# Symbolic Logic

Logic is the theory of the way in which people reason, with the aim of studying the principles of valid reasoning. The study of logic is the effort to determine the conditions under which one is justified in passing from given statements, called premises, to a conclusion that is claimed to follow from them. Logical validity is a relationship between the premises and the conclusion such that if the premises are true then the conclusion is true. There are several types of logic. The earliest and simplest of these is known as classical or traditional logic which was introduced by Aristotle who developed rules for correct syllogistic reasoning. Modern Logic: In the middle of the 19th century, the British mathematicians George Boole and Augustus De Morgan opened a new field of logic, now known as symbolic or modern logic, which was further developed by the German mathematician Gottlob Frege and especially by the British mathematicians Bertrand Russell and Alfred North Whitehead in Principia Mathematica (3 volumes, 1910-13). The logical system of Russell and Whitehead covers a far greater range of possible arguments than those that can be cast into syllogistic form. It introduces symbols for complete sentences and for the conjunctions that connect them, such as “or,””and,” and “If . . . then. . . .” It has different symbols for the logical subject and the logical predicate of a sentence; and it has symbols for classes, for members of classes, and for the relationships of class membership and class inclusion. It also differs from classical logic in its assumptions as to the existence of the things referred to in its universal statements.

Both classical logic and modern logic are systems of deductive logic. In a sense, the premises of a valid argument contain the conclusion, and the truth of the conclusion follows from the truth of the premises with certainty.

Both classical and modern logic in their usual forms assume that any well-formed sentence is either true or false.

LOGIC

Logic could be defined in verbal contents, as the art of correct reasoning. It is the study of principles and techniques use to distinguish good (correct) argument from (incorrect) argument. Logic is the analysis of language and its study involves the learning of its principles and methods employed in distinguish valid argument from those that are not valid. Symbolic Logic is a formal logic using symbols that is the branch of formal logic that studies the meaning and relationships of statements through precise mathematical methods and a standardized system of symbols and rules of inference.

We start our discussion by first examining what we mean by statement. STATEMENT/PROPOSITION

In our everyday language, we come across statements that may be interrogative, declarative or exclamatory. In this course a declarative sentence which is either true or false is called a statement. Thus, A proposition is any expression/statement that can either be true or false. One must be able to establish the truthfulness or falsehood of the statement or expression before it is considered a proposition. A proposition can either be asserted or denied. Any statement, expression or phrase that can neither be true (asserted) nor false (denied) is not a proposition. Hence questions, commands and exclamation are not propositions. e.g. Where are you?, May Almighty Allah bless you! are not propositions. Example1: each of the following is a proposition.

i. Kaduna is the capital of Kaduna state.(T)

ii. 5 + 3 = 53(F)

iii. Hardware and software are subsystem of personal computer. (P.C).(T) iv. ASICAS is located in Kano.(F)

v. Symbolic Logic is a course taken by computer science students in ASICAS.(T) Priori and Empirical Proposition

A proposition is a priori if its truth or falsity is capable of being known independent of any specific experience. On the other hand a statement/proposition is empirical if its truth or falsity...

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