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Assignment 2 in ECS 289F: Ontologies and Description Logic - Prof. Bertram T. Ludaescher, Assignments of Computer Science

University of California - DavisComputer Science
Prof. Bertram T. Ludaescher

Information about assignment 2 in the topics in scientific data management course (ecs 289f) taught by dr. Bertram ludaescher during winter 2005. The assignment covers topics related to ontologies and description logic, including translating description logic axioms into first-order predicate logic, unfolding concept expressions, and understanding the relationship between tboxes and aboxes. Students are required to complete two problems, which involve questions about the difference between tboxes and aboxes, evaluating queries, and the relationship between logic formulas and query results.

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Uploaded on 07/31/2009

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ECS289FTopicsinScientificDataManagementWinter2005
Dr.BertramLudaescherJanuary31
st
,2005
Assignment2–Ontologies/DescriptionLogic
Due:Monday,February7
th
(inclass,afterclass)
Problem1.(10+4+3Points)
Considerthefollowing(oversimplified!)descriptionlogicontology(TBox):
i. Organism≡Animal⊔Plant
ii. Person⊑Animal
iii. Grass⊑Plant
iv. Cow⊑Animal⊓∀eats.Grass
v. Carnivore≡Organism⊓∀eats.Animal
vi. Rancher≡Person⊓∀eats.Cow⊓∃owns.Ranch
a)Translatetheabovedescriptionlogic(DL)axiomsintofirst‐orderpredicatelogic(FO)formulas.
Hint:Totranslatetheconceptexpressionsontheleft‐hand‐sideandright‐hand‐sideoftheabove
axioms,usethetranslationst
x
andt
y
giveninclass.TotranslateanequivalenceC≡Doraconcept
inclusionC⊑ D,computet
x
forthelhsandrhs,respectively,anduse
• ∀x(t
x
(C)↔t
x
(D))fortheequivalenceor
• ∀x(t
x
(C)→t
x
(D))fortheimplication.
b)WhenunfoldingaconceptexpressionssayE,wecanreplaceaconceptC(occurringinE)byan
equivalentconceptD,i.e.,forwhichC≡Dholds.IfC⊑ Dholds,wecanalsoreplaceCbyDbut
needtorememberthattheresultingexpressionE’isnolongerequivalenttoE.
“Unfold”theexpressionE=Person⊓∀eats.Cow⊓∃owns.Ranch(equivalenttoRanchersinthe
aboveontology)untilitcontainsonlybaseconcepts.NotethattheresultingexpressionE’mightnot
beequivalenttoE(e.g.,ifonereplacesGrassbyPlantinaconjunction,thenapossiblylargerresultis
obtained).
c)Intheaboveontology,whatistherelationbetweenRancherandCarnivore?Forexample,isevery
RancheraCarnivore?Howabouttheotherwayround?Explain.
Problem2(1+2+3Points).
a) WhatisthedifferencebetweenaTBoxandanABox,i.e.,whatkindofinformationisstoredin
eitherone?
b) Whatisthedifferencebetweenevaluatingaqueryandreasoningwithaquery(orwithtwo
queries)?Whichproblemisharderingeneral?
c) Whatistherelationbetweenevaluatingaformula(valmappingontheslides)inlogicand
runningaquery?Saywhatcorrespondstowhat(e.g.,AinlogiccorrespondstoXindatabases,
BinlogiccorrespondstoYindatabases,etc.)

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ECS 289F Topics in Scientific Data Management Winter 2005 Dr. Bertram Ludaescher January 31 st, 2005

Assignment 2 – Ontologies / Description Logic

Due: Monday, February 7 th^ (in class, after class)

Problem 1. (10+4+3 Points) Consider the following (oversimplified!) description logic ontology (TBox): i. Organism ≡ Animal ⊔ Plant ii. Person ⊑ Animal iii. Grass ⊑ Plant iv. Cow ⊑ Animal ⊓ ∀eats.Grass v. Carnivore ≡ Organism ⊓ ∀eats.Animal vi. Rancher ≡ Person ⊓ ∀eats.Cow ⊓ ∃owns.Ranch a) Translate the above description logic (DL) axioms into first‐order predicate logic (FO) formulas. Hint: To translate the concept expressions on the left‐hand‐side and right‐hand‐side of the above axioms, use the translations t x and t y given in class. To translate an equivalence C ≡ D or a concept inclusion C ⊑ D, compute t x for the lhs and rhs, respectively, and use

  • ∀x ( tx (C) ↔ t x (D) ) for the equivalence or
  • ∀x ( tx (C)→ t x (D) ) for the implication. b) When unfolding a concept expressions say E, we can replace a concept C (occurring in E) by an equivalent concept D, i.e., for which C ≡ D holds. If C ⊑ D holds, we can also replace C by D but need to remember that the resulting expression E’ is no longer equivalent to E. “Unfold” the expression E = Person ⊓ ∀eats.Cow ⊓ ∃owns.Ranch (equivalent to Ranchers in the above ontology) until it contains only base concepts. Note that the resulting expression E’ might not be equivalent to E (e.g., if one replaces Grass by Plant in a conjunction, then a possibly larger result is obtained). c) In the above ontology, what is the relation between Rancher and Carnivore? For example, is every Rancher a Carnivore? How about the other way round? Explain. Problem 2 (1+2+3 Points). a) What is the difference between a TBox and an ABox, i.e., what kind of information is stored in either one? b) What is the difference between evaluating a query and reasoning with a query (or with two queries)? Which problem is harder in general? c) What is the relation between evaluating a formula ( val mapping on the slides) in logic and running a query? Say what corresponds to what (e.g., A in logic corresponds to X in databases, B in logic corresponds to Y in databases, etc.)