Formal semantics (natural language)

Formal semantics is the scientific study of linguistic meaning through formal tools from logic and mathematics. It is an interdisciplinary field, sometimes regarded as a subfield of both linguistics and philosophy of language. Formal semanticists rely on diverse methods to analyze natural language. Many examine the meaning of a sentence by studying the circumstances in which it would be true. They describe these circumstances using abstract mathematical models to represent entities and their features. The principle of compositionality helps them link the meaning of expressions to abstract objects in these models. This principle asserts that the meaning of a compound expression is determined by the meanings of its parts.

Propositional and predicate logic are formal systems used to analyze the semantic structure of sentences. They introduce concepts like singular terms, predicates, quantifiers, and logical connectives to represent the logical form of natural language expressions. Type theory is another approach utilized to describe sentences as nested functions with precisely defined input and output types. Various theoretical frameworks build on these systems. Possible world semantics and situation semantics evaluate truth across different hypothetical scenarios. Dynamic semantics analyzes the meaning of a sentence as the information contribution it makes.

Using these and similar theoretical tools, formal semanticists investigate a wide range of linguistic phenomena. They study quantificational expressions, which indicate the quantity of something, like the sentence "all ravens are black". An influential proposal analyzes them as relations between two sets—the set of ravens and the set of black things in this example. Quantifiers are also used to examine the meaning of definite and indefinite descriptions, which denote specific entities, like the expression "the president of Kenya". Formal semanticists are also interested in tense and aspect, which provide temporal information about events and circumstances. In addition to studying statements about what is true, semantics also investigates other sentences types such as questions and imperatives. Other investigated linguistic phenomena include intensionality, modality, negation, plural expressions, and the influence of contextual factors.

Formal semantics is relevant to various fields. In logic and computer science, formal semantics refers to the analysis of meaning in artificially constructed logical and programming languages. In cognitive science, some researchers rely on the insights of formal semantics to study the nature of the mind. Formal semantics has its roots in the development of modern logic starting in the late 19th century. Richard Montague's work in the late 1960s and early 1970s was pivotal in applying these logical principles to natural language, inspiring many scholars to refine his insights and apply them to diverse linguistic phenomena.

Formal semantics is a branch of linguistics and philosophy that studies linguistic meaning using formal methods. To analyze language in a precise and systematic manner, it incorporates ideas from logic, mathematics, and philosophy of language, like the concepts of truth conditions, model theory, and compositionality. Because of the prominence of these concepts, formal semantics is also referred to as truth-conditional semantics and model-theoretic semantics.

The primary focus of formal semantics is the analysis of natural languages such as English, Sanskrit, Quechua, and American Sign Language. They investigate diverse linguistic phenomena, including reference, quantifiers, plurality, tense, aspect, vagueness, modality, scope, binding, conditionals, questions, and imperatives.

Understood in a wide sense, formal semantics also includes the study of artificial or constructed languages. This covers the formal languages used in the logical analysis of arguments, such as the language of first-order logic, and programming languages in computer science, such as C++, JavaScript, and Python. Formal semantics is related to formal pragmatics since both are subfields of formal linguistics. One key difference is that formal pragmatics centers on how language is used in communication rather than the problem of meaning in general.

Formal semanticists rely on diverse methods, conceptual tools, and background assumptions, which distinguish the field from other branches of semantics. Most of these principles originate in logic, mathematics, and the philosophy of language. One key principle is that an adequate theory of meaning needs to accurately predict sentences' truth conditions. A sentence's truth conditions are the circumstances under which it would be true. For example, the sentence "Tina is tall and happy" is true if Tina has the property of being tall and also the property of being happy; these are its truth conditions. This principle reflects the idea that understanding a sentence requires knowing how it relates to reality and under which circumstances it would be appropriate to use it.