description logic

A description logic (DL) models concepts, roles and individuals, and their relationships.

The fundamental modeling concept of a DL is the axiom—a logical statement relating roles and/or concepts.{{Cite journal | last1 = Grau | first1 = B. C. | last2 = Horrocks | first2 = I. | author-link2 = Ian Horrocks| last3 = Motik | first3 = B. | last4 = Parsia | first4 = B. | last5 = Patel-Schneider | first5 = P. F. | last6 = Sattler | first6 = U. | author-link6 = Ulrike Sattler| doi = 10.1016/j.websem.2008.05.001 | title = OWL 2: The next step for OWL | journal = Web Semantics: Science, Services and Agents on the World Wide Web | volume = 6 | issue = 4 | pages = 309–322 | year = 2008 | url = http://www.cs.ox.ac.uk/boris.motik/pubs/ghmppss08next-steps.pdf}} This is a key difference from the frames paradigm where a frame specification declares and completely defines a class.

The description logic community uses different terminology than the first-order logic (FOL) community for operationally equivalent notions; some examples are given below. The Web Ontology Language (OWL) uses again a different terminology, also given in the table below.

There are many varieties of description logics and there is an informal naming convention, roughly describing the operators allowed. The expressivity is encoded in the label for a logic starting with one of the following basic logics:

Followed by any of the following extensions:

Some canonical DLs that do not exactly fit this convention are:

As an example, $\backslash mathcal\{ALC\}$ is a centrally important description logic from which comparisons with other varieties can be made. $\backslash mathcal\{ALC\}$ is simply $\backslash mathcal\{AL\}$ with complement of any concept allowed, not just atomic concepts. $\backslash mathcal\{ALC\}$ is used instead of the equivalent $\backslash mathcal\{ALUE\}$.

A further example, the description logic $\backslash mathcal\{SHIQ\}$ is the logic $\backslash mathcal\{ALC\}$ plus extended cardinality restrictions, and transitive and inverse roles. The naming conventions aren't purely systematic so that the logic $\backslash mathcal\{ALCOIN\}$ might be referred to as $\backslash mathcal\{ALCNIO\}$ and other abbreviations are also made where possible.

The Protégé ontology editor supports $\backslash mathcal\{SHOIN\}^\backslash mathcal\{(D)\}$. Three major biomedical informatics terminology bases, SNOMED CT, GALEN, and GO, are expressible in $\backslash mathcal\{EL\}$ (with additional role properties).

OWL 2 provides the expressiveness of $\backslash mathcal\{SROIQ\}^\backslash mathcal\{(D)\}$, OWL-DL is based on $\backslash mathcal\{SHOIN\}^\backslash mathcal\{(D)\}$, and for OWL-Lite it is $\backslash mathcal\{SHIF\}^\backslash mathcal\{(D)\}$.

Description logic was given its current name in the 1980s. Previous to this it was called (chronologically): terminological systems, and concept languages.

Frames and semantic networks lack formal (logic-based) semantics.Franz Baader, Ian Horrocks, and Ulrike Sattler Chapter 3 Description Logics. In Frank van Harmelen, Vladimir Lifschitz, and Bruce Porter, editors, Handbook of Knowledge Representation. Elsevier, 2007. DL was first introduced into knowledge representation (KR) systems to overcome this deficiency.

The first DL-based KR system was KL-ONE (by Ronald J. Brachman and Schmolze, 1985). During the '80s other DL-based systems using structural subsumption algorithms were developed including KRYPTON (1983), LOOM (1987), BACK (1988), K-REP (1991) and CLASSIC (1991). This approach featured DL with limited expressiveness but relatively efficient (polynomial time) reasoning.

In the early '90s, the introduction of a new tableau based algorithm paradigm allowed efficient reasoning on more expressive DL. DL-based systems using these algorithms — such as KRIS (1991) — show acceptable reasoning performance on typical inference problems even though the worst case complexity is no longer polynomial.

