(a) Propositional Logic Let F be the formula (A v B) –→ (B V A), and let G be the formula A→ (B → (¬B v ¬A)) →¬B. (i) Provide a constructive Sequent Calculus proof of F. (ii) Provide a constructive Natural Deduction proof of G. (iii) Is G satisfiable? Justify your answer.

(a) Propositional Logic Let F be the formula (A v B) –→ (B V A), and let G be the formula A→ (B → (¬B v ¬A)) →¬B. (i) Provide a constructive Sequent Calculus proof of F. (ii) Provide a constructive Natural Deduction proof of G. (iii) Is G satisfiable? Justify your answer.

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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Concept explainers

Inference in AI

The inference is finding a conclusion or result based on any data, events, and any information. Usually, there will be a set of conditions and the conclusion is made, which satisfies all the given conditions are true. The conclusion is made according to the inference rules. Any artificial intelligence agent or an intelligent system uses the inference engine to find a better result or output. The work of the inference engine is to analyze the fact and figures based on all circumstances. After the analysis, the machine concludes this fact and gives it to the agent. The agent uses this conclusion for further processing and decision-making. Intelligent systems will generate new logic from existing ones based on the facts.

Question

(a) Propositional Logic
Let F be the formula (A V B) –→ (B V A), and
let G be the formula A → (B → (¬B V ¬A)) →¬B.
2
(i) Provide a constructive Sequent Calculus proof of F.
(ii) Provide a constructive Natural Deduction proof of G.
(iii) Is G satisfiable? Justify your answer.

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