1 Weak definites are noun phrases which are definite in form, yet do ...

WEAK DEFINITES AND AMOUNT DEFINITESEdit Doron, The Hebrew University of JerusalemWeak definites are noun phrases which are definite in form, yet do not presuppose aunique referent, unlike regular (strong) definites. Following Poesio 1994 and Baker 2005, weview weak definite noun phrases as crucially involving relational nouns, and we extend thisapproach to the non-possessive weak definites discussed by Carlson and Sussman 2005. Wedraw attention to a type of relational nouns which has not yet been introduced in the contextof the discussion of weak definites – amount nouns, including numerals and other measurenouns. Weak definites constructed from amount nouns will be called amount definites.Amount definites have in common with amount relatives (Carlson 1977) the definiteness ofthe amount coupled with the indefiniteness of the substance. We propose an analysis of weakdefinites, and explore its consequences by explaining the properties of amount definites.The term weak definites and the original examples are due to Poesio 1994. Someexamples are shown below:(1) John got these data from the student of a linguist.(2) My aunt got attacked by the parent of a student whom she had failed.(3) He showed me the picture of a veiled woman.Poesio shows that despite the definite form of the possessive constructions in such examples,they do not presuppose uniqueness (leaving aside the strong reading, which these examplesalso have). Like indefinite NPs, they can appear discourse-initially and introduce newparticipants into the discourse; they appear in the existential construction; and they give riseto sloppy identity in VP-ellipsis.Poesio 1994, and later also Baker 2005, note that there are also examples of weakdefinites with a definite possessor:(4) It took him several minutes to reach the refrigerator nestled in the corner of the kitchen.(5) Tell the employee of the store what you are looking for and she will provide you with options.A different class of weak definites, with no possessors, was introduced by Carlsonand Sussman 2005:(6) Mary went to the store.(7) Open the window, will you please?(8) Let's take the elevator.For our account of weak definites, we adopt the use of choice functions to determinethe denotations both of indefinte and definite noun phrases, as proposed by von Heusinger2004 and Schlenker 2004. Each indefinte noun phrase in the discourse is interpreted by anew choice function Y i , which accounts for the fact that each occurrence of a student in thediscourse denotes a different individual. Definite noun phrases on the other hand areinterpreted by a single choice function Y C per context, which accounts for the fixeddenotation of the student in a given discourse (as long as the context is not updated). Theuniqueness in the latter case follows from the fact that Y C always selects the most salientindividual with the relevant property.(9) a a ~> λP. Y i [λy. P (y)]] i is a new indexb the ~> λP. Y C [λy. P (y)]] Y C selects the most salient P-individual in CFor weak definites, we propose that the ordinary interpretation of the in (9) is typeshiftedin (10) to apply to relations rather than to properties. Thus, the R in (10) turns eachrelational noun into a function. Second, the context is updated relative to the possessor x (ina way made precise in the paper).(10) the R ~> λR. [λx. Y C, x [λy. R (y, x)]] C is updated relative to xFor example, the phrase the student of a linguist of (1) is interpreted by firstcombining the relation student with the functor the R whose role it is to map the relationalinterpretation to a function interpretation, and to update the global Y C for each value of x:1

(11) student ~> λx. [λy. student (y, x)] the R -student ~> λx. Y C, x [λy. student (y, x)]This analysis predicts that weak definite readings are only found with extensionalinterpretations of relations, as they depend on the actual value of possessor. This accountsfor one contrast between weak definites like the N of NP and indefinites such as a N of NP.In (12a), under the weak reading, the noun picture is only interpreted as an extensionalrelation, i.e. as relating a particular individual to one of her pictures. On the other hand, in(12b), the noun picture may be interpreted as an intensional relation taking a veiled-womanconceptas argument.(12) a. He showed me the picture of a veiled womanb. He showed me a picture of a veiled womanOur account can be extended to non-possessive examples such as those in (6-8). Thenouns here are store, window, elevator, newspaper, radio, hospital, train etc, describingobjects characterized by their use by a user x which is also an argument of the sentence. Useis one of the qualia relations which can serve as a means of coercing sortal nouns to arelational interpretation according to Vikner and Jensen 2002. These nouns are indeedinterpreted as weak definites only in sentences involving their characteristic use (Carlson andSussman 2005). The object fulfilling this use in a given context is not a-priori unique, but aunique object is selected relative to x by Y C, x (we disagree with Carlson et al's 2006 claim ofnon-uniqueness of the denotation).Our account distinguishes between relational nouns, where the anchoring to apossessor/ user licenses a definite form, and nouns modified by adjuncts, as in (13)-(14),which are only interpreted as strongly definite, i.e. as unique in the global context:(13) Call their attention to the book on the table.(14) The truck was involved in the accident near a local intersection.Our analysis of weak definites relies on the interpretation the R of the English the or 'sin the Saxon genitive. In Modern Hebrew (MH), the R is part of the interpretation of the socalledconstruct state (CS) inflectional form of the noun. A CS noun denotes (or is coerced todenote) a relation (Heller 2002), and when it is interpreted as definite, the definiteness can beshifted from strong to weak, as is the case in the following examples observed by Danon2001:(15) a. regel ha-šulxanleg-CS the-table 'the leg of the table'b. xalon ha-mexonitwindow-CS the-car 'the window of the car'c. ovedet ha-šagrirutemployee-CS the-embassy 'the employee of the embassy'Yet in the case of amount-phrases, the two definite interpretations (weak and strong) ofdefinite determiners are given separate forms. We illustrate here with the amount noun three.(We take |y| to denote the number of atoms that the sum individual y consists of.)(16) a. šloša 'three' ~> λP. Y i [λy. P(y) & |y| = 3] i is new indefiniteb. ha-šloša 'the-three' ~> λR. [λx. Y C, x [λy. R (y, x) & |y| = 3] weak definitec. šlošet 'three-CS' ~> λx. Y C [λy. y=x & |y| = 3] strong definiteThus, šloša is an indefinite noun introducing a new choice function, ha-šloša is defined asthe corresponding weak definite, whereas šlošet is a function CS noun which serves as a test:it maps an individual to itself iff this individual consists of 3 atoms. We can thus reformulate(16c) as the identity function λx.x, in case |x| = 3. Notice that unlike the English translationof the examples in (17) below, the measure nouns šlošet 'three-CS' and kos 'glass-CS' combinewith definite NPs, therefore better translations might actually be 'the children, of which thenumber is three' and 'the wine, of which the amount is a glass'.2