From the mid '90s, reasoners were created with good practical performance on very expressive DL with high worst case complexity. Examples from this period include FaCT,{{Cite book | last1 = Tsarkov | first1 = D. | last2 = Horrocks | first2 = I. | chapter = FaCT++ Description Logic Reasoner: System Description | doi = 10.1007/11814771_26 | chapter-url = http://www.cs.ox.ac.uk/ian.horrocks/Publications/download/2006/TsHo06a.pdf| title = Automated Reasoning | series = Lecture Notes in Computer Science | volume = 4130 | pages = 292–297 | year = 2006 | isbn = 978-3-540-37187-8 | citeseerx = 10.1.1.65.2672 }} RACER (2001), CEL (2005), and KAON 2 (2005).

DL reasoners, such as FaCT, FaCT++, RACER, DLP and Pellet,{{Cite journal | last1 = Sirin | first1 = E. | last2 = Parsia | first2 = B. | last3 = Grau | first3 = B. C. | last4 = Kalyanpur | first4 = A. | last5 = Katz | first5 = Y. | title = Pellet: A practical OWL-DL reasoner | url = http://pellet.owldl.com/papers/sirin05pellet.pdf | doi = 10.1016/j.websem.2007.03.004 | journal = Web Semantics: Science, Services and Agents on the World Wide Web | volume = 5 | issue = 2 | pages = 51–53 | year = 2007 | s2cid = 101226 | url-status = dead | archive-url = https://web.archive.org/web/20070627202215/http://pellet.owldl.com/papers/sirin05pellet.pdf | archive-date = 2007-06-27 }} implement the method of analytic tableaux. KAON2 is implemented by algorithms which reduce a SHIQ(D) knowledge base to a disjunctive datalog program.

The DARPA Agent Markup Language (DAML) and Ontology Inference Layer (OIL) ontology languages for the Semantic Web can be viewed as

syntactic variants of DL.Ian Horrocks and Ulrike Sattler Ontology Reasoning in the SHOQ(D) Description Logic, in Proceedings of the Seventeenth International Joint Conference on Artificial Intelligence, 2001. In particular, the formal semantics and reasoning in OIL use the $\backslash mathcal\{SHIQ\}$ DL.{{Cite journal | last1 = Fensel | first1 = D. | last2 = Van Harmelen | first2 = F. | last3 = Horrocks | first3 = I. | last4 = McGuinness | first4 = D. L. | last5 = Patel-Schneider | first5 = P. F. | title = OIL: An ontology infrastructure for the Semantic Web | doi = 10.1109/5254.920598 | journal = IEEE Intelligent Systems | volume = 16 | issue = 2 | pages = 38–45 | year = 2001 | citeseerx = 10.1.1.307.9456 }} The DAML+OIL DL was developed as a submission toIan Horrocks and Peter F. Patel-Schneider The Generation of DAML+OIL. In Proceedings of the 2001 Description Logic Workshop (DL 2001), volume 49 of CEUR , pages 30–35, 2001.—and formed the starting point of—the World Wide Web Consortium (W3C) Web Ontology Working Group.Web Ontology Working Group Charter, 2003 In 2004, the Web Ontology Working Group completed its work by issuing the OWLW3C Press Release, 2004 recommendation. The design of OWL is based on the $\backslash mathcal\{SH\}$ family of DL{{Cite journal | last1 = Horrocks | first1 = I. | author-link1 = Ian Horrocks| last2 = Patel-Schneider | first2 = Peter| last3 = van Harmelen | first3 = Frank| author-link3 = Frank van Harmelen| doi = 10.1016/j.websem.2003.07.001 | url = http://www.comlab.ox.ac.uk/people/ian.horrocks/Publications/download/2003/HoPH03a.pdf| title = From SHIQ and RDF to OWL: The making of a Web Ontology Language | journal = Web Semantics: Science, Services and Agents on the World Wide Web | volume = 1 | pages = 7–26 | year = 2003 | citeseerx = 10.1.1.2.7039 | s2cid = 8277015 }} with OWL DL and OWL Lite based on $\backslash mathcal\{SHOIN\}^\backslash mathcal\{(D)\}$ and $\backslash mathcal\{SHIF\}^\backslash mathcal\{(D)\}$ respectively.

