Logic homework
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This document contains homework assignments on propositional and predicate logic for a 5th semester B. Sc. CSIT course. It includes: 1) Exercises on propositional logic operators and identities from the textbook. 2) A knowledge base to represent in propositional logic about whether it is raining and if Ann puts the top up on her convertible. 3) Exercises on predicate logic concepts like unification and representing family relationships in a story about a man who marries a widow and his father marries her daughter.
Logic homework
- 1. B. Sc. CSIT 5th Semester By Bal Krishna Subedi1 Home Works for Logic Propositional Logic 1. 7.4, 7.5, 7.7, 7.8 & 7.12 from Textbook (R&N) 2. The logical operator is read “if and only if”. P Q is defined as being equivalent to (P Q) ^ (Q P). Based on this definition, show that (P Q) is logically equivalent to (P Q) (Q ^ P). a. By using truth table. b. By a series of substitutions (use identities on page on Page 210) 3. Consider the knowledge base: If it is raining out then Ann puts the top up on her convertible. Ann did not put the top up on her convertible. (a) Describe a set of propositional letters which can be used to represent the knowledge base. (b) Translate the KB into propositional logic using your propositional letters from part a. (c) Is it raining? Answer this question by using logical inference rules with the KB. Predicate Logic 1. 8.2, 8.3, 8.4, 8.6, 8.7 & 8.9. 2. 9.2, 9.4, 9.9, 9.10, 9.11, 9.17, 9.18 & 9.19 3. Consider the following sentence in FOL: 3. Attempt to unify the following pair of expressions. Either show their most general unifiers or explain why they will not unify. a. P(X, Y) and p(a, Z) b. p(X, X) and p(a, b)
- 2. B. Sc. CSIT 5th Semester By Bal Krishna Subedi2 c. ancestor(X,Y) and ancestor (bill, father(bill)) d. ancestor (X, father(X)) and ancestor(david, george) e. q(X) and q(a) 4. The following story is from N. Wirth’s (1976) I married a widow (let’s call her W) who has a grown-up daughter (call her D). My father (F), who visited us quite often, fell in love with my step daughter and married her. Hence my father becomes my son-in-law and my step-daughter becomes my mother. Some months later, my wife gave birth to a son (S1), who becomes the brother-in-law of my father, as well as my uncle. The wife of my father, that is, my step-daughter, also had a son (S2). Using the predicate logic, create a set of expressions that represent the situation in the above story. Add expressions defining basic family relationships such as the definition of father-in-low and use modus ponen on this system to prove the conclusion that “I am my own grandfather”.