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For example, in many variants of transformational grammar, the English active voice sentence "Emma saw Daisy" and its passive counterpart "Daisy was seen by Emma" share a common deep structure generated by phrase structure rules, differing only in that the latter's structure is modified by a passivization transformation rule.
Rules of inference are syntactical transform rules which one can use to infer a conclusion from a premise to create an argument. 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.
In logic, a rule of replacement [1] [2] [3] is a transformation rule that may be applied to only a particular segment of an expression. A logical system may be constructed so that it uses either axioms, rules of inference, or both as transformation rules for logical expressions in the system. Whereas a rule of inference is always applied to a ...
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 ...
The two representations are linked to each other by a set of transformation rules, the totality of these rules is what constitute grammar, and what a grammatical description of a language should present. Under this theory, a speaker must have access to both structures to interpret an expression.
In transformational grammar, systems of phrase structure rules are supplemented by transformation rules, which act on an existing syntactic structure to produce a new one (performing such operations as negation, passivization, etc.). These transformations are not strictly required for generation, as the sentences they produce could be generated ...
In propositional logic, material implication [1] [2] is a valid rule of replacement that allows a conditional statement to be replaced by a disjunction in which the antecedent is negated. The rule states that P implies Q is logically equivalent to not- P {\displaystyle P} or Q {\displaystyle Q} and that either form can replace the other in ...
The reciprocal transformation, some power transformations such as the Yeo–Johnson transformation, and certain other transformations such as applying the inverse hyperbolic sine, can be meaningfully applied to data that include both positive and negative values [10] (the power transformation is invertible over all real numbers if λ is an odd ...