The W3C OWL Working Group began work in 2007 on a refinement of - and extension to - OWL.OWL Working Group Charter, 2007 In 2009, this was completed by the issuance of the OWL2 recommendation.{{cite web |url=http://www.w3.org/TR/2009/REC-owl2-primer-20091027/ |title=OWL 2 Web Ontology Language Primer

|last1=Hitzler |first1=Pascal | author-link1=Pascal Hitzler

|last2=Krötzsch |first2=Markus | author-link2=Markus Krötzsch

|last3=Parsia |first3=Bijan | author-link3=Bijan Parsia

|last4=Patel-Schneider |first4=Peter F. | author-link4=Peter F. Patel-Schneider

|last5=Rudolph |first5=Sebastian | author-link5=Sebastian Rudolph

|date=27 October 2009 |work=OWL 2 Web Ontology Language |publisher=World Wide Wed Consortium |access-date=2010-12-14}} OWL2 is based on the description logic $\backslash mathcal\{SROIQ\}^\backslash mathcal\{(D)\}$.{{cite book |title=Foundations of Semantic Web Technologies |author1=Pascal Hitzler | author-link1=Pascal Hitzler|author2=Markus Krötzsch |author3=Sebastian Rudolph |publisher=CRCPress |date=August 25, 2009 |isbn=978-1-4200-9050-5 |url=http://www.semantic-web-book.org}} Practical experience demonstrated that OWL DL lacked several key features necessary to model complex domains.

In DL, a distinction is drawn between the so-called TBox (terminological box) and the ABox (assertional box). In general, the TBox contains sentences describing concept hierarchies (i.e., relations between concepts) while the ABox contains ground sentences stating where in the hierarchy, individuals belong (i.e., relations between individuals and concepts). For example, the statement:

{{NumBlk|:|Every employee is a person|{{EquationRef|1}}}}

belongs in the TBox, while the statement:

{{NumBlk|:|Bob is an employee|{{EquationRef|2}}}}

belongs in the ABox.

Note that the TBox/ABox distinction is not significant, in the same sense that the two "kinds" of sentences are not treated differently in first-order logic (which subsumes most DL). When translated into first-order logic, a subsumption axiom like ({{EquationNote|1}}) is simply a conditional restriction to unary predicates (concepts) with only variables appearing in it. Clearly, a sentence of this form is not privileged or special over sentences in which only constants ("grounded" values) appear like ({{EquationNote|2}}).

So why was the distinction introduced? The primary reason is that the separation can be useful when describing and formulating decision-procedures for various DL. For example, a reasoner might process the TBox and ABox separately, in part because certain key inference problems are tied to one but not the other one ('classification' is related to the TBox, 'instance checking' to the ABox). Another example is that the complexity of the TBox can greatly affect the performance of a given decision-procedure for a certain DL, independently of the ABox. Thus, it is useful to have a way to talk about that specific part of the knowledge base.

The secondary reason is that the distinction can make sense from the knowledge base modeler's perspective. It is plausible to distinguish between our conception of terms/concepts in the world (class axioms in the TBox) and particular manifestations of those terms/concepts (instance assertions in the ABox). In the above example: when the hierarchy within a company is the same in every branch but the assignment to employees is different in every department (because there are other people working there), it makes sense to reuse the TBox for different branches that do not use the same ABox.

There are two features of description logic that are not shared by most other data description formalisms: DL does not make the unique name assumption (UNA) or the closed-world assumption (CWA). Not having UNA means that two concepts with different names may be allowed by some inference to be shown to be equivalent. Not having CWA, or rather having the open world assumption (OWA) means that lack of knowledge of a fact does not immediately imply knowledge of the negation of a fact.

Like first-order logic (FOL), a syntax defines which collections of symbols are legal expressions in a description logic, and semantics determine meaning. Unlike FOL, a DL may have several well known syntactic variants.

