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Inferences are steps in reasoning, moving from premises to logical consequences; etymologically, the word infer means to "carry forward". Inference is theoretically traditionally divided into deduction and induction , a distinction that in Europe dates at least to Aristotle (300s BCE).
[23] [3] An inference is the mental process of reasoning that starts from the premises and arrives at the conclusion. [18] [24] But the terms "argument" and "inference" are often used interchangeably in logic. The purpose of arguments is to convince a person that something is the case by providing reasons for this belief.
Each logic operator can be used in an assertion about variables and operations, showing a basic rule of inference. Examples: The column-14 operator (OR), shows Addition rule: when p=T (the hypothesis selects the first two lines of the table), we see (at column-14) that p∨q=T.
An example of ampliative reasoning is the inference from the premise "every raven in a random sample of 3200 ravens is black" to the conclusion "all ravens are black": the extensive random sample makes the conclusion very likely, but it does not exclude that there are rare exceptions. [36]
For example, the rule of inference called modus ponens takes two premises, one in the form "If p then q" and another in the form "p", and returns the conclusion "q". The rule is valid with respect to the semantics of classical logic (as well as the semantics of many other non-classical logics ), in the sense that if the premises are true (under ...
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.
These two definitions of formal logic are not identical, but they are closely related. For example, if the inference from p to q is deductively valid then the claim "if p then q" is a logical truth. [16] Formal logic needs to translate natural language arguments into a formal language, like first-order logic, to assess whether they are valid.
Plausible reasoning can be tested, and by this means, confirmed or refuted. Probing into plausible reasoning in a dialogue is a way of testing it. Plausible reasoning admits of degrees by testing, but of a kind different from those the standard probability values and Bayesian rules used in Pascalian probability