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Tutorial questions: reasoning with arguments
1. Below is some knowledge that an agent has about monsters, where X is a variable that can be instantiated by any constant and constants all start with lower-case letters.
Angry(cedric)
Strong(cedric)
Sleeping(cedric)
Smiling(cedric)
Smiling(X) → ¬Angry(X)
Angry(X) ∧ Strong(X) → RunAwayFrom(X) Sleeping(X) → ¬RunAwayF rom(X)
(a) Using the knowledge above, it is possible to construct two arguments that rebut one another. Identify two such arguments, giving the support and claim of each.
Answer:
Two possible answers: ⟨{Angry(cedric),
Strong(cedric),
Angry(cedric) ∧ Strong(cedric) → RunAwayF rom(cedric)}, RunAwayF rom(cedric)⟩
and
⟨{Sleeping(cedric),
Sleeping(cedric) → ¬RunAwayF rom(cedric)}, ¬RunAwayF rom(cedric)⟩
rebut each other.
⟨{Angry(cedric)},
Angry(cedric)⟩
and
⟨{Smiling(cedric),
Smiling(cedric) → ¬Angry(cedric)}, ¬Angry(cedric)⟩
rebut each other.
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(b) Using the knowledge above, it is possible to construct two arguments such that one undercuts the another. Identify two such arguments, giving the support and the claim of each and making clear which argument undercuts the other.
Answer:
⟨{Smiling(cedric),
Smiling(cedric) → ¬Angry(cedric)}, ¬Angry(cedric)⟩
undercuts
⟨{Angry(cedric),
Strong(cedric),
Angry(cedric) ∧ Strong(cedric) → RunAwayF rom(cedric)}, RunAwayF rom(cedric)⟩
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2. Consider the following abstract argumentation graph.
Which arguments are acceptable under:
(a) the grounded semantics;
(b) the preferred credulous semantics;
(c) the preferred sceptical semantics.
No arguments are acceptable under the grounded semantics. The valid labelling under the grounded semantics is:
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Under the preferred semantics, there are two valid labellings:
The arguments acceptable under the preferred credulous semantics are: b, e, h, f, d. The arguments acceptable under the preferred sceptical are: h, f.
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