linguistic semantics Semantics (from grc, σημαντικός ''sēmantikós'', "significant") is the study of reference, meaning, or truth. The term can be used to refer to subfields of several distinct disciplines, including philosophy, linguistics and comput ...

, an expression X is said to have cumulative reference if and only if the following holds: If X is true of both of ''a'' and ''b'', then it is also true of the combination of ''a'' and ''b''. Example: If two separate entities can be said to be "water", then combining them into one entity will yield more "water". If two separate entities can be said to be "a house", their combination cannot be said to be "a house". Hence, "water" has cumulative reference, while the expression "a house" does not. The

plural The plural (sometimes abbreviated pl., pl, or ), in many languages, is one of the values of the grammatical category of number. The plural of a noun typically denotes a quantity greater than the default quantity represented by that noun. This de ...

form "houses", however, ''does'' have cumulative reference. If two (groups of) entities are both "houses", then their combination will still be "houses". Cumulativity has proven relevant to the linguistic treatment of the mass/count distinction and for the characterization of grammatical

telicity In linguistics, telicity (; ) is the property of a verb or verb phrase that presents an action or event as having a specific endpoint. A verb or verb phrase with this property is said to be ''telic''; if the situation it describes is ''not'' hea ...

. Formally, a cumulative predicate ''CUM'' can be defined as follows, where capital ''X'' is a

variable Variable may refer to: * Variable (computer science), a symbolic name associated with a value and whose associated value may be changed * Variable (mathematics), a symbol that represents a quantity in a mathematical expression, as used in many ...

over sets, ''U'' is the

universe of discourse In the formal sciences, the domain of discourse, also called the universe of discourse, universal set, or simply universe, is the set of entities over which certain variables of interest in some formal treatment may range. Overview The doma ...

, ''p'' is a mereological part

structure A structure is an arrangement and organization of interrelated elements in a material object or system, or the object or system so organized. Material structures include man-made objects such as buildings and machines and natural objects such as ...

on ''U'', and

\oplus_p

is the mereological sum operation. In later work, Krifka has generalized the notion to ''n''-ary predicates, based on the phenomenon of ''cumulative quantification''. For example, the two following sentences appear to be equivalent: : John ate an apple and Mary ate a pear. : John and Mary ate an apple and a pear. This shows that the relation "eat" is cumulative. In general, an ''n''-ary predicate ''R'' is ''cumulative'' if and only if the following holds:

References

Krifka, Manfred (1989). "Nominal reference, temporal constitution and quantification in event semantics". In

Renate Bartsch Renate Irmtraut Bartsch (born 12 December 1939) is a German philosopher of language. She was a professor at the University of Amsterdam between 1974 and 2004. Career Bartsch was born on 12 December 1939 in Königsberg. She earned her Doctor title ...

, Johan van Benthem and Peter van Emde Boas (eds.), ''Semantics and Contextual Expressions'' 75–115. Dordrecht: Foris. Krifka, Manfred. 1999. "At least some determiners aren’t determiners". In ''The semantics/pragmatics interface from different points of view'', ed. K. Turner, 257–291. North-Holland:

Elsevier Elsevier () is a Dutch academic publishing company specializing in scientific, technical, and medical content. Its products include journals such as ''The Lancet'', ''Cell'', the ScienceDirect collection of electronic journals, '' Trends'', th ...

Science. Scha, Remko. 1981. "Distributive, collective, and cumulative quantification". In ''Formal methods in the study of language'', ed. T. Janssen and M. Stokhof, 483–512. Amsterdam: Mathematical Centre Tracts. {{Formal semantics Grammar Semantics Formal semantics (natural language)