THE LOGIC OF RECIPROCITY REVISITED: On the Interpretations of a Reciprocal Construction in Taiwanese''

This paper studies the semantic properties of a reciprocal construction in Taiwanese. Specific focus is on the real-world situations that this reciprocal construction may encode. First, the syntactic properties of the reciprocal construction "xiou " -V in Taiwanese, which are different from these in English, are analyzed. Next, various reciprocal situations are discussed and compared with those of English examples. In addition, general schema reciprocals proposed by Langendoen (1978) are reviewed. A new schema, based on Oehrle's Austinian pluralities, is proposed to accommodate all types of reciprocal situations. (JL) *********** i4A*********************************************-* Reproductions supplied by EDRS are the best that can be made from the original document. * *********************************************************************** 1--U.S DEPARTMENT OF EDUCATION Often of Ethfcal,onal Rosno fch and lofprovionlonl EDUCATIONAL RESOURCES INFORMATION 1 \lir CENTER (ERIC) his document has been reproduced as received from the parson or organization originating a 0 Mtnor changes have been made to improve reproduction quality Points of view or opinions stated in this document do not necessanty represent official OERI position cc policy. TV, "PERMISSION TO REPRODUCE THIS MATERIAL HAS BEEN GRANTED BY


Introduction
The purpose of this study is to investigate the semantic properties of a reciprocal construction in Taiwanese--xiou-V.We particularly focus on the realworld situations' that this reciprocal construction may e-eode.In this study, we not only find that the types of predicates are closely related to the interpretations of the reciprocal and that the semantics of the reciprocal is cross-linguistically similar by comparison with studies of reciprocals in English, but also make some new discoveries that have never been discussed in the previous studies of reciprocals.In addition, we review the general schema of reciprocals propood by Langendoen (1978) and show its inadequacies.Then, based on Oehrle's (to appear) Austinian pluralities, we propose a new schema to accommodate all types of reciprocal situations.
The organization of this paper is as follows.:'first, we briefly discuss the syntactic properties of the reciprocal construction xiou-V in Taiwanese, which are different from those in English.Then, we discuss the various reciprocal situations that xiou-V may encode and compare them with those of the English examples.At the same time, we review the general schema of reciprocals proposed by Langendoen (1978) and show its inadequacies.Following that, we propose a new schema based on Oehrle's (to appear) Austinian pluralities to accommodate all types of reciprocal situations.Kansas Working Papers in Linguistics, Volume 20, 1995, pp. 85-100 ti IvItactic Properties TLe syntactic properties of the reciprocal construction xiou-V in Taiwanese are different from those of the reciprocal.constructions in English in that English uses reciprocal pronouns such as each other to express reciprocal relations while xiou-V uses reciprocal verb construction for the same purpose.Xiou-V is composed of a vert -d a prefix xiou-, which roughly means 'reciprocally'.The verb in xiou-V is -_,rally a transitive verb,3 which can be a stative verb or an action verb.After combining with xiou-, the transitive verb becomes intransitive, as shown in (1).Besides, the subject of xiou-V must be plural.For example, the subject in (lb) is a conjoined plural subject.But in (2), the subject is singular and the sentence is ungrammatical, which is the same in English reciprocals.
he REC-hit *'He hit each other.' In fact, the claim that the subject of the reciprocal construction xiou-V must be plural is too strong because the status of ga (e.g. in (lb)) is not clear.Ga may be a conjunction like and in English or a preposition like with.For example, (3a) and (3b) are both grammatical.If we assume that a modal verb cannot intervene between elements of a conjoined subject, the ga in (3b) is more like a preposition than a conjunction.
he and/with I will REC-hit 'He and I will hit each other; he and I will fight.' b.I e ga gua xiou-pa.
he will with me REC-hit 'He will fight with me.' In addition, some xiou-V's can have a singular subject sometimes, as in (4a).( 4a) is syntactically well-formed but semantically incomplete.The complex verb xiou-kuan 'REC-look -at' is used for matchmaking occasions.On such occasions, the participants must be more than one, but the subject in (4a) is singular.This is the reason why the question in (4b) is asked.The ga in (4b) is apparently a preposition.Since the focus of this study is the semantic properties of the reciprocal instead of the syntactic properties, we would like to regard this plurality requirement as a semantic requirement: the subject of the reciprocal construction xiou-V in Taiwanese must be semantically plural.The term 'subject' here should not be taken as strictly a syntactic subject.How this phenomenon is analyzed in a syntactic study is beyond the scope of this paper.

