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Introduction In this assignment you will be practicing logical programming using Prolog language. This assignment consists of three parts: 1) Fact representation, 2) Queries, Uni cation, and Resolution, and 3) Implementation Exercises. Note that Part 1 of the assignment is due on May 10th and is to be submitted separately. See section 5 for more details. 3 Ground rules You are allowed to work on a team of 3 students at most (including yourself). Each team should designate a leader who will submit the assignment electronically. ONLY one copy of the assignment is to be submitted. This is an assessment exercise. You may not seek any assistance from others while expecting to receive credit. You must work strictly within your team). Failure to do so will result in penalties or no credit. 4 Your Assignment Your assignment is given in three parts, as follows. 1) Fact representation, which is to be submitted separately, 2) Queries, Uni cation, and Resolution, and 3) Implementation Exercises, all of which will be demoed by the whole team. 1 see submission notes (deadline for 1 is Sunday, May 10th at Noon) 2 4.1 Fact Representation Provide a knowledge-base of clauses specifying your class schedule in prolog, as demonstrated in the following. team([<>…]). student_info(‘<>’, ‘<>’, ‘<>’). takes_course(‘<>’, ‘<>’, ‘<>’, ‘<>’). course_schedule(‘<>’, ‘<>’, ‘<>’, ‘<>’, ‘<>’, <>’). dow is day of week: `sun’, `mon’, `tue’, `wed’, `thu’, `fri’, and `sat’. from-time and to-time are class start and end in military format, i.e. 0845 (8:45am), 1445 (2:45pm), etc. course-name, course-number, and course-section are all in lower case: e.g.. comp 348 aa Below is a sample knowledge-base for a group of two: John Doe and Jane Doe. Note that in this question, using single quote (‘) is mandatory. team([‘4000123’, ‘4000228’]). student_info(‘4000123’, ‘John’, ‘Doe’). student_info(‘4000228’, ‘Jane’, ‘Doe’). takes_course(‘4000123’, ‘comp’, ‘348’, ‘aa’). takes_course(‘4000123’, ‘comp’, ‘348’, ‘aaae’). takes_course(‘4000228’, ‘comp’, ‘348’, ‘ab’). takes_course(‘4000228’, ‘comp’, ‘348’, ‘abaf’). takes_course(‘4000228’, ‘comp’, ‘346’, ‘cc’). course_schedule(‘comp’, ‘348’, ‘aa’, ‘mon’, ‘1445’, ‘1715’). course_schedule(‘comp’, ‘348’, ‘aa’, ‘wed’, ‘1445’, ‘1715’). course_schedule(‘comp’, ‘348’, ‘aaae’, ‘mon’, ‘1345’, ‘1405’). course_schedule(‘comp’, ‘348’, ‘aaae’, ‘wed’, ‘1345’, ‘1405’). course_schedule(‘comp’, ‘348’, ‘ab’, ‘tue’, ‘1315’, ‘1545’). course_schedule(‘comp’, ‘348’, ‘ab’, ‘thu’, ‘1315’, ‘1545’). 3 course_schedule(‘comp’, ‘348’, ‘abaf’, ‘tue’, ‘1615’, ‘1705’). course_schedule(‘comp’, ‘348’, ‘abaf’, ‘thu’, ‘1615’, ‘1705’). course_schedule(‘comp’, ‘346’, ‘cc’, ‘tue’, ‘1830’, ‘2100’). course_schedule(‘comp’, ‘346’, ‘cc’, ‘thu’, ‘1830’, ‘2100’). John is taking one course (comp 348 aa + the tutorial aaae) and Jane is taking two courses (comp 348 ab + the tutorial abaf we well as comp 346 cc with no tutorial). Note that both courses are scheduled on multiple days. Q 1. Provide the knowledge-base of ALL courses for ALL members of the team. Create a le named `schedule-studid.pl’ where studid is the id of the leader of the team. Include all clauses in the le. Write every clause in a single line. One le per group. Submit this separately (see submission notes). Q 2. Run the following query and report the result: team(X), member(S, X), findall(S, takes_course(S, _, _, _), LL), length(LL, NN), write(S), write(‘ has only taken ‘), write(NN), write(‘ courses and tutorials in summer 2020.’), nl, fail. Is the above information correct? The above must be submitted in stage 1 (see submission notes for details). 