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Abstract Learnability in Optimality Theory

Abstract Learnability in Optimality Theory
Abstract Learnability in Optimality Theory

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Learnability in Optimality Theory

(short version)

Bruce Tesar&Paul Smolensky

October1996

Technical Report

JHU CogSci 96 2

https://www.wendangku.net/doc/965805676.html,/TechReports/

TR-Request@https://www.wendangku.net/doc/965805676.html,

Learnability in Optimality Theory

Bruce Tesar

The Center for Cognitive Science / Linguistics Department

Rutgers University

Piscataway, NJ 08855

tesar@https://www.wendangku.net/doc/965805676.html,

Paul Smolensky

Cognitive Science Department

Johns Hopkins University

Baltimore, MD 21218-2685

smolensky@https://www.wendangku.net/doc/965805676.html,

Abstract

A central claim of Optimality Theory is that grammars may differ only in how conflicts among universal well-formedness constraints are resolved: a grammar is precisely a means of resolving such conflicts via a strict priority ranking of constraints. It is shown here how this theory of Universal Grammar yields a highly general Constraint Demotion principle for grammar learning. The resulting learning procedure specifically exploits the grammatical structure of Optimality Theory, independent of the content of substantive constraints defining any given grammatical module. The learning problem is decomposed and formal results are presented for a central subproblem, deducing the constraint ranking particular to a target language, given structural descriptions of positive examples and knowledge of universal grammatical elements. Despite the potentially large size of the space of possible grammars, the structure imposed on this space by Optimality Theory allows efficient convergence to a correct grammar. Implications are discussed for learning from overt data only, learnability of partially-ranked constraint hierarchies, and the initial state. It is argued that Optimality Theory promotes a goal which, while generally desired, has been surprising elusive: confluence of the demands of more effective learnability and deeper linguistic explanation.

How exactly does a theory of grammar bear on questions of learnability? Restrictions on what counts as a possible human language can restrict the search space of the learner. But this is a coarse observation: alone it says nothing about how data may be brought to bear on the problem, and further, the number of possible languages predicted by most linguistic theories

1

is extremely large. It would clearly be a desirable result if the nature of the restrictions imposed by a theory of grammar could contribute further to language learnability.

The central claim of this paper is that the character of the restrictions imposed by Optimality Theory (Prince and Smolensky 1991, 1993) have demonstrable and significant consequences for central questions of learnability. Optimality Theory explains linguistic phenomena through the complex interaction of violable constraints. The main results of this paper demonstrate that those constraint interactions are nevertheless restricted in a way that permits the correct grammar to be inferred from grammatical structural descriptions. These results are theorems, based on a formal analysis of the Optimality Theory framework; proofs of the theorems are contained in an appendix. The results have two important properties. First, they derive from central principles of the Optimality Theory framework. Second, they are nevertheless independent of the details of any substantive analysis of particular phenomena. The results apply equally to phonology, syntax, and any other domain admitting an Optimality Theoretic analysis. Thus, these theorems provide a learnability measure of the restrictiveness inherent in Optimality Theory’s account of cross-linguistic variation per se: constraint reranking.

The structure of the paper is as follows. Section 1 formulates the Optimality Theoretic learning problem we address. Section 2 addresses this problem by developing the principle of Constraint Demotion, which is incorporated into an error-driven learning procedure in section 3. Section 4 takes up some issues and open questions raised by Constraint Demotion, and section 5 concludes. Section 6 is an appendix containing the formal definitions, theorems, and proofs.

1. Learnability and Optimality Theory

Optimality Theory (henceforth, ‘OT’) defines grammaticality by optimization over violable constraints. The defining reference is Prince and Smolensky 1993 (abbreviated ‘P&S’ here). Section 1.1 provides the necessary OT background, while section 1.2 outlines the approach to language learnability proposed here, including a decomposition of the overall problem; the results of this paper solve the subproblem involving direct modification of the grammar. 1.1 Optimality Theory

In this section, we present the basics of OT as a series of general principles, each exemplified within the Basic CV Syllable Theory of P&S.

1.1.1 Constraints and Their Violation

(1) Grammars specify functions.

