Symbolic Logic

Logic:

 Basic definition of logic is “Study of valid reasoning”. The main objective is to find whether the given set of arguments are valid (correct) or Invalid (incorrect).  Logic does not bother if the given argument or statements are true or not it only checks the truth or falsity of the inference in different cases. While talking about validity of an argument general acceptance in day-to-day life should not be considered. Reasoning of the logic can be two types.

Deductive reasoning: It is the process of reasoning from one or more statements to reach a logically certain conclusion.

Ex: If it rains, children will not play outside. Children are playing outside therefore it is not raining.

Inductive reasoning:  In this premises support the conclusion by providing strong evidence to it but it will not give absolute proof.

Ex: The grass got wet many times when it rained, therefore: the grass always gets wet when it rains.

Throughout the report we follow deductive reasoning. Logic is mainly identified by its form. Various forms of logic are:

1. Informal logic: It is the study of arguments which are in natural language. Proper format of arguments is not necessary.
2. Formal logic: It is the study of inference from the arguments which are formally arranged.
3. Symbolic logic: It is the study of arguments in the form of symbolic abstractions that retains the logical meaning and inference.
4. Mathematical logic: It is an extended form of symbolic logic which apply various mathematical theories (like set theorem) to the logic.

Symbolic logic: Symbolic logic is by far the simplest kind of logic. It is a great time-saver in argumentation. Additionally, it helps prevent logical confusion when dealing with complex arguments. Many lengthy arguments can be written in one line without any confusion.

Ex: If, if it rains then we go out and if we go out we will play, then, if it rains then we will play.

Let the case of raining be represented as R, going out as O and playing as P. Then the given statement can be written as

[pic 1]

Arguments: With respect to logic, arguments are series of statements which are presented in a logical order to present a logical conclusion.  Arguments consists of a set of premises followed by a conclusion. Premises are the statements which support conclusion. Formal definition of a statement is “A sentence which is either true or false but not both”.

Ex: “It is raining” is a statement. But “it might rain” is not a statement.

Example of argument:

[pic 2]

Validity and Soundness:

Validity is logical correctness of an argument. An argument is said to be valid if the conclusion is true when the premises are true. We cannot say that the argument is invalid if the conclusion is false or valid when the conclusion is true. An argument is sound if it is valid and premises are true. If a conclusion of an argument is valid then grammatically similar statement of that conclusion might not valid that is, not good cannot be considered as bad.