／var／logmarcus chiu

Descriptive／Description Logic (DL)

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Descriptive/Description Logic (DL)
  • syntax of Descriptive/Description Logic makes it easy to say things about objects
  • many but not all DLs are more expressive than propositional logic but less expressive than first-order logic
  • are notations that make it easier to describe definitions and properties of categories/objects
  • evolved from semantic networks in response to pressure to formalizing what networks mean while retaining emphasis on taxonomic structure
  • the principle inference tasks of description logics are:
    • subsumption - checking if one category is a subset of another by comparing their definitions
    • classification - checking whether an object belongs to a category
    • consistency - some description logic system includes consistency of a category definition (whether the membership criteria are logically satisfiable)
Syntax of CLASSIC Descriptions

for example, to say “bachelors are unmarried adult males”:

Bachelor = And(Unmarried, Adult, Male).

the equivalent in first-order logic:

Bachelor(x) ⇔ Unmarried(x) ʌ Adult(x) ʌ Male(x)

any description in CLASSIC description logic can be translated into an equivalent first-order logic sentence. but some are more straightforward in CLASSIC description logic. for example, to describe the set of men with at least 3 sons who are all unemployed and married to doctors, and at most 2 daughters who are all professors in physics or math departments:

And(Man, AtLeast(3,Son), AtMost(2,Daughter),
    All(Son, And(Unemployed, Married, All(Spouse, Doctor))),
    All(Daughter, And(Professor, Fills(Department, Physics, Math))))

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