Khadija Khaldi, Romita Banerjee and Christoph F. EickCOSC 4368: Fundamentals of Artificial Intelligence Spring 2019Problem Set3 (Individual Tasks) Version 4Deadline: Su. April 28, 11p (3% bonus); Wednesday, May 1, 11a (the latest)Available Points: 57Khadija Khaldi, Romita Banerjee and Christoph F. EickCOSC 4368: Fundamentals of Artificial Intelligence Spring 2019Problem Set3 (Individual Tasks) Version 4Deadline: Su. April 28, 11p (3% bonus); Wednesday, May 1, 11a (the latest) Available Points: 5712. Logical Reasoning (4 points) KhadijaShow using Resolution (and not by using other methods!):(1) xyz (P(x,y,z)  R(x,y) )(2) rs (P(s,s,t)  Q(s,t) )(3) ab (Q(a,a)  R(b,a) )(4) xy (R(x,y)  R(y,y) )(5) P(4,4,4)(6) ~Q(4,5)|-(X) R(4,4)First transform the FOPL formulas into clauses, and then the hunt for the empty clausecan begin! 13. Bayes’ Theorem and Belief Networks (9 points) RomitaFig. 1: Thomas Bayes 1740—279 years ago!a) Assume we have 3 symptoms S1, S2, S3, a disease D and the following probabilities:P(D)=0.01 P(S1)=P(S2)=P(S3)=0.02; P(S1|D)=0.1; P(S2|D)=0.02; P(S3|D)=0.002.How would a naïve Bayesian system compute the following probability? P(D|S1,S2,S3)=…b) Now assume the following additional knowledge has become available:P(S1,S2)=0.0002; P(S3|S1,S2)=0.08; P(S1,S2,S3|D)=0.000032; how would you usethis information to obtain a “better” estimation of P(D|S1,S2,S3)?c) How can the discrepancy with respect to the obtained probabilities between cases a)and b) be explained? Why are the numbers you obtain different? What does thisdiscrepancy tell you about naïve Bayesian systems in general?ABDECd) Assume that the following belief network is given that consists of nodes A, B, C, D, and E that can take values of true and false. - Is A|D,B d-separable from C|D,B? Give reasons for your answer! - Is A,E| d-separable from C|? Give reasons for your answer! :=”no evidence” 14. Weight Learning Computations in Neural Networks (7 points) KhadijaAssume we a 3-layer NN that is depicted in Fig. 2 is given that has 3 inputs X1, X2, andX3. A training set D is given that consists of the following examples: (1,1,1,1) and (0, 0, 1, 0),indicating values for X1, X2, X3 and the “desired” activation for O6. Assume that theinitial/current weights are w14 = 0.2, w15 = 0.2, w24 = 0.2, w25 = 0.2, w34 = 0.2, w35 =0.2, w36 = 0.5, w46 = 0.5, and w56 = 0.5. Use =0.5 as your learning rate. Show whatnew weights will be obtained after processing the two training instances of data set D.Use g(x) = 1/(1+e**(-x)) as the activation function; that is: g'(x)=(e**(-x))/(1+e**(-x))**2). List all important computations that lead to the reported weight updates. S# X1 X2 X3 O6 Des-O6 Error w14 w15 w24 w25 w34 w35 w36 w46 w56 0 0.2 0.2 0.2 0.2 0.2 0.2 0.5 0.5 0.51 1 1 1 12 0 0 1 015. Using a Belief Network Tool (20 points) KhadijaFig. 3: Multiple Astronomers Looking at the SkyAssume we have 3 astronomers in different parts of the world who make measurementsM1, M2, and M3 of the number1 of stars N in some region of the sky. Normally, there is aprobability of 0.05 that the astronomer counts a single star twice (overcounts by one star;you can assume that the three astronomers never undercount; moreover, if there is no starvisible (N=0) the astronomer never overcounts). Moreover, there is a 10% probability(P(Fi=1)=0.1 for i=1,2,3) that a telescope is out of focus (represented using randomvariables F1, F2, and F3), in which the astronomer undercounts by 2 or more stars (e.g. ifN is 4 and her telescope is out of focus, the astronomer will count 2, 1 or 0 stars; you canassume if information is missing that each case has the same probability). Design a beliefnetwork, and compute the probability of the other variables assuming the followingpieces of evidence are given (feel free to use Netica (http://www.norsys.com/download.html ) or anyanother belief network tool to compute your answer2!): 1. M1=3 M2=3 M3=1 2. M1=3 M2=3 M3=03. N=4, M2=1, M3=04. M1=0 M2=3 M3=25. N=3 F1=0 F2=0 F3=16. M1=4 M2=4 F3=1Submit the complete Belief Network you created—including all its probability tables—,and the findings you obtained for the six cases listed above!1 You can assume that N is limited to 4—but the astronomer do not know that: M1, M2 and M3 are therefore limited to values 0 through 5.2 Including the answer ‘inconsistent’ in the case that the evidence is inconsistent, e.g, the evidence N=1 M1=3 is inconsistent—as it is ‘impossible’ because astronomer1 never overcounts by more than 1 star!16. Ethical Problems of AI (17 points) RomitaWrite an essay of at least 800 words, focusing on the Ethics and Governance of ArtificialIntelligence Systems. Your essay should cover issues like balance between regulation andinnovation, how AI is used to spread information, how to ensure that the AI systemsfollow our principles when making decisions and what responsibilities should they haveamong others. Fig. 4: AI & Ethics Be aware of the fact that plagiarism will not be tolerated in this course; however, thisdoes not mean that you are not allowed to use material on the internet and taken from thescientific literature when writing your essay; you just need to cite the material you usedand you will need to use quotations, if you use (parts of) sentences “unchanged” fromother publications in your essay!Some hopefully useful links for identifying a topic for your essay:1. http://web.stanford.edu/class/cs122/2. https://www.vanderbilt.edu/strategicplan/undergraduate-residential-education/universitycourses-2018/ethics_of_artificial_intelligence.php3.