The validity conditions of various sentences we may encounter in arguments will depend upon their meaning, and so conscientious logicians cannot completely avoid the need to provide some treatment of the meaning of these sentences. [This is false. The validity of an argument does not depend at all on sentence meaning. "If P, then Q. P. Therefore, Q." is a valid argument regardless of the meaning of 'P' and 'Q'.] 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. Proposition is a term used in logic to describe the content of assertions. ...
Until the advent of modern logic, Aristotle's Organon, especially On Interpretation, 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. This article is about Aristotles logical works. ... De Interpretatione or Hermeneutics (Peri Hermeneias) is a work of the ancient Greek philosopher Aristotle, mainly on the philosophy of language. ... In language and logic, quantification is a construct that specifies the extent of validity of a predicate, that is the extent to which a predicate holds over a range of things. ... The problem of multiple generality names a failure in Aristotelian logic to describe certain intuitively valid inferences. ... Traditional logic, also known as term logic, is a loose term for the logical tradition that originated with Aristotle and survived broadly unchanged until the advent of modern predicate logic in the late nineteenth century. ...
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 the truth values "true" and "false". Model-theoretic semantics provides the foundations for an approach to the theory of meaning known as Truth-conditional semantics, which was pioneered by Donald Davidson. Kripke semantics introduces innovations, but is broadly in the Tarskian mold.
Proof-theoretic semantics associates the meaning of propositions with the roles that they can play in inferences. Gerhard Gentzen, Dag Prawitz and Michael Dummett are generally seen as the founders of this approach; it is heavily influenced by Ludwig Wittgenstein's later philosophy, especially his aphorism "meaning is use".
Truth-value semantics (also commonly referred to as substitutional quantification) was advocated by Ruth Barcan Marcus for modal logics in the early 1960s and later championed by Dunn, Belnap, and Leblanc for standard first-order logic. James Garson has given some results in the areas of adequacy for intensional logics outfitted with such a semantics. The truth conditions for quantified formulas are given purely in terms of truth with no appeal to domains whatsoever (and hence its name truth-value semantics).
Game-theoretical semantics has made a resurgence lately mainly due to Jaakko Hintikka for logics of (finite) partially ordered quantification which were originally investigated by Leon Henkin who studied Henkin quantifiers.
Probabilistic semantics originated from H. Field and has been shown equivalent to and a natural generalization of truth-value semantics. Like truth-value semantics, it is also non-referential in nature.
In theoretical computer science, formalsemantics is the field concerned with the rigorous mathematical study of the meaning of programming languages and models of computation.
The formalsemantics of a language is given by a mathematical model that describes the possible computations described by the language.
Operational semantics loosely corresponds to interpretation, although again the "implementation language" of the interpreter is generally a mathematical formalism.
Semantics is contrasted with two other aspects of meaningful expression, namely, syntax, the construction of complex signs from simpler signs, and pragmatics, the practical use of signs by agents or communities of interpretation in particular circumstances and contexts.
In linguistics, semantics is the subfield that is devoted to the study of meaning, as borne on the syntactic levels of words, phrases, sentences, and sometimes larger units of discourse, generically referred to as texts.
In psychology, semantic memory is memory for meaning, in other words, the aspect of memory that preserves only the gist, the general significance, of remembered experience, while episodic memory is memory for the ephemeral details, the individual features, or the unique particulars of experience.
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