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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.
The Polish logician Alfred Tarski identified three features of an adequate characterization of entailment: (1) The logical consequence relation relies on the logical form of the sentences: (2) The relation is a priori, i.e., it can be determined with or without regard to empirical evidence (sense experience); and (3) The logical consequence ...
Inferences are steps in logical 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).
Logical reasoning happens by inferring a conclusion from a set of premises. [3] Premises and conclusions are normally seen as propositions. A proposition is a statement that makes a claim about what is the case. In this regard, propositions act as truth-bearers: they are either true or false. [18] [19] [3] For example, the sentence "The water ...
Corner quotes, also called “Quine quotes”; for quasi-quotation, i.e. quoting specific context of unspecified (“variable”) expressions; [3] also used for denoting Gödel number; [4] for example “āGā” denotes the Gödel number of G. (Typographical note: although the quotes appears as a “pair” in unicode (231C and 231D), they ...
A male cat paying a "call" on a female cat, who then serves up kittens, insinuating that the "results" of children is predicated on a male "catcall". An innuendo is a hint, insinuation or intimation about a person or thing, especially of a denigrating or derogatory nature.
An immediate inference is an inference which can be made from only one statement or proposition. [1] For instance, from the statement "All toads are green", the immediate inference can be made that "no toads are not green" or "no toads are non-green" (Obverse).
If P and Q are "equivalent" statements, i.e. , it is possible to infer P under the condition Q. For example, the statements "It is August 13, so it is my birthday" P → Q {\displaystyle P\to Q} and "It is my birthday, so it is August 13" Q → P {\displaystyle Q\to P} are equivalent and both true consequences of the statement "August 13 is my ...