The syntax of a member of the description logic family is characterized by its recursive definition, in which the constructors that can be used to form concept terms are stated. Some constructors are related to logical constructors in first-order logic (FOL) such as intersection or conjunction of concepts, union or disjunction of concepts, negation or complement of concepts, universal restriction and existential restriction. Other constructors have no corresponding construction in FOL including restrictions on roles for example, inverse, transitivity and functionality.

Let C and D be concepts, a and b be individuals, and R be a role.

If a is R-related to b, then b is called an R-successor of a.

The prototypical DL Attributive Concept Language with Complements ($\backslash mathcal\{ALC\}$) was introduced by Manfred Schmidt-Schauß and Gert Smolka in 1991, and is the basis of many more expressive DLs. The following definitions follow the treatment in Baader et al.

Let $N\_C$, $N\_R$ and $N\_O$ be (respectively) sets of concept names (also known as atomic concepts), role names and individual names (also known as individuals, nominals or objects). Then the ordered triple ($N\_C$, $N\_R$, $N\_O$) is the signature.

The set of $\backslash mathcal\{ALC\}$ concepts is the smallest set such that:

• The following are concepts:
• $\backslash top$ (top is a concept)
• $\backslash bot$ (bottom is a concept)
• Every $A\; \backslash in\; N\_C$ (all atomic concepts are concepts)
• If $C$ and $D$ are concepts and $R\; \backslash in\; N\_R$ then the following are concepts:
• $C\backslash sqcap\; D$ (the intersection of two concepts is a concept)
• $C\backslash sqcup\; D$ (the union of two concepts is a concept)
• $\backslash neg\; C$ (the complement of a concept is a concept)
• $\backslash forall\; R.C$ (the universal restriction of a concept by a role is a concept)
• $\backslash exists\; R.C$ (the existential restriction of a concept by a role is a concept)

A general concept inclusion (GCI) has the form $C\; \backslash sqsubseteq\; D$ where $C$ and $D$ are concepts. Write $C\; \backslash equiv\; D$ when $C\; \backslash sqsubseteq\; D$ and $D\; \backslash sqsubseteq\; C$. A TBox is any finite set of GCIs.

{{Anchor|concept_assertion}}

• A concept assertion is a statement of the form $a\; :\; C$ where $a\; \backslash in\; N\_O$ and C is a concept.
• A role assertion is a statement of the form $(a,b)\; :\; R$ where $a,\; b\; \backslash in\; N\_O$ and R is a role.

An ABox is a finite set of assertional axioms.

A knowledge base (KB) is an ordered pair $(\backslash mathcal\{T\},\; \backslash mathcal\{A\})$ for TBox $\backslash mathcal\{T\}$ and ABox $\backslash mathcal\{A\}$.

The semantics of description logics are defined by interpreting concepts as sets of individuals and roles as sets of ordered pairs of individuals. Those individuals are typically assumed from a given domain. The semantics of non-atomic concepts and roles is then defined in terms of atomic concepts and roles. This is done by using a recursive definition similar to the syntax.

The following definitions follow the treatment in Baader et al.

A terminological interpretation $\backslash mathcal\{I\}=(\backslash Delta^\{\backslash mathcal\{I\}\},\; \backslash cdot^\{\backslash mathcal\{I\}\})$ over a signature $(N\_C,N\_R,N\_O)$ consists of