Semantic Properties
As noted by Lichtenberk (1985), the reciprocal construction in many languages may encode more than one type of real-world situation.The situations represented by the reciprocal construction in English have been discussed in Fiengo & Lasnik (1973) and Langendoen (1978), among others.Langendoen further proposed a general schema for the truth conditions of the reciprocals, namely weak reciprocity (WR) and weak reciprocity for subsets (WRS), as given in (5a) and (5b).(5a) is a schema for relations (R) betWeen atomic elements of a set A and (5b) is a generalization of the notion of WR to relations between subsets of A. (5a") a situation described by (5a') and it satisfies WR. (5b") is a situation described by (5b') and it satisfies WRS.-31 In this section, we are going to discuss the various situations that the Taiwanese and pile up and follow in English.Xiou-Vpil is used for this type in the discussion.These five types are discussed in the following five subsections respectively.In the discussion, we not only show that the types of situations that the reciprocal encodes are closely related to the types of predicates, as also noticed by Fiengo & Lasnik (1973), we also show that the semantic properties of the reciprocal construction are cross-linguistically similar, and that the WR/WRS schema proposed by Langendoen in (5a) and (5b) cannot accommodate all the cases of reciprocal situations in Taiwanese as well as in English.
Xiou-V,,,,c Xiou-Va is the first semantic type of xiou-V.In each situation, each participant bears the relation denoted by the predicate to every one else.For example, in (8a), every single member of the group denoted by in 'they' must know every other member in the group to satisfy the reciprocal situations, as illustrated in (8b), for instance.(The arrowheads indicate the directions of knowing.)Partitioning the participants into subgroups is not possible, as also noticed by Fiengo & Lasnik (1973).6.7 A situation which A and B know each other and C and D know each other but A does not know C and D nor does B, as illustrated in (8c), is not a situation for (8a).11) a. @ F> 0 b.:0 ® c.

d. @
® Xiou-jim 'REC-kiss' and xiou-kuan 'REC-look-at' are two special cases in the type of xiou-V,ion.They are used on special occasions and the number of the participants is normally two: xiou-jim is used to refer to lip kisses only and xioukuan is used on matchmaking occasions.But it is also possible that on an occasion of xiou-kuan, two men and two women are involved, as in (12).Hence, these two items may be special, but they are not exceptional cases of WR/WRS.12) Zanga u si-e lang li jia xiou-kuan.yesterday have four-CL person in here REC-look-at 'Yesterday, there were four people here (e.g. in a romantic restaurant) to look at each other.' The third semantic type of reciprocal is called 'linear configurationals' in Fiengo & Lasnik (1973) and the 'chaining situations' in Lichtenberk (1985).The relation denoted by the predicate is asymmetric, i.e. if the relation A -' B holds, then B -A does not.For example, in (13), if dish A is stacked on top of dish B, dish B cannot be stacked on top of dish A.
13) The dishes are stacked on top of each other.And the relation denoted by this type of reciprocal holds only between atomic items.That is, the relation illustrated in (14a) is such a relation but that in (14b) is not, and (15a) is a possible situation for ( 13) but (15b) is not.As noted in Langendoen (1978), WR/WRS can satisfy an asymmetric, disconnected relation R on an indefinite set A for which the relation is not wellfounded, as in ( 16), but it does not cover the situations that are well-founded, such as ( 13) and (14a).Hence, WR/WRS is not an adequate schema for 'jou-Vsucceed 16) Xiou-VwaR The fourth semantic type of reciprocal consists of verbs such as xioudan 'REC-wait-for' in Taiwanese and wait for in English.The peculiarity of this type is that, like xiou-Vw, the relation denoted by the predicate is asymmetric and cannot be accommodated by WR/WRS, nor can it be represented by the atomically linearly ordered situation in (14a).For example, (17a) and (17b) may be satisfied by a single situation in which A waits for B and B does not wait for A, as in (18a), or by a situation in which A waits for B and A and B wait for C, as in (18b).9But they are not likely a description of a situation in which A waits for B, and A leaves when B arrives, and then B waits for C alone.17) a. Lan minazai li e qia-tao xiou-dan.we tomorrow in Part car-head REC-wait 'Let's wait for each other at the station tomorrow.' b.We will wait for each other at the mall.Geng xiou-jyu lai kan hi.