4 Q 3. Create below mentioned rules to query the designation information from your knowlegebase. Hint: Use the cut operator where applicable. all_sections(CNAM, CNUM, L) :- … /* L contains a list of all sections of course CNAME, CNUM, i.e. calling all_sections(‘comp’, ‘348’, L) will result in L=[‘aa’, ‘ab’]; no duplicates */ has_taken(S, [CNAM|[CNUM|[SEC|[]]]]) :- … /* true if student S takes the course CNAM CNUM SEC, e.g. takes(‘4000123’, [‘comp’, ‘348’, ‘aa’]) */ has_taken2(S, [CNAM|[CNUM|[]]]) :- … /* true if S takes any sections of the course CNAM CNUM, e.g. takes(‘4000123’, [‘comp’, ‘348’]) */ all_subjects(S, L) :- … /* L contains all the courses subjects that have been taken by student S, i.e. [‘comp’, ‘soen’]; no duplicates */ all_courses(S, L) :- … /* L contains all the courses that have been taken by student S, i.e. all_courses(‘4000123’, L) will result in L=[[‘comp’, ‘348’, ‘aa’], [‘comp’, ‘348’, ‘ab’]] */ all_courses2(S, L) :- … /* similar to all_courses but without section info; no duplicates */ Q 4. Modify the code in Q2 to count only the courses regardless of their sections (i.e. comp 348 aa and aaae will be counted as one) Q 5. Compare the result for all_courses2(‘4000123′, L) vs. all_courses2(4000123, L). Explain the dierence. 5 4.2 Queries, Uni cation, and Resolution Q 6. Uni cation: Indicate which of the following pairs of terms can be uni ed together? If they can’t be uni ed, please provide the reason for it. In case of error, indicate the error. If they can be uni ed successfully, wherever relevant, provide the variable instantiations that lead to successful uni cation. (Note that `=’ indicates uni cation) 1. food(bread, X) = Food(Y, soup) 2. Bread = soup 3. Bread = Soup 4. food(bread, X, milk) = food(Y, salad, X) 5. manager(X) = Y 6. meal(healthyFood(bread), drink(milk)) = meal(X,Y) 7. meal(eat(Z), drink(milk)) = [X] 8. [eat(Z), drink(milk)] = [X, Y | Z] 9. f(X, t(b, c)) = f(l, t(Z, c)) 10. ancestor(french(jean), B) = ancestor(A, scottish(joe)) 11. meal(healthyFood(bread), Y) = meal(X, drink(water)) 12. [H|T] = [a, b, c] 13. [H, T] = [a, b, c] 14. breakfast(healthyFood(bread), egg, milk) = breakfast(healthyFood(Y), Y, Z) 15. dinner(X, Y, Time) = dinner(jack, cook( egg, oil), Evening) 16. k(s(g), Y) = k(X, t(k)) 17. equation(Z, f(x, 17, M), L*M, 17) = equation(C, f(D, D, y), C, E) 18. a(X, b(c, d), [H|T]) = a(X, b(c, X), b) 6 Q 7. Queries: Assume we have the following database in a Prolog program: course(hit_transfer, mechanical). course(web_design,computer). course(design_methods, fine-arts). course(poetry, literature). course(leadership, management). course(biology,medicin). lab_number(mechanical,15). lab_number(fine_arts,10). lab_number(X, Z) :-course(X, Y), lab_number(Y, Z). field(mechanical,engineering). field(computer, engineering). field(fine-arts, art). field(literature, social). field(management, buisiness). field(X, Y) :- course(X, Z), field(Z, Y). student(anna, hit_transfer). student(daniel, hit_transfer). student(adrian, web_design). student(ava, design_methods). student(jack, poetry). student(lee, leadership). student(X, Y) :- field(Z, Y), student(X, Z). student(X):- student(X,_). Determine the type of each of the following queries (ground/non-ground), and explain what will Prolog respond for each of these queries (write all the steps of uni cations and resolutions for each query)? 1. ? field(hit_transfer,engineering). 2. ? lab_number(fine_arts,X). 3. ? field(computer, literature). 4. ? course(X,Y). 5. ? student(adrian). 6. ? student(anna, engineering). 