# TU Wien:Knowledge-based Systems VU (Egly, Eiter, Tompits)/Übungstest 13.06.2018

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## First-order logic & Rules

### Example 1

For the following sentences, where c is a constant, R a binary and P a unary predicate:

• a) Give an interpretation structure under which sentence (1)-(4) become true.
• b) Give a formal definition of Entailment in first-order logic.
• (1) • (2) • (3) • (4) ### Example 2

• a) Give a formale definition of a rule. When is a rule applicable?
• b) For the following problem write some rules in CLIPS to model the problem.
• A person has either a dog or a cat, but not both. If a person is allergic, then he can't have a cat. If a person has a dog, then he needs at least 1 hour of sparetime to take the dog for a walk. A person who doesn't have enough money to pay a vet, can't afford a pet.

## Description Logics and Truth Maintenance Systems

### Example 3

• Construct a knowledge base (we do not need an RBox here) expressing the following knowledge concerning employees and their hierarchy.
• Every person who is an employee is either a supervisor or a worker.
• A supervisor is a person who manages at least 1 or more workers.
• No worker manages himself.
• Alice and Bob have jointsupervisor.

Use the class name , the role names and the individual names • What does it mean in that a knowledge base is satisfiable.

### Example 4

• Using the tableau algorith for concept satisfiability, show that the GCI (didn't remember it :/) is not satisfied by each interpretation.
• What is an interpretation?

## Answer Set Programming

### Example 5

• a) What is grounding?
• b) The combinatorial graph problem vertex cover is defined as follow:

INSTANCE: Given a graph G = (V,E) and a positive integer k ≤ |V|.
QUESTION: Does there a subset D ⊆ V such that |D| ≤ k and such that for each edge(x,y) ∈ E is either x ∈ D or y ∈ D.

Define all required predicates, rules, and constraints to represent the vertex cover problem as an anser-set program such that

• each vertex v ∈ V of G is denoted by a fact v(v),
• each edge(u,v) ∈ E of G is denoted by a fact edge(u,v),
• the integer k is given by a single fact size(k), and
• answer sets of c(X) correspond to solutions D.

### Example 6

Consider the following normal logic program P, where p,q,r and s are atoms.

• a) Given the program.      • Reason if the sets , are stable models of P and if so explain why.
• b) Which kind of negation in ASP do you know and what are their differences?