ASP / Clingo

Question 1

What does ASP stand for?

Answer 1

Answer Set Programming

Question 2

Define an atom in the context of ASP.

Answer 2

An atom is a basic unit of meaning in ASP, usually representing a proposition.

Question 3

What is a literal?

Answer 3

A literal is an atom or its negation.

Question 4

Identify the atoms in the following ASP statement: a :- b, not c.

Answer 4

The atoms are a, b, and c.

Question 5

What is Clingo?

Answer 5

Clingo is a software package that includes an ASP grounder (gringo) and solver (clasp). It’s used to find stable models of logic programs.

Question 6

Name a primary function of Clingo’s grounder (gringo).

Answer 6

It converts a high-level logic program into a ground (variable-free) format.

Question 7

Name a primary function of Clingo’s solver (clasp).

Answer 7

It finds the stable models of a ground logic program.

Question 8

Define a rule in ASP.

Answer 8

A rule in ASP is a statement of the form head <- body, where head is an atom and body is a conjunction of literals.

Question 9

What does the head of a rule represent?

Answer 9

The head represents what is derived when the body of the rule is satisfied.

Question 10

What does the body of a rule represent?

Answer 10

The body represents the conditions that must be satisfied for the head to be derived.

Question 11

Identify the head and body in the following ASP rule: a :- b, not c.

Answer 11

The head is a and the body is b, not c.

Question 12

What is a stable model?

Answer 12

A stable model is a set of atoms that represents a possible world where all the rules of the program are satisfied.

Question 13

How does a stable model relate to ground instances?

Answer 13

A stable model is a set of ground instances of atoms that make the program self-consistent.

Question 14

Are stable models unique?

Answer 14

No, an ASP program can have multiple stable models, or none at all.

Question 15

What are ground instances in ASP?

Answer 15

Ground instances are specific atoms that result from substituting all variables in a rule with concrete terms. For example, for the rule p(X) :- q(X, Y), r(Y). and terms X = 1, Y = 2, the ground instance is p(1) :- q(1, 2), r(2).

Question 16

What does negation as failure mean in the context of stable models?

Answer 16

Negation as failure, denoted as not a, means that a is not part of the stable model. In other words, not a is true in a stable model if a cannot be derived from the program rules given the stable model.

Question 17

How would you write a rule to express that if a is true then b must be true?

Answer 17

b :- a.

Question 18

How would you write a rule to express that c is true only if a and b are false?

Answer 18

c :- not a, not b.

Question 19

How would you write a rule to express that d is true if either a or b is true, but not both?

Answer 19

d :- a, not b. d :- b, not a.

Question 20

How would you write a rule to express that if a and b are true, then c or d must be true, but not both?

Answer 20

{ c; d } :- a, b. :- c, d, a, b.

Question 21

What is a choice rule in ASP?

Answer 21

A choice rule allows for optional inclusion of atoms in the stable model. It has the form { head } :- body.

Question 22

How would you write a choice rule to express that a can be true if b is true?

Answer 22

{ a } :- b.

Question 23

What does the following choice rule express: { a; b } :- c.

Answer 23

If c is true, either a, b, or both a and b can be true.

Question 24

What is a proposition in ASP?

Answer 24

A proposition is an atom without variables, essentially a statement that is either true or false.

Question 25

What is a predicate in ASP?

Answer 25

A predicate is a template for generating atoms. It consists of a name and a list of variables or terms.

Question 26

How would you write a predicate to represent a relation between x and y?

Answer 26

relation(x, y).

Question 27

Can a predicate have a single variable? Provide an example.

Answer 27

Yes, for example, student(X).

Question 28

How would you write a predicate to express the parent-child relationship?

Answer 28

parent(x, y). where x is the parent and y is the child.

Question 29

What would the atom sibling(a, b) represent if sibling is a predicate?

Answer 29

It would represent that a and b are siblings.

Question 30

How would you write a predicate to express the ancestor relationship recursively?

Answer 30

ancestor(X, Y) :- parent(X, Y). ancestor(X, Y) :- parent(X, Z), ancestor(Z, Y).

Question 31

What is a common use of predicates involving arithmetic operations?

Answer 31

Predicates often use arithmetic to express relationships like greater than or less than. For example, greater(X, Y) :- X = Y + 1.

Question 32

What are cardinality restrictions in ASP?

Answer 32

Cardinality restrictions specify the minimum and/or maximum number of literals that must be true in a stable model.

Question 33

How would you write a rule that allows for at least 2 and at most 3 instances of a to be true?

Answer 33

2 { a(X) } 3.

Question 34

How would you enforce that exactly one of a, b, or c is true?

Answer 34

1 { a; b; c } 1.

Question 35

What does the cardinality restriction 2 { a(X); b(X) } 3 mean when combined with a(1). a(2). b(1). b(2). b(3).

Answer 35

It means that in a stable model, at least 2 and at most 3 of the atoms generated from a(X) and b(X) must be true. Possible combinations could be { a(1), a(2) }, { b(1), b(2), b(3) }, etc.

Question 36

How would you use cardinality to express that at least one student must be in a class?

Answer 36

1 { in_class(X) : student(X) }.

Question 37

How would you use cardinality to express that a committee must have between 3 and 5 members?

Answer 37

3 { committee_member(X) : person(X) } 5.

Question 38

What are the stable models for the program a :- not a.?

Answer 38

The stable model is {} (empty). This might seem counterintuitive because one could think that a should be true if a is not true. However, in stable model semantics, the empty set is the only closed set under this program.

Question 39

What are the stable models for the program a :- b. b :- a.?

Answer 39

There are no stable models. This can be counterintuitive due to the cyclic dependency between a and b.

Question 40

What are the stable models for the choice rule { a } :- b. combined with b.?

Answer 40

The stable models are {b} and {a, b}. This may seem counterintuitive if you’re expecting a deterministic outcome.

Question 41

Given the program a :- b, not c. b. c :- not a. what are the stable models?

Answer 41

There are no stable models. This might be counterintuitive as one could expect b to lead to a, but a being absent also leads to c, creating a contradiction.

Question 42

Given the program 1 { a; b } 1. a :- b. b :- a. what are the stable models?

Answer 42

The stable models are {a} and {b}. This might be counterintuitive because despite the cyclic dependency, the cardinality restriction enforces that only one of a or b can be true.

Question 43

What is an aggregate in Clingo?

Answer 43

An aggregate in Clingo is a construct like #sum, #count, or #min that performs an operation over a set. For example, #count { X:fruit(X) } = N counts the number of fruits and stores the count in N.

Question 44

How do you use external atoms in Clingo?

Answer 44

External atoms in Clingo are prefixed with & and can be used to interface with external computations. For example, &is_prime(X) could check if X is a prime number.

Question 45

What is optimization in Clingo, and how is it done?

Answer 45

Optimization in Clingo is done using #minimize or #maximize. For example, #minimize { X:fruit(X) } would find the answer set that minimizes the number of fruits.

Question 46

How do you specify constraints in Clingo?

Answer 46

Constraints in Clingo are rules with an empty head. For example, :- not fruit(X), eat(X). specifies that you cannot eat X if X is not a fruit.