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A variety of basic concepts is used in the study and analysis of logical reasoning. Logical reasoning happens by inferring a conclusion from a set of premises. [3] Premises and conclusions are normally seen as propositions. A proposition is a statement that makes a claim about what is the case.
A way of writing mathematical and logical expressions where the operator precedes its operands, facilitating unambiguous interpretation without parentheses. prelinearity axiom The formula (P → Q) ∨ (Q → P). [237] [238] premise A statement in an argument that provides support or evidence for the conclusion. prenex normal form
An example of this is the use of the rules of inference found within symbolic logic. Aristotle held that any logical argument could be reduced to two premises and a conclusion. [2] Premises are sometimes left unstated, in which case, they are called missing premises, for example: Socrates is mortal because all men are mortal.
For example, it could be said that "2 + 2 = 4" and "two plus two equals four" are two different sentences expressing the same statement. As another example, consider that the Arabic numeral '7', the Roman numeral 'VII', and the English word 'seven' are all distinct from the underlying number .
For example, if A. Plato was mortal, and B. Socrates was like Plato in other respects, then asserting that C. Socrates was mortal is an example of argument by analogy because the reasoning employed in it proceeds from a particular truth in a premise (Plato was mortal) to a similar particular truth in the conclusion, namely that Socrates was mortal.
The word "logic" originates from the Greek word logos, which has a variety of translations, such as reason, discourse, or language. [4] Logic is traditionally defined as the study of the laws of thought or correct reasoning, [5] and is usually understood in terms of inferences or arguments. Reasoning is the activity of drawing inferences.
Logic is the formal science of using reason and is considered a branch of both philosophy and mathematics and to a lesser extent computer science. Logic investigates and classifies the structure of statements and arguments, both through the study of formal systems of inference and the study of arguments in natural language .
In this way all logical connectives can be expressed in terms of preserving logical truth. The logical form of a sentence is determined by its semantic or syntactic structure and by the placement of logical constants. Logical constants determine whether a statement is a logical truth when they are combined with a language that limits its meaning.