Question

John and Mary sign the following contract:

- If it rains on May 1, 2017, then John must give Mary a check for $10,000 on May 2, 2017
- Mary must mow the lawn on May 3, 2017 if and only if John gives Mary a check for $10,000 on May 2, 2017.

What truly happened those days is the following:
- it did not rain on May 1, 2017
- John gave Mary a check for $10,000 on May 2, 2017
- Mary mowed the lawn on May 3, 2017.

Part a: Write a first order logic statement to express the contract. Make sure that you clearly define what constants and predicates that you use are. (NOTE: DO NOT use functions)

Part b: Write a logical statement to express what truly happened. When possible, use the same predicates and constants as in question 6a. If you need to define any new predicates or constants, clearly define what they stand for.

Part c: Define the symbols required to convert any KB involved in the above domanin from FOL to Propositional logic. Use this to convert the answers to part a and b to Propositional Logic.

Part d: Was the contract violated or not, Justify your answer [Note: Contract is not violated if the sequence of events entails the contract]

Answer 1

The following is the solutions which are 100% correct please do upvoteThank you.

R(z) --Rained on day z (domain for z is day)
G(x,y,z) - x gives cheque of 10000 to y on day z//domain of x and y are people
M(x,z) -- x mow the lawn on day z

The contract

R(May 1,2017)-->G(John,Mary,May 2,2017)
G(John,Mary,May 2,2017)->M(Mary,May 3,2017)

Actual happened

Not R(May 1,2017)
G(John,Mary,May 2,2017)
M(Mary,May 3,2017)

The contract did not get violated. The statement says if it rains then John must
give the cheque to Mary.So if it does not rain it is upto John whether he gives
cheque to Mary or not. But once cheque has been given every thing has happened
as per the contract.