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.
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Logic homework
This document contains homework assignments for a 5th semester B.Sc. course in logic, including:
1) Exercises on propositional and predicate logic from textbooks.
2) Problems analyzing logical operators and knowledge bases using propositional logic.
3) Unification problems to combine logical expressions using predicate logic.
4) A story problem to represent family relationships in a situation using predicate logic and derive the conclusion that "I am my own grandfather."
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I am Asst. Professor at Center Department of Computer Science and IT, Tribhuvan University
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Logic homework
This document contains homework assignments for a 5th semester B.Sc. course in logic, including:
1) Exercises on propositional and predicate logic from textbooks.
2) Problems analyzing logical operators and knowledge bases using propositional logic.
3) Unification problems to combine logical expressions using predicate logic.
4) A story problem to represent family relationships in a situation using predicate logic and derive the conclusion that "I am my own grandfather."
Lecture 7 se
This chapter discusses the design and implementation of a system. It was prepared by Assistant Professor Bal Krishna Subedi of Tribhuvan University. The chapter contains 43 numbered sections that likely outline the various design considerations, implementation steps, and components of the system. It concludes by thanking the reader and inviting any queries about the content.
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Uncertainty
1) The document discusses reasoning with uncertainty in artificial intelligence and different approaches for handling uncertainty. It describes problems like partial observability, noisy sensors, uncertain action outcomes, and complexity of modeling.
2) Instead of providing all possible conditions for a rule, it is better to express the degree of belief in sentences using probabilities. For example, the probability that a toothache indicates a cavity could be 0.8.
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2. An agent receives percepts over time and maps these percept sequences to actions. Agents aim to be autonomous, interactive, reactive, and goal-directed.
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2) Ontologies define terminology and objects/relationships in a systematic way to enable knowledge sharing between agents.
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Logic 2
The document discusses predicate logic and its use in representing knowledge in artificial intelligence. It introduces several key concepts:
- Predicate logic uses predicates, constants, variables, functions and quantifiers to represent objects and their relations in a knowledge base.
- Well-formed formulas in predicate logic can be used to represent facts about the world. Logical inference rules like resolution and unification can be used to derive new facts or answer queries.
- Knowledge bases can be represented as sets of clauses in conjunctive normal form to apply inference rules like resolution and forward/backward chaining. Converting to clausal form involves techniques like Skolemization.
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Search 2
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Uncertainty
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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”.