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A sentence can be viewed as expressing a proposition, something that must be true or false. The restriction of having no free variables is needed to make sure that sentences can have concrete, fixed truth values : as the free variables of a (general) formula can range over several values, the truth value of such a formula may vary.
The fundamental difference between modern formal logic and traditional, or Aristotelian logic, lies in their differing analysis of the logical form of the sentences they treat: On the traditional view, the form of the sentence consists of (1) a subject (e.g., "man") plus a sign of quantity ("all" or "some" or "no"); (2) the copula , which is of ...
Students learn spelling through the Carden "controls", a set of rules for deconstructing a word into its basic phonic parts. The controls are essentially a distillation of classic dictionary marks, but are "presented in such a way that the students are able to remember how and why a word is spelled" and to also explain the reasons why letters are pronounced differently. [4]
A formal grammar (also called formation rules) is a precise description of the well-formed formulas of a formal language. It is synonymous with the set of strings over the alphabet of the formal language which constitute well formed formulas. However, it does not describe their semantics (i.e. what they mean).
Traditional grammar (also known as classical grammar) is a framework for the description of the structure of a language or group of languages. [1] The roots of traditional grammar are in the work of classical Greek and Latin philologists. [2] The formal study of grammar based on these models became popular during the Renaissance. [3]
In practice, there are many languages that can be described by rules, such as regular languages or context-free languages. The notion of a formal grammar may be closer to the intuitive concept of a "language", one described by syntactic rules. By an abuse of the definition, a particular formal language is often thought of as being accompanied ...
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