Mathematical logic is often used for logical proofs. The following are some examples of predicates − A predicate with variables can be made a proposition by either assigning a value to the variable or by quantifying the variable. It is because unless we give a specific value of A, we cannot say whether the statement is true or false.Ī predicate is an expression of one or more variables defined on some specific domain. "12 + 9 = 3 – 2", it returns truth value FALSE."Man is Mortal", it returns truth value TRUE.Some examples of Propositions are given below − The connectives connect the propositional variables. We denote the propositional variables by capital letters (A, B, etc). A propositional consists of propositional variables and connectives. Rules of Inference provide the templates or guidelines for constructing valid arguments from the statements that we already have.Ī proposition is a collection of declarative statements that has either a truth value "true" or a truth value "false". Rules of Inference − To deduce new statements from the statements whose truth that we already know, Rules of Inference are used. A predicate represents an expression of one or more variables. Predicate Logic − Predicate Logic deals with predicates, which are propositions containing variables. The purpose is to analyse these statements either individually or in a composite manner. Propositional Logic − Propositional Logic is concerned with statements to which the truth values, "true" and "false", can be assigned. Mathematical logics can be broadly categorized into three categories.
It has many practical applications in computer science like design of computing machines, artificial intelligence, definition of data structures for programming languages etc. Logical reasoning provides the theoretical base for many areas of mathematics and consequently computer science. Greek philosopher, Aristotle, was the pioneer of logical reasoning. The rules of mathematical logic specify methods of reasoning mathematical statements.
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