   in logic, formal semantics or logical semantics,winfried nÃ¶th handbook of semiotics p.103p.64pp.32-3 is the study of the semantics, or interpretations, of formal and (idealizations of) natural languages usually trying to capture the pre-theoretic notion of entailment. (although both linguistics and logic lay claim to providing theories of natural language, according to geach, logic generally ignores the "idiotism of idiom", and sees natural languages as cluttered with idioms of no logical interest.) the truth conditions of various sentences we may encounter in arguments will depend upon their meaning, and so logicians cannot completely avoid the need to provide some treatment of the meaning of these sentences. the semantics of logic refers to the approaches that logicians have introduced to understand and determine that part of meaning in which they are interested; the logician traditionally is not interested in the sentence as uttered but in the proposition, an idealised sentence suitable for logical manipulation. until the advent of modern logic, aristotle's organon, especially de interpretatione, provided the basis for understanding the significance of logic. the introduction of quantification, needed to solve the problem of multiple generality, rendered impossible the kind of subject-predicate analysis that governed aristotle's account, although there is a renewed interest in term logic, attempting to find calculi in the spirit of aristotle's syllogistic but with the generality of modern logics based on the quantifier. the main modern approaches to semantics for formal languages are the following: * model-theoretic semantics is the archetype of alfred tarski's semantic theory of truth, based on his t-schema, and is one of the founding concepts of model theory. this is the most widespread approach, and is based on the idea that the meaning of the various parts of the propositions are given by the possible ways we can give a recursively specified group of interpretation functions from them to some predefined mathematical domains: an interpretation of first-order predicate logic is given by a mapping from terms to a universe of individuals, and a mapping from propositions to th
Philosophy_of_language Semantics