• a non-empty set $\backslash Delta^\{\backslash mathcal\{I\}\}$ called the domain
• a interpretation function $\backslash cdot^\{\backslash mathcal\{I\}\}$ that maps:
• every individual $a$ to an element $a^\{\backslash mathcal\{I\}\}\; \backslash in\; \backslash Delta^\{\backslash mathcal\{I\}\}$
• every concept to a subset of $\backslash Delta^\{\backslash mathcal\{I\}\}$
• every role name to a subset of $\backslash Delta^\{\backslash mathcal\{I\}\}\; \backslash times\; \backslash Delta^\{\backslash mathcal\{I\}\}$

such that

• $\backslash top^\{\backslash mathcal\{I\}\}\; =\; \backslash Delta^\{\backslash mathcal\{I\}\}$
• $\backslash bot^\{\backslash mathcal\{I\}\}\; =\; \backslash emptyset$
• $(C\; \backslash sqcup\; D)^\{\backslash mathcal\{I\}\}\; =\; C^\{\backslash mathcal\{I\}\}\; \backslash cup\; D^\{\backslash mathcal\{I\}\}$ (union means disjunction)
• $(C\; \backslash sqcap\; D)^\{\backslash mathcal\{I\}\}\; =\; C^\{\backslash mathcal\{I\}\}\; \backslash cap\; D^\{\backslash mathcal\{I\}\}$ (intersection means conjunction)
• $(\backslash neg\; C)^\{\backslash mathcal\{I\}\}\; =\; \backslash Delta^\{\backslash mathcal\{I\}\}\; \backslash setminus\; C^\{\backslash mathcal\{I\}\}$ (complement means negation)
• $(\backslash forall\; R.C)^\{\backslash mathcal\{I\}\}\; =\; \backslash \{x\; \backslash in\; \backslash Delta^\{\backslash mathcal\{I\}\}\; |\; \backslash text\{for\}\; \backslash ;\; \backslash text\{every\}\; \backslash ;\; y,\; (x,y)\; \backslash in\; R^\{\backslash mathcal\{I\}\}\; \backslash ;\; \backslash text\{implies\}\; \backslash ;\; y\; \backslash in\; C^\{\backslash mathcal\{I\}\}\; \backslash \}$
• $(\backslash exists\; R.C)^\{\backslash mathcal\{I\}\}\; =\; \backslash \{x\; \backslash in\; \backslash Delta^\{\backslash mathcal\{I\}\}\; |\; \backslash text\{there\}\; \backslash ;\; \backslash text\{exists\}\; \backslash ;\; y,\; (x,y)\; \backslash in\; R^\{\backslash mathcal\{I\}\}\; \backslash ;\; \backslash text\{and\}\; \backslash ;\; y\; \backslash in\; C^\{\backslash mathcal\{I\}\}\backslash \}$

Define $\backslash mathcal\{I\}\; \backslash models$ (read in I holds) as follows

• $\backslash mathcal\{I\}\; \backslash models\; C\; \backslash sqsubseteq\; D$ if and only if $C^\{\backslash mathcal\{I\}\}\; \backslash subseteq\; D^\{\backslash mathcal\{I\}\}$
• $\backslash mathcal\{I\}\; \backslash models\; \backslash mathcal\{T\}$ if and only if $\backslash mathcal\{I\}\; \backslash models\; \backslash Phi$ for every $\backslash Phi\; \backslash in\; \backslash mathcal\{T\}$

• $\backslash mathcal\{I\}\; \backslash models\; a\; :\; C$ if and only if $a^\{\backslash mathcal\{I\}\}\; \backslash in\; C^\{\backslash mathcal\{I\}\}$
• $\backslash mathcal\{I\}\; \backslash models\; (a,b)\; :\; R$ if and only if $(a^\{\backslash mathcal\{I\}\},b^\{\backslash mathcal\{I\}\})\; \backslash in\; R^\{\backslash mathcal\{I\}\}$
• $\backslash mathcal\{I\}\; \backslash models\; \backslash mathcal\{A\}$ if and only if $\backslash mathcal\{I\}\; \backslash models\; \backslash phi$ for every $\backslash phi\; \backslash in\; \backslash mathcal\{A\}$

Let $\backslash mathcal\{K\}\; =\; (\backslash mathcal\{T\},\; \backslash mathcal\{A\})$ be a knowledge base.

