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Prolog Programming Exercises on Fibonacci, GCD, and First-Order Logic

This document outlines a series of intelligent systems programming exercises using Prolog, focusing on foundational concepts. The exercises include a program to calculate Fibonacci numbers using a recursive function, finding the greatest common divisor (GCD) through subtraction-based recursion, and various queries involving list manipulations. Additionally, the document presents first-order logic (FOL) statements that express relationships regarding students' love for AI, including rules for quantifiers such as "all," "some," "at least two," "exactly two," and "at most two."

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Prolog Programming Exercises on Fibonacci, GCD, and First-Order Logic

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  1. King Saud University College of Computer and Information Sciences Information Technology Department IT327 - Intelligent systems Prolog And FOL Exercises

  2. Question 1 • Write a Prolog Program to find Fibonnaci Number defined as follows: f(1) = 1, f(2) = 1, ∀ n > 2 : f(n) = f(n − 1) + f(n − 2) fibonacci(1,1). fibonacci(2,1). fibonacci(N,F) :- N>2, N1 is N-1, fibonacci(N1,F1), N2 is N-2, fibonacci(N2,F2), F is F1+F2.

  3. Question 2 • Write a Prolog program to find the greatest common divisor using the following algorithm gcd(a,b) = a if a=b gcd(a,b) = gcd(a-b,b) if a>b gcd(a,b) = gcd(a,b-a) if b>a gcd(A,A,A). gcd(A,B,Result) :- (A>B -> (Temp is A-B, gcd(Temp,B,Result)); B>A -> (Temp is B-A, gcd(A,Temp,Result))).

  4. Question 3 Solve the following Prolog queries ?- op(X) is op(1). ERROR: Arithmetic: ‘op/1’ is not a function ?- op(X) = op(1). X = 1 ?- op(op(Z),Y) = op(X, op(1)). Y = op(1) Z = _G157 X = op(_G157) ?- op(X,Y) = op(op(Y),op(X)). X = op(op(op(op(op(op(op(op(op(op(...)))))))))) Y = op(op(op(op(op(op(op(op(op(op(...))))))))))

  5. Question 4 Solve the following Prolog queries using lists ?-[1,2,3] = [1|X]. X = [2,3] ?- [1,2,3] = [1,2|X]. X = [3] ?- [1 | [2,3]] = [1,2,X]. X = 3 ?- [1 | [2,3,4]] = [1,2,X]. No ?- [1 | [2,3,4]] = [1,2|X]. X = [3,4]

  6. FOL question Express the following sentences in first-order logic: (a) All students love AI (b) Some students love AI (c) At least two students love AI (d) Exactly two students love AI (e) At most two students love AI

  7. FOL question • All students love AI • ∀ x Student(x) => Loves(x, AI) • Some students love AI • Ǝ x Student(x)  Loves(x, AI) • At least two students love AI  • Ǝ x,y (x≠y)  Student(x)  Loves(x,AI)  Student(y)  Loves(y,AI) • Exactly two students love AI • Ǝ x,y ∀ z x≠yx≠zy≠z Student(x)  Loves(x,AI)  Student(y)  Loves(y,AI)  Student(z)  ┐Loves(z,AI) • Or • Ǝ x,y (x≠y Student(x)  Loves(x,AI)  Student(y)  Loves(y,AI)  ∀ z (Student(z)  Loves(z,AI) < --> (x=z V y=z)) ) • At most two students love AI ∀ x,y ,z Student(x)  Loves(x,AI)  Student(y)  Loves(y,AI)  Student(z)  Loves(z,AI)  (x=y Vx=z V y=z)

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