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=== Syntax-semantics interface ===

[[File:ParseTree.svg|thumb|A [[parse tree|syntax tree]] in which the sentence ''S'' is made up of a noun phrase ''NP'' and a verb phrase ''VP'', which is itself made up of smaller [[constituent (linguistics)|constituent]]s.]]

The meaning of a sentence depends in part on its syntactic structure. For instance, the sentences "John saw Mary" and "Mary saw John" contain the same words but have different meanings because they differ in their syntactic structure. Thus, theories of compositional semantics will provide interpretation rules that map [[parse tree|syntactic tree]]s to their meanings. The nature of these rules depends in part on which model of syntax is assumed. Many theories of semantics assume a [[generative linguistics|generative]] model of syntax, such as [[Government and binding theory]] or [[Minimalist program|minimalism]], while other common approaches include [[categorial grammar]] and [[HPSG]].<ref>{{multiref | {{harvnb|Sailer|2016|pp=629-631}} | {{harvnb|Coppock|Champollion|2025|pp=291–294}} | {{harvnb|Heim|Kratzer|1998|pp=26-27, 45-47}}}}</ref>

In such theories, the interpretation system often uses rules such as the following. These rules specify how to start with a syntactic node <math>\alpha</math> and calculate its denotation, written <math>[\![\alpha]\!]</math>. These rules are applied [[recursion|recursively]].<ref>{{multiref | {{harvnb|Heim|Kratzer|1998|pp=13–15, 43–49}}{{harvnb|Coppock|Champollion|2025|pp=212–213}}}}</ref>

*'''Terminal Node:''' If <math>\alpha</math> is a [[Node (computer science)|syntactic node]] with no daughters, then <math>[\![\alpha]\!]</math> is specified in the [[lexicon]].
*'''Nonbranching Node:''' If <math>\alpha</math> is a node whose sole daughter is <math>\beta</math>, then <math>[\![\alpha]\!]=[\![\beta]\!]</math>.
*'''Function Application:''' If <math>\alpha</math> is a node with daughters <math>\beta</math> and <math>\gamma</math> where <math>[\![\beta]\!]</math> is a function whose domain contains <math>[\![\gamma]\!]</math>, then <math>[\![\alpha]\!]=[\![\beta]\!]([\![\gamma]\!])</math>.

A major debate in the syntax-semantics interface concerns the proper treatment of apparent mismatches between form and meaning, particularly related to [[scope (formal semantics)|scope]]. One common approach posits a level of grammatical structure called [[logical form (linguistics)|logical form]]. In this view, sentences do not have a unique syntactic form, but rather a phonological form, which gets pronounced, and a separate logical form, which undergoes semantic interpretation. In these approaches, apparent mismatches between form and meaning can be explained using syntactic mechanisms such as [[syntactic movement|movement]]. This is in contrast to approaches such as Direct Compositionality, which assume that the surface grammatical form is the only grammatical form and that mismatches should be explained using other semantic mechanisms such as [[type shifter|type shifting]]. Empirical evidence informing this debate includes [[Antecedent-contained deletion|ACD]], scope [[Wh-movement#Extraction_islands|islands]], and data from languages such as [[Hungarian language|Hungarian]] which has been argued to "wear its LF on its sleeve".<ref>{{multiref | {{harvnb|Coppock|Champollion|2025|pp=291–294}} {{harvnb|Sailer|2016|pp=645-654}} {{harvnb|Heim|Kratzer|1998|loc=Chapter 3.2, Chapter 7}} {{harvnb|Ruys|Winter|2011|pp=20–37}} {{harvnb|Szabolcsi|2001|pp=607–632}} }}</ref>