Search results
Results From The WOW.Com Content Network
Inductive reasoning refers to a variety of methods of reasoning in which broad generalizations or principles are derived from a set of observations. [1] [2] Unlike deductive reasoning (such as mathematical induction), where the conclusion is certain, given the premises are correct, inductive reasoning produces conclusions that are at best probable, given the evidence provided.
Mathematical induction can be informally illustrated by reference to the sequential effect of falling dominoes. [1] [2]Mathematical induction is a method for proving that a statement () is true for every natural number, that is, that the infinitely many cases (), (), (), (), … all hold.
While deductive logic allows one to arrive at a conclusion with certainty, inductive logic can only provide a conclusion that is probably true. [non-primary source needed] It is mistaken to frame the difference between deductive and inductive logic as one between general to specific reasoning and specific to general reasoning. This is a common ...
Here, the inductive bias is a logical formula that, together with the training data, logically entails the hypothesis generated by the learner. However, this strict formalism fails in many practical cases in which the inductive bias can only be given as a rough description (e.g., in the case of artificial neural networks), or not at all.
Petals Around the Rose is a mathematically challenging puzzle in which the object is to work out the formula by which a number is derived from the roll of a set of five or six dice. It is often used as an exercise in inductive reasoning . [ 1 ]
Argument from analogy is a special type of inductive argument, where perceived similarities are used as a basis to infer some further similarity that has not been observed yet. Analogical reasoning is one of the most common methods by which human beings try to understand the world and make decisions. [ 1 ]
If an instance in which the phenomenon under investigation occurs, and an instance in which it does not occur, have every circumstance save one in common, that one occurring only in the former; the circumstance in which alone the two instances differ, is the effect, or cause, or an indispensable part of the cause, of the phenomenon.
Pure inductive logic (PIL) is the area of mathematical logic concerned with the philosophical and mathematical foundations of probabilistic inductive reasoning. It combines classical predicate logic and probability theory ( Bayesian inference ).