7 7. ? student(X, engineering). 8. ? student(X,fine-arts), course(fine_arts, Y). 9. ? field(_,X). 10. ? lab_number(_,X), field(X,Y). 11. ? lab_number(X,15), field(X,Y). 12. ? student(X), !, student(X,_). % note to cut here 13. ? student(X), student(X,_), !. 14. ? course(X,_), \+ student(_,X). % \+ is for negation (not) Q 8. Uni cation, Resolution, and Backtracking: Assume, you are working with the following knowledge base: house_elf(dobby). witch(hermione). witch(mcGonagall). witch(rita_skeeter). wizard(dobby). magic(X):- house_elf(X). magic(X):- wizard(X). magic(X):- witch(X). Write the details of steps of search (uni cation, resolutions, and back tracking) and also the answer for each of the following queries: ? magic(Hermione). ? magic(hermione). 8 4.3 Implementation Exercises Q 9. Assume, you are working with the following knowledge base:: family( person(john, cohen, date(17,may,1990), unemployed), person(lily, cohen, date(9,may,1990), unemployed),[] ). family( person(john, armstrong, date(7,may,1988), unemployed), person(lily, armstrong, date(29,may,1961), unemployed),[]). family( person(eric, baily, date(7,may,1963), works( bbc, 2200)), person(grace, baily, date(9,may,1965), works( ntu, 1000)), [ person(louie, baily, date(25,may,1983), unemployed) ] ). family( person(eric, baily, date(7,may,1963), works( acc, 21200)), person(grace, baily, date(9,may,1965), works(ntnu, 12000)), [ person( louie, baily, date(25,may,1983), unemployed) ]). family( person(eric, fox, date(27,may,1970), works(bbc, 25200)), person(grace, fox, date(9,may,1971), works(ntbu, 13000)), [ person(louie, fox, date(5,may,1993), unemployed) ]). family( person(tom, cohen, date(7,may,1960), works( bcd, 15200)), person(ann, cohen, date(29,may,1961), unemployed), [ person(pat, cohen, date(5,may,1983), works(bcd, 15200)), person(jim, cohen, date(5,may,1983), works(bcd, 15200))]). family( person(bob, armstrong, date(12,oct,1977), works(ntnu, 12000)), person(liz,armstrong, date(6,oct,1975), unemployed), [ person(bob, armstrong, date(6,oct,1999), unemployed), person(sam,armstrong, date(8,oct,1998), unemployed) ]). family( person(tony, oliver, date(7,may,1960), works( bbc, 35200)), person(anny, oliver, date(9,may,1961), unemployed), [ person(patty, oliver, date(8,may,1984), unemployed), person(jimey, oliver, date(5,may,1983), unemployed) ]). 9 family( person(jack, fox, date(27,may,1940), unemployed), person(jane, fox, date(9,aug,1941), works( ntu, 13050)), [ person(andy, fox, date(5,aug,1967), works(com, 12000)), person(kai, fox, date(5,jul,1969), unemployed) ]). husband(X) :- family( X, _, _). wife(X) :- family( _, X, _). child(X) :- family( _, _, Children), member(X, Children). exists(Person) :- husband(Person); wife(Person); child(Person). dateofbirth(person(_, _, Date, _), Date). salary(person(_, _, _, works(_, S)), S). salary(person(_, _, _, unemployed), 0). a) Write a prolog rule totalIncome/2 to compute the total income of a family. b) Write a prolog query to print total income of each family. c) Write a prolog query to print family details of each family that has income per family member less than 2000. d) Write a prolog query to print family details of each family where children’s total income is more than their parents. 