Quiz: Knowledge Representation
Methods of AI — SoSe 2026
Q1 — KR
Question: What is the difference between TBox and ABox in a description logic knowledge base?
Answer
- TBox (Terminological Box): contains general statements about classes and their relationships — concept inclusions (C ⊑ D), concept equivalences (C ≡ D). Analogous to a database schema. Example:
Student ⊑ Person,UG-Student ≡ Student ⊓ ∀attends.UGC- ABox (Assertion Box): contains facts about specific individuals — concept assertions (
Mary : Teacher) and role assertions ((Mary, CS600) : teaches). Analogous to database content.
Together: knowledge base K = (T, A) forms an ontology.
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Q2 — KR
Question: What is a General Concept Inclusion (GCI)? What does Flu ⊑ Illness mean formally?
Answer
A GCI is an expression of the form C ⊑ D, read “D subsumes C” or “every C is a D”.
Formally: interpretation I satisfies C ⊑ D iff C^I ⊆ D^I (the extension of C is a subset of the extension of D).
Flu ⊑ Illnessmeans: every individual that is a Flu is also an Illness — every instance of Flu is an instance of Illness.
Note direction: C ⊑ D means C is more specific than D. Flu is more specific than Illness.
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Q4 — KR
Question: Explain the ALC concept constructors ∀R.C and ∃R.C and give an example of each.
Answer
- ∀R.C (Value restriction): the set of individuals a such that all R-relations from a lead to C. “Everyone that a is related via R to must be in C.”
Example:Professor ⊓ ∀teaches.Postgrad= professors who teach only postgrad courses.- ∃R.C (Existential restriction): the set of individuals a such that there exists at least one R-relation from a to something in C. “There is someone in C that a is related to via R.”
Example:∃teaches.UGCourse= individuals who teach at least one undergraduate course.
Key: ∀ = “all”, ∃ = “at least one”.
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Q5 — KR
Question: How does the Tableaux algorithm prove subsumption C ⊑ D?
Answer
Subsumption C ⊑ D is equivalent to: C ⊓ ¬D is unsatisfiable (nothing can be in C but not D).
The tableaux algorithm:
- Form the concept C ⊓ ¬D
- Push all negations inward (negation normal form)
- Try to construct a finite model for this concept
- Apply expansion rules (for ⊓, ⊔, ∃R, ∀R) until no more rules apply
- If all branches lead to a contradiction → C ⊓ ¬D is unsatisfiable → C ⊑ D holds
- If a model is found → C ⊑ D does NOT hold
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Q6 — KR
Question: Name all 7 basic Allen interval relations (and their inverses). How are they used in temporal reasoning?
Answer
7 basic relations (13 with inverses, 1 symmetric):
- BEFORE / AFTER
- MEETS / IS-MET-BY
- OVERLAPS / IS-OVERLAPPED-BY
- STARTS / IS-STARTED-BY
- FINISHES / IS-FINISHED-BY
- DURING / CONTAINS
- EQUAL (symmetric)
Used via composition table: given R(I1,I2) and R(I2,I3), which relations are possible between I1 and I3? This enables qualitative temporal inference (e.g. planning, natural language understanding) without exact time values.
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Q7 — KR
Question: What is the key trade-off in knowledge representation? Give an example.
Answer
Expressivity vs. Practicality (tractability):
- More expressive languages can represent more complex knowledge, but reasoning becomes harder or undecidable.
- First-Order Logic (FOL): maximally expressive, but theorem proving is undecidable in general.
- ALC (Description Logic): less expressive than FOL, but reasoning (subsumption, satisfiability) is decidable and efficiently implementable via tableaux.
- Example: adding role composition (R∘S) to ALC pushes reasoning out of 2-variable logic → exponential or worse complexity.
Trade-off: design your language to be expressive enough for your domain, but tractable enough to reason with.
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Beyond the lecture (optional)
These questions go beyond the SoSe 2026 lecture slides (textbook / external additions). Kept for depth, not exam-critical.
Q3 — KR
Question: What is the difference between the Open World Assumption (OWA) and the Closed World Assumption (CWA)? Which does STRIPS use, which do Description Logics use?
Answer
- CWA (Closed World Assumption): what is not explicitly stated is assumed false. Used in STRIPS, databases. If “on(A,B)” is not in the state → it’s false.
- OWA (Open World Assumption): what is not stated is unknown (not necessarily false). Used in Description Logics, OWL, Situation Calculus.
Practical implication: CWA is efficient for planning but assumes complete knowledge. OWA is more realistic for incomplete knowledge domains (ontologies, web).
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