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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.
Logical consequence is necessary and formal, by way of examples that explain with formal proof and models of interpretation. [1] A sentence is said to be a logical consequence of a set of sentences, for a given language , if and only if , using only logic (i.e., without regard to any personal interpretations of the sentences) the sentence must ...
Text inferencing describes the tacit or active process of logical induction or deduction during reading. Inferences are used to bridge current text ideas with antecedent text ideas or ideas in the reader's store of prior world knowledge. Text inferencing is an area of study within the fields of cognitive psychology and linguistics. Much of the ...
[68] For example, starting from the empirical observation that "all ravens I have seen so far are black", inductive reasoning can be used to infer that "all ravens are black". In a slightly weaker form, induction can also be used to infer an individual conclusion about a single case, for example, that "the next raven I will see is black".
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 ...
Pages in category "Rules of inference" ... This list may not reflect recent changes. ... Text is available under the Creative Commons Attribution-ShareAlike 4.0 ...
In the TE framework, the entailing and entailed texts are termed text (t) and hypothesis (h), respectively.Textual entailment is not the same as pure logical entailment – it has a more relaxed definition: "t entails h" (t ⇒ h) if, typically, a human reading t would infer that h is most likely true. [1]
Inference using vague concepts. Inferences that involve reasoning near the boundaries of a vague concept are often uncertain. 8. Finding expected utility. This is the problem of choosing between actions whose consequences are uncertain. In such a case, a choice may be made based on the likelihoods of the various outcomes with their desirability. 9.