subscription }}</ref> or relational algebra.<ref>Behnke, R., Berghammer, R., Meyer, E. and Schneider, P., 1998. RELVIEW—A system for calculating with relations and relational programming. In Fundamental Approaches to Software Engineering: First International Conference, FASE'98 Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS'98 Lisbon, Portugal, March 28–April 4, 1998 Proceedings 1 (pp. 318-321). Springer Berlin Heidelberg.</ref>

	=== Semantics of Horn clause programs ===		=== Semantics of Horn clause programs ===

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