• $\backslash mathcal\{I\}\; \backslash models\; \backslash mathcal\{K\}$ if and only if $\backslash mathcal\{I\}\; \backslash models\; \backslash mathcal\{T\}$ and $\backslash mathcal\{I\}\; \backslash models\; \backslash mathcal\{A\}$

In addition to the ability to describe concepts formally, one also would like to employ the description of a set of concepts to ask questions about the concepts and instances described. The most common decision problems are basic database-query-like questions like instance checking (is a particular instance (member of an ABox) a member of a given concept) and relation checking (does a relation/role hold between two instances, in other words does a have property b), and the more global-database-questions like subsumption (is a concept a subset of another concept), and concept consistency (is there no contradiction among the definitions or chain of definitions). The more operators one includes in a logic and the more complicated the TBox (having cycles, allowing non-atomic concepts to include each other), usually the higher the computational complexity is for each of these problems (see [http://www.cs.man.ac.uk/~ezolin/dl/ Description Logic Complexity Navigator] for examples).

Many DLs are decidable fragments of first-order logic (FOL) and are usually fragments of two-variable logic or guarded logic. In addition, some DLs have features that are not covered in FOL; this includes concrete domains (such as integer or strings, which can be used as ranges for roles such as hasAge or hasName) or an operator on roles for the transitive closure of that role.

Fuzzy description logics combines fuzzy logic with DLs. Since many concepts that are needed for intelligent systems lack well defined boundaries, or precisely defined criteria of membership, fuzzy logic is needed to deal with notions of vagueness and imprecision. This offers a motivation for a generalization of description logic towards dealing with imprecise and vague concepts.

Description logic is related to—but developed independently of—modal logic (ML). Many—but not all—DLs are syntactic variants of ML.

In general, an object corresponds to a possible world, a concept corresponds to a modal proposition, and a role-bounded quantifier to a modal operator with that role as its accessibility relation.

Operations on roles (such as composition, inversion, etc.) correspond to the modal operations used in dynamic logic.{{cite web|last=Schild|first=Klaus|title=Correspondence theory for terminological logics: Preliminary Report|url=http://www.cs.man.ac.uk/~ezolin/dl/bib/Correspondence_theory_for_terminological_logics_%28IJCAI_1991%29.pdf|work=KIT Report 91|publisher=KIT-BACK|access-date=2012-10-25}}

Temporal description logic represents—and allows reasoning about—time dependent concepts and many different approaches to this problem exist.Alessandro Artale and Enrico Franconi "Temporal Description Logics". In "Handbook of Temporal Reasoning in Artificial Intelligence", 2005. For example, a description logic might be combined with a modal temporal logic such as linear temporal logic.

{{Portal|Philosophy}}

• Formal concept analysis
• Lattice (order)
• Formal semantics (natural language)
• Semantic parameterization
• Semantic reasoner

