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The following table lists many common symbols, together with their name, how they should be read out loud, and the related field of mathematics. Additionally, the subsequent columns contains an informal explanation, a short example, the Unicode location, the name for use in HTML documents, [ 1 ] and the LaTeX symbol.
A logical rule that justifies the transition from a set of premises to a conclusion, forming the basis of deductive reasoning. rule of replacement A rule in formal logic allowing for the substitution of equivalent expressions within logical proofs, maintaining the validity of the argument.
For valid arguments, the logical structure of the premises and the conclusion follows a pattern called a rule of inference. [12] For example, modus ponens is a rule of inference according to which all arguments of the form "(1) p , (2) if p then q , (3) therefore q " are valid, independent of what the terms p and q stand for. [ 13 ]
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.
Naturalistic fallacy – inferring evaluative conclusions from purely factual premises [105] [106] in violation of fact-value distinction. Naturalistic fallacy (sometimes confused with appeal to nature) is the inverse of moralistic fallacy. Is–ought fallacy [107] – deduce a conclusion about what ought to be, on the basis of what is.
The Wason selection task (or four-card problem) is a logic puzzle devised by Peter Cathcart Wason in 1966. [1] [2] [3] It is one of the most famous tasks in the study of deductive reasoning. [4] An example of the puzzle is: You are shown a set of four cards placed on a table, each of which has a number on one side and a color on the other.
A truth table is a mathematical table used in logic—specifically in connection with Boolean algebra, Boolean functions, and propositional calculus—which sets out the functional values of logical expressions on each of their functional arguments, that is, for each combination of values taken by their logical variables. [1]
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 .