1. (a) Express each of the following formulas

• in informal conversational English and
• in first-order logic.

i. Person ∩∀ ParentOf.CSstudent ⊆ HappyParent

ii. HockeyPlayer ⊆ ∃Plizys_for.Team

(b) Express the following assertions about the faculty at a university in ALC:

• Faculty members are either professors or lecturers
• Professors supervise graduate students and postdocs
• Lecturers do not supervise anyone
• Profs have a degree which is a PhD
• Lecturers have a degree which is a MSc or PhD

(c) Prove using the tableaux algorithm that each of the following holds or otherwise give an interpretation in which the statement is false. Explain all steps

i. ¬(∀R. ¬C ∩ ∀R.(¬D U ¬E)) ⊆ ∃R.(C U D)

ii. ¬(∀R. (¬C ∩ ¬D)) ⊆ ¬(∀R.C ∩ ¬ ∀R.D)

2. For the two argumentation networks below, give all admissable sets, preferred extensions and stable extensions.

3. Consider the following assertions

{l, l → c, x, x → ¬l, ¬a, f, f Λ ¬a → ¬x}

with intended interpretations;

l: Levels of CO₂ are increasing.

c: Global temperatures are increasing.

l → c: Increase in levels of CO₂ leads to global temperatures increasing.

x: Study x is reliable.

x → ¬l: If study x is reliable then (it shows that) levels of CO₂ are not increasing.

f: Funding for study x is provided by AcmeOil,

¬a: Study x is not done at arm's length (i.e. with no outside interference).

f → ¬a: If funding for study x is from AcmeOil, it's not done at arm's length.

¬a → ¬x: If study x is riot done at arm's length, it's results are not reliable.

Express this in the Besnard-Hunter framework. That is give

(a) The various relevant arguments, and

(b) Provide an argument graph showing whether c is warranted or not, fully giving all information (such as undercutters, etc). (If no argument graph can be given, explain why not.)

Attachment:- Assignment.rar