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Deductive reasoning. Deductive reasoning is the process of drawing valid inferences. An inference is valid if its conclusion follows logically from its premises, meaning that it is impossible for the premises to be true and the conclusion to be false. For example, the inference from the premises "all men are mortal" and " Socrates is a man" to ...
A Mastermind player uses abduction to infer the secret colors (top) from summaries (bottom left) of discrepancies in their guesses (bottom right). Abductive reasoning (also called abduction, [1] abductive inference, [1] or retroduction[2]) is a form of logical inference that seeks the simplest and most likely conclusion from a set of observations.
Logical reasoning is a mental activity that aims to arrive at a conclusion in a rigorous way. It happens in the form of inferences or arguments by starting from a set of premises and reasoning to a conclusion supported by these premises. The premises and the conclusion are propositions, i.e. true or false claims about what is the case.
Transformation rules. In logic and the philosophy of logic, specifically in deductive reasoning, a rule of inference, inference rule or transformation rule is a logical form consisting of a function which takes premises, analyzes their syntax, and returns a conclusion (or conclusions). For example, the rule of inference called modus ponens ...
Universal generalization / instantiation. Existential generalization / instantiation. In propositional logic, material implication[1][2] is a valid rule of replacement that allows a conditional statement to be replaced by a disjunction in which the antecedent is negated. The rule states that P implies Q is logically equivalent to not- or and ...
Definition. The process by which a conclusion is inferred from multiple observations is called inductive reasoning. The conclusion may be correct or incorrect, or correct to within a certain degree of accuracy, or correct in certain situations. Conclusions inferred from multiple observations may be tested by additional observations.
Analogy. Analogy is a comparison or correspondence between two things (or two groups of things) because of a third element that they are considered to share. [1] In logic, it is an inference or an argument from one particular to another particular, as opposed to deduction, induction, and abduction. It is also used of where at least one of the ...
An inference is the dropping of a true premiss; it is the dissolution of an implication". [24] In other words, in a long "string" of inferences, after each inference we can detach the "consequent" "⊦q" from the symbol string "⊦p, ⊦(p⊃q)" and not carry these symbols forward in an ever-lengthening string of symbols.
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