Answer set programming: Difference between revisions

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{{Short description|Programming paradigm focused on difficult search problems}}

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'''Answer set programming''' ('''ASP''') is a form of [[declarative programming]] oriented towards difficult (primarily [[NP-hard]]) [[search algorithm|search problems]]. It is based on the [[stable model semantics|stable model]] (answer set) semantics of [[logic programming]]. In ASP, search problems are reduced to computing stable models, and ''answer set solvers''—programs for generating stable models—are used to perform search. The computational process employed in the design of many answer set solvers is an enhancement of the [[DPLL algorithm]] and, in principle, it always terminates (unlike [[Prolog]] query evaluation, which may lead to an [[infinite loop]]).

In a more general sense, ASP includes all applications of answer sets to [[knowledge representation and reasoning]]<ref>{{cite book |first=Chitta |last=Baral |title=Knowledge Representation, Reasoning and Declarative Problem Solving |url=https://archive.org/details/knowledgereprese00bara |url-access=registration |year=2003 |publisher=Cambridge University Press |isbn=978-0-521-81802-5}}</ref><ref>{{cite book |first=Michael |last=Gelfond |chapter=Answer sets |editor1-first=Frank |editor1-last=van Harmelen |editor2-first=Vladimir |editor2-last=Lifschitz |editor3-first=Bruce |editor3-last=Porter |title=Handbook of Knowledge Representation |chapter-url=https://books.google.com/books?id=xwBDylHhJhYC&pg=PA285 |year=2008 |publisher=Elsevier |isbn=978-0-08-055702-1 |pages=285–316 }} [http://www.depts.ttu.edu/cs/research/krlab/pdfs/papers/gel07b.pdf as PDF] {{Webarchive|url=https://web.archive.org/web/20160303231241/http://www.depts.ttu.edu/cs/research/krlab/pdfs/papers/gel07b.pdf |date=2016-03-03 }}</ref> and the use of Prolog-style query evaluation for solving problems arising in these applications.

==History==

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==Answer set programming language AnsProlog==

[http://www.tcs.hut.fi/Software/smodels/lparse.ps Lparse] is the name of the program that was originally created as a [[Symbol grounding|grounding]] tool (front-end) for the answer set solver [http://www.tcs.hut.fi/Software/smodels/ smodels]. The language that Lparse accepts is now commonly called AnsProlog,<ref>{{Cite thesis |type=Ph.D. |title=Superoptimisation: Provably Optimal Code Generation using Answer Set Programming |url=http://opus.bath.ac.uk/20352/1/UnivBath_PhD_2009_T_Crick.pdf |last=Crick |first=Tom |year=2009 |publisher=University of Bath |docket=20352 |access-date=2011-05-27 |archive-url=https://web.archive.org/web/20160304035502/http://opus.bath.ac.uk/20352/1/UnivBath_PhD_2009_T_Crick.pdf |archive-date=2016-03-04 |url-status=dead }}</ref> short for ''Answer Set Programming in Logic''.<ref>{{cite web |author=Rogelio Davila |title=AnsProlog, an overview |url=http://www.rogeliodavila.com.mx/Programacion%20Logica/PL%20Notas/AnsProlog%20Overview.ppt |format=PowerPoint}}</ref> It is now used in the same way in many other answer set solvers, including [https://web.archive.org/web/20110717180541/http://assat.cs.ust.hk/ assat], [httphttps://wwwpotassco.cs.uni-potsdam.deorg/clasp/ clasp], [http://www.cs.utexas.edu/users/tag/cmodels/ cmodels], [http://www.tcs.hut.fi/Software/gnt/ gNt], [http://www.cs.uni-potsdam.de/nomore/ nomore++] and [http://www.cs.uky.edu/ai/pbmodels/ pbmodels]. ([http://www.dbai.tuwien.ac.at/proj/dlv/ dlv] is an exception; the syntax of ASP programs written for dlv is somewhat different.)

An AnsProlog program consists of rules of the form

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<syntaxhighlight lang="prolog">

p(a). p(b). p(c).

{q(a), q(b), q(c)}2.

</syntaxhighlight>

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(start..end)

</syntaxhighlight>

where start and end are constant -valued arithmetic expressions. A range is a notational shortcut that is mainly used to define numerical domains in a compatible way. For example, the fact

<syntaxhighlight lang="prolog">

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</syntaxhighlight>

If the extension of <code>q</code> is <code>{q(a1), q(a2), ... , q(aN)}</code>, the above condition is semantically equivalent to writing <code>{p(a1), p(a2), ... , p(aN)}</code> in the place of the condition. For example,

<syntaxhighlight lang="prolog">

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and run smodels on it, with the numeric value of <math>n</math> specified on the command line, then the atoms of the form <math>\mathrm{color}(\dots,\dots)</math> in the output of smodels will represent an <math>n</math>-coloring of <math>G</math>.