A grammar is a specification of a function which assigns to each input a unique

structural description or output. (A grammar per se does not provide an algorithm for computing this function, e.g., by sequential derivation.)

In Basic CV Syllable Theory (henceforth, ‘CVT’), an input is a string of Cs and Vs,

e.g., /VCVC/. An output is a parse of the string into syllables, denoted as follows:

(2)a..V.CVC. = V] CVC]

[.[.

[.

b.+V,.CV.+C,= V CV] C

′′

c.+V,.CV.C~. = V CV] C~]

[.[.

[.[.

d..~V.CV.+C, = ~V] CV] C

(These four forms will be referred to frequently in the paper, and will be consistently labeled a–d.)

Output a is an onsetless open syllable followed by a closed syllable; periods denote the boundaries of syllables (.). Output b contains only one, open, syllable. The initial V and final C of the input are not parsed into syllable structure, as notated by the angle brackets +,. These segments exemplify underparsing, and are not phonetically realized, so b is ‘pronounced’ simply as .CV. The form .CV. is the overt form contained in b. Parse c consists of a pair of open syllables, in which the nucleus of the second syllable is not filled by

an input segment. This empty nucleus is notated ~, and exemplifies overparsing. The phonetic interpretation of this empty nucleus is an epenthetic vowel. Thus c has .CV.CV. as its overt form. As in b, the initial V of the input is unparsed in c. Parse d is also a pair of open syllables (phonetically, .CV.CV.), but this time it is the onset of the first syllable which is unfilled (notated ~; phonetically, an epenthetic consonant), while the final C is unparsed.

(3) Gen: Universal Grammar provides a function Gen which, given any input I, generates

Gen(I), the set of candidate structural descriptions for I.

The input I is an identified substructure contained within each of its candidate outputs in Gen(I). The domain of Gen implicitly defines the space of possible inputs.

In CVT, for any input I, the candidate outputs in Gen(I) consist in all possible parsings of the string into syllables, including the possible over- and underparsing structures exemplified above in (b–d). All syllables are assumed to contain a nucleus position, with optional preceding onset and following coda positions. CVT adopts the simplifying assumption (true of many languages) that the syllable positions onset and coda may each contain at most one C, and the nucleus position may contain at most one V. The four candidates of /VCVC/ in (2) are only illustrative of the full set Gen(/VCVC/). Since the possibilities of overparsing are unlimited, Gen(/VCVC/) in fact contains an infinite number of candidates.

The next principle identifies the formal character of substantive grammatical principles.

(4) Con: Universal Grammar provides a set Con of universal well-formedness constraints.

The constraints in Con evaluate the candidate outputs for a given input in parallel (i.e., simultaneously). Given a candidate output, each constraint assesses a multi-set of marks, where each mark corresponds to one violation of the constraint. The collection of all marks assessed a candidate parse p is denoted marks(p). A mark assessed by a constraint ÷ is denoted *÷. A parse a is more marked than a parse b with respect to ÷ iff ÷ assesses more marks to a than to b. (The theory recognizes the notions more- and less-marked, but not absolute numerical levels of markedness.)

The CVT constraints are given in (5).

(5) Basic CV Syllable Theory Constraints

O NSET Syllables have onsets.

N O C ODA Syllables do not have codas.

P ARSE Underlying (input) material is parsed into syllable structure.

F ILL Nuc

Nucleus positions are filled with underlying material.

Onset positions (when present) are filled with underlying material.

F ILL Ons

These constraints can be illustrated with the candidate outputs in (a–d). The marks incurred by these candidates are summarized in table (6).

L 1

(6) Constraint Tableau for

This is an OT constraint tableau . The competing candidates are shown in the left column. The other columns are for the universal constraints, each indicated by the label at the top of the column. Constraint violations are indicated with ‘*’, one for each violation.Candidate a = .V.CVC. violates O NSET in its first syllable and N O C ODA in its second;the remaining constraints are satisfied. The single mark which O NSET assesses .V.CVC. is denoted *O NSET . This candidate is a faithful parse: it involves neither under- nor overparsing, and therefore satisfies the faithfulness constraints P ARSE and F ILL . By contrast,2b = +V ,.CV.+C , violates P ARSE , and more than once. This tableau will be further explained below.

