Editing Description logic (section)

==Relationship with other logics==
===First-order logic===
Many DLs are [[Decidability (logic)|decidable]] [[fragment (logic)|fragments]] of [[first-order logic]] (FOL)<ref name="DLHB"/> 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.<ref name="DLHB"/>

===Fuzzy description logic===
Fuzzy description logics combines [[fuzzy logic]] with DLs. Since many concepts that are needed for [[Artificial intelligence|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.

===Modal logic===
Description logic is related to—but developed independently of—[[modal logic]] (ML).<ref name="DLHB"/> Many—but not all—DLs are syntactic variants of ML.<ref name="DLHB"/>

In general, an object corresponds to a [[Kripke semantics|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 (modal logic)|dynamic logic]].<ref name=CTTL>{{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}}</ref>

====Examples====
{| style="width:20%" class="wikitable sortable"
|+ Syntactic variants
|-
! DL
! ML
|-
| <math>\mathcal{ALC}</math>
| '''K'''<ref name="DLHB"/>
|-
| <math>\mathcal{SR}</math>
| '''[[Propositional dynamic logic|PDL]]'''<ref name=CTTL/>
|-
| <math>\mathcal{FSR}</math>
| '''DPDL''' (deterministic PDL)<ref name=CTTL/>
|-
| <math>\mathcal{TSL}\text{, or }\mathcal{SRI}</math>
| Converse-'''[[Propositional dynamic logic|PDL]]'''<ref name=CTTL/>
|-
| <math>\mathcal{FSL}\text{, or }\mathcal{FSRI}</math>
| Converse-'''DPDL''' (deterministic PDL)<ref name=CTTL/>
|}

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