10 Q 10. The following circuit represents a half-adder where A and B are the inputs, and S and C represent the Sum and Carry bits, respectively. a) Implement the above circuit in prolog. b) Write the query to calculate the outputs for S and C for A = 0 and B = _. Provide the output. Q 11. Write a Prolog query with arity 2 to return the rst n numbers of a Lucas sequence in a list. https://brilliant.org/wiki/lucas-numbers/ The Lucas sequence has the same recursive relationship as the Fibonacci sequence, where each term is the sum of the two previous terms, except that the rst two numbers in the sequence are: 2, and 1. The rst few elements of the sequence are: 2, 1, 3, 4, 7, 11, 18, … 11 5 What to Submit This assignment is submitted in two stages. Stage 1 – Fact Representation The rst part of the assignment (1) is submitted by Sunday, May 10th at Noon. It has to be completed by ALL members of the team in one submission le. The knowledge-base le must contain all the facts for all the members of the team, all merged in one single le. You submission includes one single le namely `schedule-studid.pl’ where studid is the id of the leader of the team. Failure to submit may result in 0 mark for the whole assignment for the whole team. Make sure there is no syntax error. Make sure the query in (2) succeeds. Test before submission. Do not include the query nor result of 2 in this submission. Stage 2 – Whole Assignment The whole assignment (including 1 and 2) is submitted by the due date under the corresponding assignment box. Your instructor will provide you with more details. Submission Notes Note: The following applies to stage 2 (Whole Assignment Submission). Clearly include the names and student IDs of all members of the team in the submission. Indicate the team leader. IMPORTANT: You are allowed to work on a team of 3 students at most (including yourself). Any teams of 4 or more students will result in 0 marks for all team members. If your work on a team, ONLY one copy of the assignment is to be submitted. You must make sure that you upload the assignment to the correct assignment box on Moodle. No email submissions are accepted. Assignments uploaded to the wrong system, wrong folder, or submitted via email will be discarded and no resubmission will be allowed. Make sure you can access Moodle prior to the submission deadline. The deadline will not be extended. 12 Naming convention for uploaded le: Create one zip le, containing all needed les for your assignment using the following naming convention. The zip le should be called a#_studids, where # is the number of the assignment, and studids is the list of student ids of all team members, separated by (_). For example, for the rst assignment, student 12345678 would submit a zip le named a1_12345678.zip. If you work on a team of two and your IDs are 12345678 and 34567890, you would submit a zip le named a1_12345678_34567890.zip. Submit your assignment electronically on Moodle based on the instruction given by your instructor as indicated above: https://moodle.concordia.ca Please see course outline for submission rules and format, as well as for the required demo of the assignment. A working copy of the code and a sample output should be submitted for the tasks that require them. A text le with answers to the dierent tasks should be provided. Put it all in a le layout as explained below, archive it with any archiving and compressing utility, such as WinZip, WinRAR, tar, gzip, bzip2, or others. You must keep a record of your submission con rmation. This is your proof of submission, which you may need should a submission problem arises. 6 Grading Scheme Q1-Q2 2 marks Q3-Q5 5 marks Q6 5 marks Q7 5 marks Q8 5 marks Q9 10 marks Q10 3 marks Q11 5 marks Total: 40 marks. 13 References 1. swi-prolog: https://swish.swi-prolog.org 2. Lucas sequence: https://brilliant.org/wiki/lucas-numbers/ 3. Half-Adder: http://www.circuitstoday.com/half-adder-and-full-adder 14
