An abductive meta-interpreter

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Two kinds of logical reasoning can be distinguished in addition to formal deduction: induction and abduction. Given a precondition, a conclusion and a rule that implies the conclusion given the precondition, we can differentiate the three kinds of logical reasoning developed by the philosopher C.S. Peirce.

  • Deductive reasoning determines whether the truth of a conclusion can be determined for that rule, based solely on the truth of the premises. Mathematical logic and philosophical logic are examples of this type of reasoning.
  • Inductive reasoning attempts to support a determination of the rule. It hypothesizes a rule after numerous examples are taken to be a conclu- sion that follows from a precondition in terms of such a rule.
  • Abductive reasoning/ given a true conclusion and a rule, it attempts to select some possible premises that, if true, can support the conclusion. This kind of reasoning can be used to develop a hypothesis, which in turn can be tested by additional reasoning or data. Detectives and diagnosticians often use this type of reasoning.

It is important to notice that inductive and abductive reasoning are not sound, in other words, they do not contain in themselves their logical validity and must be confirmed empirically: confirmation can never be absolute, but only in terms of probability.