we REC-ask come see opera 'We asked each other to come to the opera.'These situation types are not unique in Taiwanese.They are also found in English.The general schema WR/WRS proposed by Langendoen (1978) can accommodate the first two types but not the last three.Hence, a new schema is presented and discussed in the following section.

A General Schema
As discussed above, the situations encoded in the reciprocal construction cannot be completely accommodated by the truth conditional schema in Langendeon (1978).A new general schema is needed.Hence, we adopt Oehrle's (to appear) schema of Austinian pluralities for the reciprocal situations with some adjustments, which is discussed in the first subsection.In the second subsection, the application of the general schema to the different semantic types of the reciprocal is discussed.And the third subsection is a brief summary of the discussion.
Oehrle's Schema and the Adjustments Oehrle (to appear) proposes a schema of plurality based on two ideas: the Austinian propositions" and the assumption that both individuals and situations constitute domains structured by a sum operation.An Austinian proposition is regarded as about a structured set of situations rather than a single situation, and such a proposition may involve similarly-structured set of individuals as the arguments of the relation involved.The schema of plurality proposed by Oehrle is in (20), where the relation 'a (3' holds when a is a minimal model of (3. In (20), npi and np2 are plural noun phrases and v is a transitive verb in a sentence np, v np2.The interpretation of each noun phrase is represented as a join of individuals satisfying the interpretive constraints of its component parts and the interpretation of the sentence is represented as a join of situations satisfying the binary relation v' associated with v.These structures are linked with a common index set I, together with indexed indeterminates.
Based on the schema in (20), Oehrle develops the schema in ( 21) for reciprocals in English by adding some constraints.First, reciprocal pronouns in English such as each other cannot be bound by singular noun phrases.This is taken care of by the constraint xi )1; in the relational schema.Second, in reciprocal sentences, both arguments of the verb (i.e. the subject np, and the object each other (np2) for example) have the same interpretation; therefore, (1J, ,(Y,))= 1-lie1(xi) is required.

21) iliEi(si
Oehrle's account in ( 21) is compatible not only with interpretations of the form (AxA)\ Athe cross-product of the argument interpretation A with itself minus the diagonal A of AxA--but also with much weaker relations among the members of the argument interpretation A, as studied by Langendoen (1978).The formulation treats those readings of the reciprocal as special cases of the single, general and simple schema in (21).
However, as pointed out by Langendoen (personal communication), the condition that requires the relation holds of distinct pairs <xoyi> -in ( 21) is inadequate for the reciprocals.The condition xi should be modified to xi fl yi=0, because, for example, ( 22) can be satisfied by the join of situations in which A hit B, B hit C and C hit A, or by the join of situations in which A and B hit C, B and C hit A, and A and C hit B, etc., but it cannot be satisfied As discussed previously, the xiou-V,, type exhibits strong reciprocity.It requires that the relation v' corresponding to the stative verb holds symmetrically between atomic elements.But the schema in ( 23) is too weak to provide the xiou-Vs., reciprocal with correct situations.For example, the situations illustrated in (24) satisfy the relational schema in (23) but they are not situations described by sentence (8a).
8) a.In u xiou-bal.they Asp REC-know 'They know each other.' 24) CI -.3) --> ® Therefore, to guarantee that the symmetric relation holds, an extra condition ( 25) is needed in addition to the condition that x; and y, must be atomic:12 25) If v'(x,y) is true, v'(y,x) must also be true: v'(x,y) v'(y,x) (v' is the binary relation denoted by a V,,,,e.)(25) is not an implication rule.It is interpreted as: if a situation si that satisfies v'(x,y) is found, another situation s2 that satisfies v'(y,x) must also be found.For example, in (8a), if A knows B, then B must also know A to satisfy the situation described by the sentence; if A knows B but B does not know A, ( 25) is violated and it is not a legitimate situation for (8a).
