Logic and Artificial Intelligence Programming
Logic coursework 1
Lecturer : F. Sadri
Date set : 24 October 2017
Date due : 10 November 2017
Please submit electronically.
Answer all the questions.
Companies Registration House (CRH) keeps a record of registered companies and a register
of disqualified directors. Formalise in predicate logic the sentences (i)-(v), below, that govern
the activities of CRH. Use any of the predicates listed below and <, ≤, = that you can use both for comparing dates and for comparing share values, and in the case of = for comparing names as well. Ensure that you present your formulas clearly, using brackets to correctly identify the scope of quantifiers and disambiguate where necessary. reg(C) to mean C is a registered company. dir(D, C) to mean D is the director of company C. reqReg(ID, C, D, S) to mean request ID is for registering a company by the name C, with director D and share capital S. reject(ID) to mean the request identified by ID for a company registration is rejected. accept(ID) to mean the request identified by ID for a company registration is accepted. disq(D) to mean D is disqualified. insolvent(C) to mean C is insolvent. share(C,Value) to mean the share capital of company C is set to Value. acc_due(C, P, D) to mean the accounts of company C for period P are due on date D. acc_filed(C, P, D) to mean the accounts of company C for period P are filed on date D. warn(D, C) to mean director D is warned about company C. i) Every registered company has exactly one director. ii) Any request for registering a company is rejected if a company of that name is already registered, or if the director is disqualified, or if the share capital of the company is less than £5000, otherwise the request is accepted. iii) A director is disqualified and the share capital of all of his registered companies is set to zero if at least one of his registered companies becomes insolvent. iv) The director of a registered company who is not disqualified is warned if on at least two occasions the company’s accounts have not been filed by the due deadlines. v) If a director has been warned about one of his companies and the share capital of that company falls more than 80% below its initial capital (as noted in the request for the company’s registration) then the director is disqualified. (Use the predicate share(C,Value) here to denote the share value of the company.) The questions have equal marks.