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.
![62_Figure.png](https://secure.tutorsglobe.com/CMSImages/62_Figure.png)
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