Propositional Logic, Natural Rules for Deduction, Derived Rules for Deduction, and Predicate Logic

The aim of logic in computer science is to develop languages to model the situations we encounter as computer science professionals, in such a way that we can reason about them formally. Reasoning about situations means constructing arguments about them; we want to do this formally, so that the arguments are valid and can be defended rigorously, or executed on a machine.

What you’ll learn

- Understand the basics of Propositional logic.
- Acquire skills on natural detection rules to handle Propositional logic.
- Acquire skills on derived rules to handle Propositional logic.
- Understand the First order Logic.

Course Content

- Introduction to propositional Logic –> 5 lectures • 58min.
- Natural Deduction of Propositional Logic –> 3 lectures • 45min.
- Derived rules for Propositional Logic –> 3 lectures • 29min.
- Introduction to Predicate Logic –> 3 lectures • 24min.

Requirements

The aim of logic in computer science is to develop languages to model the situations we encounter as computer science professionals, in such a way that we can reason about them formally. Reasoning about situations means constructing arguments about them; we want to do this formally, so that the arguments are valid and can be defended rigorously, or executed on a machine.

In order to make arguments rigorous, we need to develop a language in which we can express sentences in such a way that brings out their logical structure. The language we begin with is the language of propositional logic. It is based on propositions, or declarative sentences which one can, in principle, argueas being true or false.

The outline of this course is given as,

Introduction to Propositional Logic, Parse tree, valuation of Propositional Logic statements, Model in propositional logic

How do we go about constructing a calculus for reasoning about propositions given a certain arrangement of premises. – Natural Rules for Deduction, Examples of Natural Deduction Rules

Derived Rules for Deduction, Proof by contradiction, Modus Tollens,Law of Excluded middle portion and Double negation elimination

Introduction to Predicate Logic, Natural language statements to Predicate logic statements

Parse tree, substitution and Model in First order logic