{{Reflist}}

• F. Baader, D. Calvanese, D. L. McGuinness, D. Nardi, P. F. Patel-Schneider: The Description Logic Handbook: Theory, Implementation, Applications. Cambridge University Press, Cambridge, UK, 2003. {{ISBN|0-521-78176-0}}
• Ian Horrocks, Ulrike Sattler: [https://web.archive.org/web/20120218092244/http://lat.inf.tu-dresden.de/research/papers-2001.html#HorrocksSattler-IJCAI Ontology Reasoning in the SHOQ(D) Description Logic], in Proceedings of the Seventeenth International Joint Conference on Artificial Intelligence, 2001.
• D. Fensel, F. van Harmelen, I. Horrocks, D. McGuinness, and P. F. Patel-Schneider: [http://www.comlab.ox.ac.uk/people/ian.horrocks/Publications/download/2001/IEEE-IS01.pdf OIL: An Ontology Infrastructure for the Semantic Web]. IEEE Intelligent Systems, 16(2):38-45, 2001.
• Ian Horrocks and Peter F. Patel-Schneider: [http://www.comlab.ox.ac.uk/people/ian.horrocks/Publications/download/2001/HoPa01.pdf The Generation of DAML+OIL]. In Proceedings of the 2001 Description Logic Workshop (DL 2001), volume 49 of CEUR , pages 30–35, 2001.
• Ian Horrocks, Peter F. Patel-Schneider, and Frank van Harmelen: [http://www.comlab.ox.ac.uk/people/ian.horrocks/Publications/download/2003/HoPH03a.pdf From SHIQ and RDF to OWL: The Making of a Web Ontology Language]. Journal of Web Semantics, 1(1):7-26, 2003.
• Bernardo Cuenca Grau, Ian Horrocks, Boris Motik, Bijan Parsia, Peter Patel-Schneider, and Ulrike Sattler: [http://web.comlab.ox.ac.uk/people/Ian.Horrocks/Publications/download/2008/CHMP+08.pdf OWL 2: The next step for OWL]. Journal of Web Semantics, 6(4):309–322, November 2008.
• Franz Baader, Ian Horrocks, and Ulrike Sattler: [http://www.comlab.ox.ac.uk/people/ian.horrocks/Publications/download/2007/BaHS07a.pdf Chapter 3 Description Logics]. In Frank van Harmelen, Vladimir Lifschitz, and Bruce Porter, editors, Handbook of Knowledge Representation. Elsevier, 2007.
• Alessandro Artale and Enrico Franconi: [http://www.inf.unibz.it/~franconi/papers/time-handbook.ps.gz Temporal Description Logics]. In Handbook of Temporal Reasoning in Artificial Intelligence, 2005.
• [http://www.w3.org/2001/sw/WebOnt/charter Web Ontology (WebONT) Working Group Charter]. W3C, 2003
• [http://www.w3.org/2004/01/sws-pressrelease World Wide Web Consortium Issues RDF and OWL Recommendations]. Press Release. W3C, 2004.
• [http://www.w3.org/2007/06/OWLCharter.html OWL Working Group Charter]. W3C, 2007.
• [http://www.w3.org/2009/10/owl2-pr OWL 2 Connects the Web of Knowledge with the Web of Data]. Press Release. W3C, 2009.
• Markus Krötzsch, František Simančík, Ian Horrocks: A Description Logic Primer. CoRR {{ArXiv|1201.4089}}. 2012. A very first introduction for readers without a formal logic background.
• Sebastian Rudolph: [http://www.aifb.kit.edu/images/1/19/DL-Intro.pdf Foundations of Description Logics]. In Reasoning Web: Semantic Technologies for the Web of Data, 7th International Summer School, volume 6848 of Lecture Notes in Computer Science, pages 76–136. Springer, 2011. ([https://doi.org/10.1007%2F978-3-642-23032-5_2 springerlink])Introductory text with a focus on modelling and formal semantics. There are also [http://www.semantic-web-book.org/w/images/a/a9/DL-Foundations-RW2011.pdf slides].
• Jens Lehmann: DL-Learner: Learning concepts in description logics, Journal of Machine Learning Research, 2009.
• Stefan Heindorf, Lukas Blübaum, Nick Düsterhus, Till Werner, Varun Nandkumar Golani, Caglar Demir, and Axel-Cyrille Ngonga Ngomo. Evolearner: Learning description logics with evolutionary algorithms. In Proceedings of the ACM Web Conference 2022, pp. 818-828. 2022.
• Franz Baader: [https://web.archive.org/web/20120301231310/http://lat.inf.tu-dresden.de/research/papers-2009.html#Baader09 Description Logics]. In Reasoning Web: Semantic Technologies for Information Systems, 5th International Summer School, volume 5689 of Lecture Notes in Computer Science, pages 1–39. Springer, 2009. ([https://doi.org/10.1007%2F978-3-642-03754-2_1 springerlink]) Introductory text with a focus on reasoning and language design, and an extended historical overview.
• Enrico Franconi: [http://www.inf.unibz.it/~franconi/dl/course/ Introduction to Description Logics]. Course materials. Faculty of Computer Science, Free University of Bolzano, Italy, 2002. Lecture slides and many literature pointers, somewhat dated.
• Ian Horrocks: [http://web.comlab.ox.ac.uk/people/Ian.Horrocks/Publications/download/2008/Horr08a.pdf Ontologies and the Semantic Web]. Communications of the ACM, 51(12):58-67, December 2008. A general overview of knowledge representation in Semantic Web technologies.

