Semantics

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Semantics (from Ancient Greek: σημαντικός sēmantikós, “significant”) is that part of linguistics that studies the meaning of words (lexical semantics), of sets of individual letters (in and ancient alphabets) and sentences (phrasal semantics), and of texts. In linguistics, it was introduced in 1883 by M. Bréal to designate the until then neglected study of “the laws that preside over the transformation of meanings, the choice of new expressions, the birth and death of idioms.”

It is a science in close relationship with other disciplines, such as semiology, semiotics, logic, psychology, communication theory, stylistics, philosophy of language, linguistic anthropology and symbolic anthropology. By extension, in logic, the study of the relationships between expressions in a language and the objects to which those expressions refer.

A set of terms that have a semantic factor in common is called a semantic field.

The new science, illustrated by Bréal especially in Essai de sémantique (1897), had a precursor in the German humanist philologist C. C. Reisig, who had divided grammar into three sections: etymology, syntax and semasiology (1825). However, it is worth noting that annotations of semantic interest can already be found in ancient Greek and Latin authors.

Semantics has been defined as “a typical frontier science” because it involves specific competences of various disciplines, besides linguistics, and particularly of psychology, sociology, philosophy and semiology. Conceived at first as a historical science with the specific task of studying diachronically the evolution of meanings (attributable mainly to “enlargements”, “narrowings”, “transfers”, “worsening”, “improvements” of meaning, and classic rhetorical figures such as metaphor, metonymy, synecdoche, hyperbole, and lithothese), semantics has increasingly defined itself as a synchronic discipline (responsible for the description of the significant contents of single words, of more complex syntagmatic units and of whole sentences, and in particular for the study of the relations between language and thought).

Structural linguistics has renewed the methods and perspectives of semantic research by insisting above all on the fact that not only sounds and grammatical forms, but also words and their meanings must be studied not in isolation but in the wider context of their formal, notional, historical and stylistic relations, forming a system whose terms condition each other. F. de Saussure had already drawn attention to the associative relationships that unite words by sense and/or form; further progress in this direction was made by J. Trier (who introduced the theory of the “semantic field” for which every modification of a concept determines a change in related concepts and, consequently, in the words that express them), Ch. Bally (to whom we owe the notion of “associative field”), G. Matoré (who formulated the theory of “notional fields”), P. Guiraud (who elaborated the notion of “morpho-semantic field”).

More recently, S. Ullmann has proposed a functional classification of semantic changes, distinguishing between changes due to “linguistic conservatism” and those due to “linguistic innovation”, for which the latter can have transpositions of nouns or transpositions of senses, either by similarity or contiguity, and more complex composite transpositions. With his work, Ullmann laid the foundations of a typological semantics and floated the possibility of creating a “panchronic” semantics that would highlight universal elements common to all languages and all epochs.

The studies of semantics have become more and more intertwined with those of semiotics, which retrieves from linguistics the theories of meaning and extends them to all forms of signification. In this sense, the idea of “encyclopedia” formulated by U. Eco, as a rhizomatic structure of knowledge, fully falls within the scope of semantics. Similarly, the generative theory of meaning, as developed by A. J. Greimas, is configured as an attempt to formally explain the constitution of meaning, from the smallest units of the signifier to the most complex texts.

Logic

Semantics studies those notions that express relations between objects and designations such as, for example, that of denotation, satisfaction, definition, truth, and so on. If we have a theory T, given by a language L and a universe of objects U to which the terms of L refer, we say that the semantics of T is that particular meta-theory that studies the relations that exist between the language-object and the universe of the theory-object.

In order to be able to make a semantic investigation, it is necessary to have a meta-theoretical language that has signs that denote elements of the language-object, signs that denote elements of the universe of the theory-object and that can express the relationships that exist between them; moreover, it is necessary to have a precise procedure of interpretation that allows to make every sign of L correspond to an element of U.

With the work of G. F. Frege and his theory of meaning are laid the foundations of the distinction between semantics and syntax, but it is only after the crisis of the foundations and towards the end of the twenties that the semantic study of logical theories is developed. If the first investigations of L. Lowenheim and T. A. Skolem have an insiemistic and intuitive approach to semantic aspects, the necessity and the importance of a rigorous semantic approach to logical problems are becoming more and more evident.

The development of semantic research was subject to the solution of some fundamental problems, such as the need to distinguish between theory and metatheory, and in particular between the language of theory and metatheoretical language (a distinction that also reduces the possibility of antinomies); the need to establish the relationship between rigorously defined syntactic notions and intuitively accepted semantic notions. It was also necessary to clarify the notion of truth, given its centrality to every interpretative process. These problems were addressed in the twenties especially by the Polish schools of logic. It is to S. Lesniewski that we owe the awareness of the desirability of distinguishing between the language of which we speak and the language in which we speak, that is, between object language and metalanguage, as well as to A. Tarski in the thirties an awareness of the opportunity to distinguish between language of which we speak and language in which we speak, that is, between object language and metalanguage. Tarski in the thirties a rigorous clarification of semantics and the development of an adequate theory of truth.

Also in the thirties, Skolem, Tarski, K. Gödel and others gradually specified the relationship between syntax and semantics. Following Gödel’s theorem, semantic investigation is satisfactory only for elementary logic precisely because it shows the semantic incompleteness of logical systems of higher order than the first. It should be noted, however, that the methods of semantic investigation, reconnecting more closely to practical mathematical research, algebraic and topological in particular, have proved extremely fruitful for the latter, as evidenced by the works of L. Henkim, J. D. Monk, Tarski and A. Malcev. These methods are at the basis of the particularly fruitful developments of theories such as those of models that have their roots in Tarski’s semantic theory. It is precisely this fruitfulness that is at the root of the revival of semantic research in areas that are often particular and very diverse among themselves in the fifties and sixties by Tarski, Malcev, S. Kripke, C. R. Karp, R. Vaught.

Informatics

Defining the computational meaning of a program. When devising a programming language, the semantics of its constructs must be defined to ensure that a program actually performs the desired function. This semantics can be defined formally in terms of transformations of values over appropriate algbebraic domains, or informally, typically by expressing in natural language the requirements that a compiler or interpreter for the language must satisfy. As far as formal definition is concerned, we generally distinguish between denotational and operational semantics. The former allows to define what is the mathematical entity, for example a set, a relation or a function, computed by a certain program, so that two fundamental requirements are met:

  • that each program fragment has a denotation;
  • that the denotation of a compound fragment be incrementally obtainable so that it depends only on the denotations of the component fragments until the denotation of the entire program is constructed.

While this property is easily secured for expressions involving only the basic operations provided by the language, particular attention must be paid to constructing the meaning of fragments that incorporate alternative structures, of the if-then-else, iterative, while-type, or recursive type, that is, in which a program can call itself. For this reason, the construction of semantics requires that the space of denotations, i.e., of entities that can be taken as interpretations of the program, has a certain structure. Particularly used are the spaces that have a structure of complete partial order (cpo). In fact, continuous functions that transform elements of a cpo into elements of the same or another cpo can be used as definitions of the meaning of a program.

The semantics of programs acting on domains more complex than natural numbers requires richer algebraic structures, often defined by category theory. Operational semantics, on the other hand, defines the meaning of the program in terms of the state transformations of an abstract machine, in which, for example, particular registers maintain the value of the final result. In a programming language based on a virtual machine, such as Java or small talk, operational semantics is defined by specifying for each instruction the transformations that occur in the virtual machine as a result of its execution. Depending on the type of semantics adopted, a program may receive different interpretations.

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