Note that for this question, you can in addition use ``land" for the symbol A ` `lor" for the symbol V ``Inot" for the symbol- Given the following three sentences: A) Every mathematician is married to an engineer. B) A bachelor is not married to anyone. C) If George is a mathematician, then he is not a bachelor. a) Convert A,B,C into three FOL sentences, where Mn(x): x is a mathematician. Er(x): x is an engineer. Md(x,y): x is married to y. Br(x): x is a bachelor. george: George is a constant. b) Show that A does-not-entail C. (Hint: Consider defining an interpretation / such that / models A, but does-not-model C.) c) Show that (A,B) entails C. (Hint: For a given interpretation I, consider two difference cases, the case where Mn(george) is true, and the case Mn(george) is false. For both cases, argue that it is always that I models C). d) Convert A,B, Inot C into a set of clausal forms, number your clauses. (Note that C is negated here!) e) Derive the empty clause from the set of clauses obtained in d), using resolutions. Your answer should be in clearly steps, one example step is like: Step 5: C3 resolves with C7 on literal L, with substitution x/george, resulting C8: [Er(x)].

Note that for this question, you can in addition use ``land" for the symbol A ` `lor" for the symbol V ``Inot" for the symbol- Given the following three sentences: A) Every mathematician is married to an engineer. B) A bachelor is not married to anyone. C) If George is a mathematician, then he is not a bachelor. a) Convert A,B,C into three FOL sentences, where Mn(x): x is a mathematician. Er(x): x is an engineer. Md(x,y): x is married to y. Br(x): x is a bachelor. george: George is a constant. b) Show that A does-not-entail C. (Hint: Consider defining an interpretation / such that / models A, but does-not-model C.) c) Show that (A,B) entails C. (Hint: For a given interpretation I, consider two difference cases, the case where Mn(george) is true, and the case Mn(george) is false. For both cases, argue that it is always that I models C). d) Convert A,B, Inot C into a set of clausal forms, number your clauses. (Note that C is negated here!) e) Derive the empty clause from the set of clauses obtained in d), using resolutions. Your answer should be in clearly steps, one example step is like: Step 5: C3 resolves with C7 on literal L, with substitution x/george, resulting C8: [Er(x)].

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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