(17) a. šlošet ha-yeladim b. kos ha-yayinthree-CS the-childrenglass-CS the-wine'the three chilren''the glass of wine'We now illustrate the contrast in interpretation between the strong definite noun phrase as in(17a/18a) and the corresponding weak definite in (18b), which we call an amount definite.(18) ha-mišpaxot imthe-families witha. # šlošet ha-yeladim b. ha-šloša yeladimthree-CS the-childrenthe-three childrenboth: 'the families with the three children'We construct the two different interpretations of the sentences in (18), and account for theirdifference in acceptability:(19) a. NP Y C * [λu. family(u) & with(u, Y C * [λy. ∃x child (y,x)])]3 presupposition: |Y C * [λy. ∃x child (y,x)]| = 3N PP λu.with(u, Y * C [λy. ∃x child (y,x)])| 2ha-mišpaxot P NP Y * C [λy. ∃x child (y,x)]| 2 presupposition: |Y * C [λy. ∃x child (y,x)]| = 3im N NP| |λx. Y C [λy. y=x & |y| = 3] šlošet ha-yeladim Y * C [λy. ∃x child (y,x)]The oddity of (18a/19a) stems from the fact that the families in its denotation all include thesame unique group of three children, i.e. the most salient plurality (typically the maximalone) of three children. Knowledge of the word tells us that different families normally havedifferent groups of children. In (18b/19b) on the other hand, with the the amount definite,each family u has a different group of children yielded by Y C, u .(19) b. NP Y * C [λu. family(u) & with(u, Y C, u [λy. children(y,u) & |y| = 3])]3N PP λu.with(u, [λx. Y C, x [λy. children(y,x) & |y| = 3]](u) )| 3ha-mišpaxot P NP λx. Y C, x [λy. children(y,x) & |y| = 3]| 2im NP N| |λR. [λx. Y C, x [λy. R(y,x) & |y| = 3] ha-šloša yeladim λx. λz children (z,x)References: Barker, Chris. 2005. Possessive weak definites. In Kim, Ji-Yung, Yuri Lander and Barbara Partee(eds.) Possessives and Beyond: Semantics and Syntax. Amherst, MA: GLSA Publications. Carlson, Greg N.1977. Amount Relatives. Language 53,3: 520-542. Carlson, Greg and Rachel Sussman. 2005. Seeminglyindefinite definites. In Linguistic Evidence, eds., S. Kepsar and M. Reis. Berlin: de Gruyter. 71-86. CarlsonGreg, Rachel Sussman, Natalie Klein and Michael Tanenhaus. 2006. Weak Definite Noun Phrases.Proceedings of NELS 36. Amherst, MA: GLSA. 179-196. Danon, Gabi. 2001. Syntactic definiteness in thegrammar of Modern Hebrew. Linguistics 39.6: 1071–1116. Danon, Gabi. 2008. Definiteness agreement withPP modifiers. In Sharon Armon-Lotem, Gabi Danon and Susan Rothstein (eds) Current Issues in GenerativeHebrew Linguistics. John Benjamins. 137-160. Heller, Daphna. 2002. Possession as a Lexical Relation:Evidence from the Hebrew Construct State. In L. Mikkelsen and C. Potts (eds.) Proceedings of WCCFL 21:127–140. von Heusinger, Klaus. 2004. Choice Functions and the Anaphoric Semantics of Definite NPs.Research on Language and Computation 2: 309–329. Poesio, Massimo. 1994. Weak Definites. Proceedings ofthe Fourth Conference on Semantics and Linguistics Theory, SALT-4. Schlenker, Philippe. 2004. Conditionalsas Definite Descriptions (A Referential Analysis). Research on Language and Computation 2: 417–462.Vikner, Carl and Per Anker Jensen. 2002. A semantic analysis of the English genitive. Interaction of lexicaland formal semantics. Studia Linguistica 56:191-226.3