Formal semantics studies the relationship between language and reality. Linguists define the truth conditions of statements and use mathematical equations, such as typed lambda calculus, to analyze language. Different branches of formal semantics have developed, including Montague Grammar, categorical grammar, Glue semantics, and discourse representation theory. Quantifiers and implication play a role in determining truth conditions. Formal semantics is a multidisciplinary field involving linguists, philosophers, logicians, mathematicians, and programmers.
Formal semantics is a broad linguistic theory, intended to study how language works and its relationship to reality. Linguists carefully define the truth conditions of any statement, which are those situations that must be made in order for the statement to be true. The sentences are then written into mathematical equations, mostly using typed lambda calculus.
The theory of formal semantics was first developed by the American philosopher and mathematician Richard Montague in the 1960s. Its specific version is known as Montague Grammar. Since that time, this theory has developed in many directions, including categorical grammar, pioneered by Yehoshua Bar-Hillel in the 1970s, and Glue semantics, published by Mary Dalrymple in the 1990s.
Another type, discourse representation theory, was developed in 1981 by the Dutch linguist Hans Kamp. This specific linguistic theory is sometimes referred to by the generic term formal semantics. Discourse representation theory attempts to analyze whole speech, or conversation, rather than isolated sentences, and present it in mathematical equations.
All branches of formal semantics focus on the relationship between language and reality; in other words, their goal is to find the connection between what is being said and what is. Words are called signifiers while the things themselves are called denoted or, in discourse representation theory, discourse referents. In the sentence “The dog barks,” the word “dog” is a signifier, while the actual dog is a discourse referent.
A statement can have more than one truth condition, or requirement for it to be true. Often these truth conditions lead to implication, which is the term used when the truth of one sentence requires another to be true. In other words, in an implied situation, if statement A is true, then statement B must also be true.
To determine the truth conditions of a statement, linguists must look for all quantifiers present. A quantifier is a word that indicates how many things are involved, such as each, every, any, and some. These words can substantially change the meaning of a statement.
The type of mathematics most often used to parse language in formal semantics is the typed lambda calculus. Words can be identified as different variables and placed within an equation; in discourse representation theory, these equations are known as discourse representation structures. While primarily a linguistic theory, formal semantics is a multidisciplinary field. Linguists, philosophers, logicians, mathematicians and programmers are involved. Analyzing and creating programming languages and even studying artificial intelligence can involve formal semantics.
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