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A set of rules can be used to infer any valid conclusion if it is complete, while never inferring an invalid conclusion, if it is sound. A sound and complete set of rules need not include every rule in the following list, as many of the rules are redundant, and can be proven with the other rules.
A rule of inference is a scheme of drawing conclusions that depends only on the logical form of the premises and the conclusion but not on their specific content. [39] [40] The most-discussed rule of inference is the modus ponens. It has the following form: p; if p then q; therefore q. This scheme is deductively valid no matter what p and q ...
If P, then Q. Not Q. Therefore, not P. The first premise is a conditional ("if-then") claim, such as P implies Q. The second premise is an assertion that Q, the consequent of the conditional claim, is not the case. From these two premises it can be logically concluded that P, the antecedent of the conditional claim, is also not the case. For ...
Example requires a quantifier over predicates, which cannot be implemented in single-sorted first-order logic: Zj → ∃X(Xj∧Xp). Quantification over properties Santa Claus has all the attributes of a sadist. Example requires quantifiers over predicates, which cannot be implemented in single-sorted first-order logic: ∀X(∀x(Sx → Xx) → ...
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The rules worked by querying and asserting values of the objects. The inference engine is an automated reasoning system that evaluates the current state of the knowledge-base, applies relevant rules, and then asserts new knowledge into the knowledge base. The inference engine may also include abilities for explanation, so that it can explain to ...
A 2016 study of a sample of academic journals (not news publications) that set out to test Betteridge's law and Hinchliffe's rule (see below) found that few titles were posed as questions and of those that were questions, few were yes/no questions and they were more often answered "yes" in the body of the article rather than "no".
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