The program in this example illustrates the "generate-and-test" organization that is often found in simple ASP programs. The choice rule describes a set of "potential solutions" — a—a simple superset of the set of solutions to the given search problem. It is followed by a constraint, which eliminates all potential solutions that are not acceptable. However, the search process employed by smodels and other answer set solvers is not based on [[trial and error]].

===Large clique===

A [[Clique (graph theory)|clique]] in a graph is a set of pairwise adjacent vertices. The following Lparse program finds a clique of size <math>\geq n</math> in a given directed graph, or determines that it does not exist:

<syntaxhighlight lang="prolog" line="1">

n {in(X) : v(X)}.

:- in(X), in(Y), v(X), v(Y), X!=Y, not e(X,Y), not e(Y,X).

</syntaxhighlight>

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==Comparison of implementations==

Early systems, such as Smodelssmodels, used [[backtracking]] to find solutions. As the theory and practice of [[Boolean SAT solver]]s evolved, a number of ASP solvers were built on top of SAT solvers, including ASSAT and Cmodels. These converted ASP formula into SAT propositions, applied the SAT solver, and then converted the solutions back to ASP form. More recent systems, such as Clasp, use a hybrid approach, using conflict-driven algorithms inspired by SAT, without fullfully converting into a Boolean-logic form. These approaches allow for significant improvements of performance, often by an order of magnitude, over earlier backtracking algorithms.

The [https://potassco.org/ Potassco] project acts as an umbrella for many of the systems below, including ''clasp'', grounding systems (''gringo''), incremental systems (''iclingo''), constraint solvers (''clingcon''), [[action language]] to ASP compilers (''coala''), distributed MPI[[Message Passing Interface]] implementations (''claspar''), and many others.

Most systems support variables, but only indirectly, by forcing grounding, by using a grounding system such as ''Lparse'' or ''gringo'' as a front end. The need for grounding can cause a combinatorial explosion of clauses; thus, systems that perform on-the-fly grounding might have an advantage.<ref>{{Cite journal|last1=Lefèvre|first1=Claire|last2=Béatrix|first2=Christopher|last3=Stéphan|first3=Igor|last4=Garcia|first4=Laurent|date=May 2017|title=ASPeRiX, a first-order forward chaining approach for answer set computing*|url=https://www.cambridge.org/core/journals/theory-and-practice-of-logic-programming/article/abs/asperix-a-firstorder-forward-chaining-approach-for-answer-set-computing/2318F5D6647DF24A8F9A452F4C7B4D49|journal=Theory and Practice of Logic Programming|language=en|volume=17|issue=3|pages=266–310|doi=10.1017/S1471068416000569|arxiv=1503.07717 |s2cid=2371655 |issn=1471-0684}}</ref>

Query-driven implementations of answer set programming, such as the Galliwasp system<ref>

{{cite book |first1=Kyle. |last1=Marple |first2=Gopal. |last2=Gupta |chapter=Galliwasp: A Goal-Directed Answer Set Solver |editor-first=Elvira|editor-last=Albert |title=Logic-Based Program Synthesis and Transformation, 22nd International Symposium, LOPSTR 2012, Leuven, Belgium, September 18-20, 2012, Revised Selected Papers |year=2012 |publisher=Springer |pages=122–136}}</ref> and s(CASP)<ref>{{cite journal |first1=J. |last1=Arias |first2=M. |last2=Carro |first3=E. |last3=Salazar |first4=K. |last4=Marple |first5=G. |last5=Gupta |title=Constraint Answer Set Programming without Grounding |journal=Theory and Practice of Logic Programming |volume=18 |issue=3–4 |pages=337–354 |date=2018|doi=10.1017/S1471068418000285 |s2cid=13754645 |doi-access=free |arxiv=1804.11162 }}</ref> avoid grounding altogether by using a combination of [[resolution (logic)|resolution]] and [[coinduction]].

{| class="wikitable"

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|{{rh}}|[http://www.info.univ-angers.fr/pub/claire/asperix/ ASPeRiX] {{Webarchive|url=https://web.archive.org/web/20161108121331/http://www.info.univ-angers.fr/pub/claire/asperix/ |date=2016-11-08 }}

|[[Linux]]

|[[GPL]]

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|{{rh}}|[http://www.nku.edu/~wardj1/Research/smodels_cc.html Smodels-cc] {{Webarchive|url=https://web.archive.org/web/20151115171208/http://www.nku.edu/~wardj1/Research/smodels_cc.html |date=2015-11-15 }}

|[[Linux]]

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*[http://www.kr.tuwien.ac.at/staff/tkren/deb.html A variety of answer set solvers packaged for Debian / Ubuntu]

*[http://www.cs.uni-potsdam.de/clasp/ Clasp Answer Set Solver]

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{{DEFAULTSORT:Answer Set Programming}}