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An interpretation is an assignment of meaning to the symbols of a formal language.Many formal languages used in mathematics, logic, and theoretical computer science are defined in solely syntactic terms, and as such do not have any meaning until they are given some interpretation.
Interpretation (logic), an assignment of meaning to the symbols of a formal language; De Interpretatione, a work by Aristotle; Exegesis, a critical explanation or interpretation of a text; Hermeneutics, the study of interpretation theory; Semantics, the study of meaning in words, phrases, signs, and symbols; Interpretant, a concept in semiotics
For example, in written text each symbol or letter conveys information relevant to the word it is part of, each word conveys information relevant to the phrase it is part of, each phrase conveys information relevant to the sentence it is part of, and so on until at the final step information is interpreted and becomes knowledge in a given domain.
Semantics studies meaning in language, which is limited to the meaning of linguistic expressions. It concerns how signs are interpreted and what information they contain. An example is the meaning of words provided in dictionary definitions by giving synonymous expressions or paraphrases, like defining the meaning of the term ram as adult male sheep. [22]
An idiom is an expression that has a figurative meaning often related, but different from the literal meaning of the phrase. Example: You should keep your eye out for him. A pun is an expression intended for a humorous or rhetorical effect by exploiting different meanings of words. Example: I wondered why the ball was getting bigger. Then it ...
Legal interpreting can be the consecutive interpretation of witnesses' testimony, for example, or the simultaneous interpretation of entire proceedings, by electronic means, for one person, or all of the people attending. In a legal context, where ramifications of misinterpretation may be dire, accuracy is paramount.
In this example, both sentences happen to have the common form () for some individual , in the first sentence the value of the variable x is "Socrates", and in the second sentence it is "Plato". Due to the ability to speak about non-logical individuals along with the original logical connectives, first-order logic includes propositional logic.
In the latter case, a (declarative) sentence is just one way of expressing an underlying statement. A statement is what a sentence means, it is the notion or idea that a sentence expresses, i.e., what it represents. For example, it could be said that "2 + 2 = 4" and "two plus two equals four" are two different sentences expressing the same ...