Even with (25), the schema in ( 23) is still too weak for the xiou-V,,,, reciprocal because it wrongly allows situations such as (26a) and (26b) to be legitimate situations of (8a).To prevent this from happening, another condition (27) is needed.
Like ( 25), ( 27) is not an implication rule nor a transitive rule.It is interpreted as: whenever an sl that satisfies v'(x,y) and an s2 that satisfies v'(y,z) are found, an s3 that satisfies v'(x,z) must also be found.For example, if A knows B and B knows C, A must also know C to satisfy the situation described by (8a).U,E(s, (v'(xi)(Yi)) A )(in yi= 0 A xi,y; 0) In this paper, we have discussed the semantic properties of the reciprocal xiou-V in Taiwanese and classified them into five semantic groups according to their corresponding real-world situations.We have also compared the reciprocal situations in Taiwanese and English and found that the semantic properties of the reciprocal are cross-linguistically similar: the five semantic types of the reciprocal are found both in Taiwanese and English and different predicates in the reciprocal construction may denote different real-world :situations, e.g. the difference between xiou-V5.1, and xiou-Vac,ion.In addition, based on Oehrle's (to appear) Austinian pluralities, we have also given the various semantic types of the reciprocal a general schema and specific conditions in order to supply them with correct real-world situations.
The relation between reciprOcals and plurals have been well discussed in Langendoen (1978) and Oehrle (to appear), among others.Now the questions that may be aroused by this study of the reciprocal are: Why do different types of predicates denote different reciprocal situations?What principle may underlie the relation between predicates in the reciprocal construction and predicates in general?We will leave them for future research.

13
BEST COPY AVAILABLE NOTES I would like to thank D. Terence Langendoen and Richard Oehrle for giving me helpful comments and for being the consultants I would also like to thank Jane Tsay for giving me judgments about data from Taiwanese and Peg Lewis for judgments about data from English.My gratitute also goes to those who gave me comments when a previous version of this paper was presented in LASSO XXIII.Of course, all the errors are mine.
Taiwanese is a variety of South Min (a Chinese dialect), which includes Amoy, Zhangzhou, Quanzhou, and many other dialects spoken in the southern part of Fukien (Min) Province and some part of Kwangtung Province.Some varieties of South Min are spoken by the Chinese in Malaysia, Singapore and other Southeastern Asian countries.The reason that 'Taiwanese' is used as the name of the language in the present study is that it is now the most common name for the language and that the data under study are drawn from the variety spoken in Taiwan, mostly my own dialect.

2
The term 'situation' has two slightly different meanings in this paper.
What we refer to as a situation in the first three sections may be a set of situations referred to by the schema discussed in the fourth section.Xiong-ho 'REC-nice' is a special case of xiou-V in that ho is an adjective or a non-transitive stative verb that requires a plural subject if the interpretation of ho in xiong-ho is intended, as shown in (i).In jin xiong-ho.they very REC-nice 'They are friends to each other.' (ia) is ambiguous.When it means the first and second readings, the subject can be singular.When the third reading is intended, the subject must be plural.(ib) has the same meaning as the third reading of (ia).Not all cases of xiou-V are reciprocals.For example, xiong-xin 'believe' is a transitive verb like believe in English and has no meaning of any type of reciprocity discussed in this section.Xiou-pien 'cheat each other' and xiou-sang 'see off' can have a singular subject, as in (i).But when they have certain plural subjects, they are interpreted as reciprocals as in (ii).
In Langendoen (1978), there are six possible truth-conditional schemata for reciprocals.WR and PIR in (i) are two of them.When the members of the set A are no me -e than four, PIR equals WR.When the members are more than four, PIR implies WR but not vice versa. ( 11d) is a situation of WR but not of PIR. 9 Note that if the sentence is in past tense, such as (i), the situation may be different.(i) can be satisfied when A waited for B in one corner of the mall while B waited for A in another corner at the same time.But (i) is not likely to be satisfied if the real situation is that A waited for B and not vice versa.
