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ABSTRACT:

Possessive constructions like ‘John’s teacher’, ‘John’s team’, ‘friend of John’s’ offer several interesting semantic problems and challenges. The first and most basic problem is a compositionality problem: is it possible to give a unified semantic analysis to possessives with both "plain nouns" (one-place predicates) as in ‘John’s team’, ‘John’s dog’ and relational or "transitive" nouns as in ‘John’s friend’, ‘John’s teacher’?
   On the analyses of Partee (1983/97) and Barker (1991), the DP in a possessive phrase (i.e. ‘John’ in ‘John’s’) is always an argument of some relation, but the relation does not always come from the head noun. Possessives with "transitive nouns" are argument-like, while possessives with "plain nouns" are more modifier-like, with the modifier meaning including an implicit free relation variable. Recent proposals by Jensen and Vikner (1994), Vikner and Jensen (ms.1999) and Partee and Borschev (1998, 2000) analyze all possessives as argument-like, coercing plain nouns to take on relational meanings. 
   The unified analysis thus achieved is theoretically attractive, and has an advantage over the earlier "two kinds of possessives" analysis in offering a natural account of the ambiguity of ‘Mary’s former mansion’. But it is not clear that predicate possessives, as in ‘This is Mary’s’, can be or should be assimilated to this argument-like treatment of possessives. Partee and Borschev (2001) argue that the uniform analysis may be correct for ("normal") Russian genitives, but incorrect for English.
   The main issue to be addressed is the question of whether all, some, or no possessives are best treated as arguments of nouns, and if so which ones? and how can we tell?  The question will be examined from several perspectives, including cross-linguistic perspectives, but will not be settled.

References:
Barker, Chris (1991) Possessive Descriptions. Ph.D. dissertation, Univ. of California, Santa Cruz.
Borschev, Vladimir and Barbara H. Partee (1999) "Semantic Types and the Russian Genitive Modifier
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Jensen, Per Anker and Carl Vikner (1994) "Lexical knowledge and the semantic analysis of Danish genitive
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Partee, Barbara (1983/1997) Uniformity vs. versatility: the genitive, a case study. Appendix to Theo Janssen (1997),
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Partee, Barbara H. and Vladimir Borschev (1998). Integrating lexical and formal semantics: Genitives, relational
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Partee, Barbara H. and Vladimir Borschev (2000). "Genitives, relational nouns, and the argument-modifier
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