Formal semantics (natural language)

Formal semantics is the study of grammatical meaning in natural languages using formal tools from logic, mathematics and theoretical computer science. It is an interdisciplinary field, sometimes regarded as a subfield of both linguistics and philosophy of language. It provides accounts of what linguistic expressions mean and how their meanings are composed from the meanings of their parts. The enterprise of formal semantics can be thought of as that of reverse-engineering the semantic components of natural languages' grammars. Formal semantics studies the denotations of natural language expressions. High-level concerns include compositionality, reference, and the nature of meaning. Key topic areas include scope, modality, binding, tense, and aspect. Semantics is distinct from pragmatics, which encompasses aspects of meaning which arise from interaction and communicative intent. Formal semantics is an interdisciplinary field, often viewed as a subfield of both linguistics and philosophy, while also incorporating work from computer science, mathematical logic, and cognitive psychology. Within philosophy, formal semanticists typically adopt a Platonistic ontology and an externalist view of meaning. Within linguistics, it is more common to view formal semantics as part of the study of linguistic cognition. As a result, philosophers put more of an emphasis on conceptual issues while linguists are more likely to focus on the syntax–semantics interface and crosslinguistic variation. The fundamental question of formal semantics is what you know when you know how to interpret expressions of a language. A common assumption is that knowing the meaning of a sentence requires knowing its truth conditions, or in other words knowing what the world would have to be like for the sentence to be true. For instance, to know the meaning of the English sentence "Nancy smokes" one has to know that it is true when the person Nancy performs the action of smoking. However, many current approaches to formal semantics posit that there is more to meaning than truth-conditions.

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Categorial grammar is a family of formalisms in natural language syntax that share the central assumption that syntactic constituents combine as functions and arguments. Categorial grammar posits a close relationship between the syntax and semantic composition, since it typically treats syntactic categories as corresponding to semantic types. Categorial grammars were developed in the 1930s by Kazimierz Ajdukiewicz and in the 1950s by Yehoshua Bar-Hillel and Joachim Lambek.

Scope (formal semantics)

In formal semantics, the scope of a semantic operator is the semantic object to which it applies. For instance, in the sentence "Paulina doesn't drink beer but she does drink wine," the proposition that Paulina drinks beer occurs within the scope of negation, but the proposition that Paulina drinks wine does not. Scope can be thought of as the semantic order of operations. One of the major concerns of research in formal semantics is the relationship between operators' syntactic positions and their semantic scope.

Truth condition

In semantics and pragmatics, a truth condition is the condition under which a sentence is true. For example, "It is snowing in Nebraska" is true precisely when it is snowing in Nebraska. Truth conditions of a sentence do not necessarily reflect current reality. They are merely the conditions under which the statement would be true. More formally, a truth condition makes for the truth of a sentence in an inductive definition of truth (for details, see the semantic theory of truth).

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