(i) We (A and B) waited for each other at the mall yesterday.Also, if there is a frequency adverb such as always in the sentence, the situation may he different, too.For example, (ii) cannot be satisfied if A waits for B every time.
(ii) We always wait for each other.Since the interaction among reciprocal situations, frequency adverbs and temproal relations is beyond the scope of this study, I will leave it for future research.
11' It is interesting to note that in English pile up and stack are used as in pile up on top of and stack on top of, in which a direction is explicitly expressed.In Taiwanese, there is no direction incorporated explicitly in xiou-tah 'REC-pile'.But implicitly, a direction like that in English is incorporated, as shown in (i).
(Ga in (i) is like ba in the ba construction in Mandarin.See Li (1994) for details.) i) a. Ga hi-de pan-a tah e ji-de pan-a ding-tao.
GA tlIat-CL dish pile on this-CL dish top-head 'Put that dish on top of this one.'b. *Ga hi-de pan-a tah e ji-de pan-a e-tao.
GA that-CL dish pile on this-CL dish down-head 'Put that dish underneath this one.'Similarly, xiou-de 'REC-follow' in Taiwanese is like follow each other in English in that a direction is incorporated.But in Taiwanese, there is no counterpart of precede each other, which is not an acceptable usage in English, either.Maybe there is some universal constraint on spatial and temporal relations of reciprocals, as noted by Langendoen (1978).II The definition of 'Austinian proposition' according to Barwise (1989: 273) is: '...for each situation s and each s-infon a, there is a proposition p expressing the claim that s a.This proposition is written: (s a).Call such a proposition an Austinian proposition.'Infons are objects which actual situations .makefactual and serve to characterize the intrinsic nature of a situation.
12 For some symmetric stative predicates such as similar, (25) may be redundant. 13 The specific condition for xiou-V,,,, in ( 30) is still inadequate.I would like to leave it for future research.
,,, The second semantic class of the xiou-V reciprocal is xiou-Vacon, which consists of action verbs.Examples are given in (9).
Part.REC-pile 'The dishes are piled up on top of each other.'Summary In the discussion above, the situations denoted by the xiou-V reciprocal are classified into five types: xiou -VSO, xiou-V,d, xiou-V,,,,a and xiou-Vp,.Different situation types are related to different predicates.
v'(x,y) and v'(y,z) are true, v'(x,z) must also be true: v'(x,y) &. v'(y,z) = v'(x,z) (v' is the binary relation denoted by a Vs,,,, added to (23).Now we come to the types xiou-V,,,, xiou-V", and xiou-Vpile.As noted above, the relation denoted by these predicates is asymmetric.And that is what makes them unable to be accommodated to the schema in (23).If we treat the ,d 31) 3 'They are very nice.' 'They are in good condition.''They are good friends.' b.
i) Partitioned Intermediate Reciprocity (PIR) Let Ar----,A1U...Uk and (vi,j, AinAj=0) and (Vk,11.qk...c.n)(card Ak 2): (vi, 1.itc..n)(vx,yEAi) {x -[xRy V (3n > 0)(3zi,...,z,,E A)(xRzi A ... A znRy)1} Vpile The fifth semantic type, xiou-Voc, is a mixed type of xiou-V.1 and xiou-Vwait.The relation denoted by the predicate of this type is also asymmetric and may hold between linearly ordered atoms like that of xiou-V5".4 in (14a) and (15a), or the situations like those denoted by xiou-V,,,ah and those in (14b) and (15b) can also meet the requirement.Xiou-tah 'REC-pile', xiou-jyu 'REC-ask' and xiou-de 'REC-follow' are examples of this type from Taiwanese and pile up and follow are examples from English.For instance, (19a) can be interpreted as that A told B "Let's go to the opera" and then B told C "Let's go to the opera", like (14a), or that A told B "let's go to the opera" and then A and B together told C "Let's go to the opera", like (18b). (19b) is also vague in that it can indicate a situation in which one dish is stacked on top of the other, like (15a), or in which, say, two dishes are stacked on top of the other(s), like (15b).Pile up and follow in English reciprocal sentences denote the same situations as xiou-tah in