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In logic, a set of symbols is commonly used to express logical representation. The following table lists many common symbols, together with their name, how they should be read out loud, and the related field of mathematics.
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 formal languages, truth functions are represented by unambiguous symbols.This allows logical statements to not be understood in an ambiguous way. These symbols are called logical connectives, logical operators, propositional operators, or, in classical logic, truth-functional connectives.
Philosophy of logic is the area of philosophy that studies the nature of logic. [1] [2] Like many other disciplines, logic involves various philosophical presuppositions which are addressed by the philosophy of logic. [3]
philosophy of logic A branch of philosophy that examines the nature and scope of logic, including the assumptions, methodologies, and implications of various logical systems. platonism In the philosophy of mathematics, the view that abstract mathematical objects exist independently of human thought. Plato's beard
The corresponding logical symbols are "", "", [6] and , [10] and sometimes "iff".These are usually treated as equivalent. However, some texts of mathematical logic (particularly those on first-order logic, rather than propositional logic) make a distinction between these, in which the first, ↔, is used as a symbol in logic formulas, while ⇔ is used in reasoning about those logic formulas ...
In this sense, it forms one area of the philosophy of logic. [1] Central to philosophical logic is an understanding of what logic is and what role philosophical logics play in it. Logic can be defined as the study of valid inferences. [4] [6] [9] An inference is the step of reasoning in which it moves from the premises to a conclusion. [10]
The equality predicate (usually written '=') is also treated as a logical constant in many systems of logic. One of the fundamental questions in the philosophy of logic is "What is a logical constant?"; [1] that is, what special feature of certain constants makes them logical in nature? [2] Some symbols that are commonly treated as logical ...