• [http://www.cs.man.ac.uk/~ezolin/dl/ Description Logic Complexity Navigator], maintained by Evgeny Zolin at the Department of Computer Science
• [http://owl.cs.manchester.ac.uk/tools/list-of-reasoners/ List of Reasoners], OWL research at the University of Manchester
• [https://dl.kr.org/ Description Logics Workshop], homepage of the collecting information about the community and archives of the workshop proceedings

There are some semantic reasoners that deal with OWL and DL. These are some of the most popular:

• [http://lat.inf.tu-dresden.de/systems/cel/ CEL] is an open source LISP-based reasoner (Apache 2.0 License).
• [https://web.archive.org/web/20060419191746/http://www.cerebra.com/ Cerebra Engine] was a commercial C++-based reasoner, acquired in 2006 by webMethods.
• [http://owl.man.ac.uk/factplusplus FaCT++ ] is a free open-source C++-based reasoner.
• KAON2 is a free (for non-commercial use) Java-based reasoner, offering fast reasoning support for OWL ontologies.
• [http://www.cs.man.ac.uk/~schmidt/mspass/ MSPASS] is a free open-source C reasoner for numerous DL models.
• [https://web.archive.org/web/20070925082014/http://pellet.owldl.com/ Pellet] is a dual-licensed (AGPL and proprietary) commercial, Java-based reasoner.
• [http://www.racer-systems.com/ RacerPro] of Racer Systems was a commercial (free trials and research licenses are available) lisp-based reasoner, today both an open source version of RACER exists from the original developers at Lübeck University using the BSD 3 license, and also a commercialized version, still named [https://franz.com/agraph/racer/racer_features.lhtml RacerPro by Franz Inc.]
• [http://sim-dl.sourceforge.net/ Sim-DL] is a free open-source Java-based reasoner for the language ALCHQ. It also provides a similarity measurement functionality between concepts. To access this functionality a Protégé plugin can be used.
• [http://hermit-reasoner.com/ HermiT] is an open-source reasoner based on the "hypertableau" calculus. It is developed by the University of Oxford.
• [https://owlready2.readthedocs.io/en/latest/ Owlready2] is a package for ontology-oriented programming in Python. It can load OWL 2.0 ontologies as Python objects, modify them, save them, and perform reasoning via [http://hermit-reasoner.com/ HermiT] (included). Owlready2 allows a transparent access to OWL ontologies (contrary to usual Java-based API).
• [https://github.com/dice-group/owlapy/releases OWLAPY]. OWLAPY is an open-source Python framework for creating, manipulating, and reasoning with OWL ontologies. It includes a built-in StructuralReasoner for efficient, lightweight reasoning and wrappers for well-known Java-based reasoners like HermiT, Pellet, JFact, and Openllet.

• Protégé is a free, open-source ontology editor and a knowledge base framework, which can use DL reasoners offering DIG Interface as a back end for consistency checks.
• {{GitHub|ronwalf/swoop|SWOOP}}, an OWL browser/editor that takes the standard web browser as the basic UI paradigm.

• {{SourceForge|dig|DIG Interface}}, a standardized XML interface to DLs systems developed by the [http://dl.kr.org/dig/ DL Implementation Group (DIG)].
• {{SourceForge|owlapi|OWL API}}, a Java interface and implementation for the Web Ontology Language, used to represent Semantic Web ontologies.
• {{GitHub|dice-group/owlapy|OWLAPY}}, a Python interface and implementation for the Web Ontology Language, used to represent Semantic Web ontologies.

{{Non-classical logic}}

{{Computer science}}

{{Semantic Web}}

{{DEFAULTSORT:Description Logic}}

Category:Knowledge representation languages

Category:Non-classical logic

Category:Information science

Category:Formal semantics (natural language)

Category:Artificial intelligence