1.1.2 Optimality and Harmonic Ordering

The central notion of optimality now makes its appearance. The idea is that by examining the marks assigned by the universal constraints to all the candidate outputs for a given input, we can find the least marked, or optimal, one; the only well-formed parse assigned by the grammar to the input is the optimal one (or optimal ones, if several parses should tie for optimality). The relevant notion of ‘least marked’ is not the simplistic one of just counting numbers of violations. Rather, in a given language, different constraints have

different strengths or priorities: they are not all equal in force. When a choice must be made between satisfying one constraint or another, the stronger must take priority. The result is that the weaker will be violated in a well-formed structural description.

(7) Constraint Ranking: a grammar ranks the universal constraints in a dominance

hierarchy.

÷1÷2

When one constraint dominates another constraint in the hierarchy, the relation is ÷1÷2

denoted >> . The ranking defining a grammar is total: the hierarchy determines the relative dominance of every pair of constraints:

>> >> t>>

÷1÷2÷n

(8) Harmonic Ordering: a grammar’s constraint ranking induces a harmonic ordering of

all structural descriptions. Two structures a and b are compared by identifying the highest-ranked constraint ÷ with respect to which a and b are not equally marked: the candidate which is less marked with respect to ÷ is the more harmonic, or the one with higher Harmony (with respect to the given ranking).

a b denotes that a is less harmonic than b. The harmonic ordering determines the relative Harmony of every pair of candidates. For a given input, the most harmonic of the candidate outputs provided by Gen is the optimal candidate: it is the one assigned to the input by the grammar. Only this optimal candidate is well-formed; all less harmonic candidates are ill-formed. 3

A formulation of harmonic ordering that will prove quite useful for learning involves Mark Cancellation. Consider a pair of competing candidates a and b, with corresponding lists of violation marks marks(a) and marks(b). Mark Cancellation is a process applied to a pair of lists of marks, and it cancels violation marks in common to the two lists. Thus, if a constraint ÷ assesses one or more marks *÷ to both marks(a) and marks(b), an instance of

L 1*÷ is removed from each list, and the process is repeated until at most one of the lists still contains a mark *÷. (Note that if a and b are equally marked with respect to ÷, the two lists contain equally many marks *÷, and all occurrences of *÷ are eventually removed.) The resulting lists of uncancelled marks are denoted marks N (a ) and marks N (b ). If a mark *÷remains in the uncancelled mark list of a , then a is more marked with respect to ÷. If the highest-ranked constraint assessing an uncancelled mark has a mark in marks N (a ), then a b :this is the definition of harmonic ordering in terms of mark cancellation. Mark cancellation is indicated with diagonal shading in the tableau (9): one mark *P ARSE cancels between the first two candidates of (6), d and b , and one uncancelled mark *P ARSE remains in marks N (b ).

(9) Mark Cancellation

Defining grammaticality via harmonic ordering has an important consequence:

(10) Minimal Violation: the grammatical candidate minimally violates the constraints, relative

to the constraint ranking.

The constraints of UG are violable : they are potentially violated in well-formed structures.Such violation is minimal , however, in the sense that the grammatical parse p of an input I will best satisfy a constraint ÷, unless all candidates that fare better than p on ÷ also fare worse than p on some constraint which is higher ranked than ÷.

Harmonic ordering can be illustrated with CVT by reexamining the tableau (6) under the assumption that the universal constraints are ranked by a particular grammar, , with the ranking given in (11).

L 1L 1-CV

ep,del L 1L 2L 2F ILL Nuc F ILL Ons (11) Constraint hierachy for :O NSET >> N O C ODA >> >> P ARSE >> The constraints (and their columns) are ordered in (6) left-to-right, reflecting the hierarchy in (11). The candidates in this tableau have been listed in harmonic order, from highest to lowest Harmony; the optimal candidate is marked manually . Starting at the bottom of the 4tableau, a c can be verified as follows. The first step is to cancel common marks: here,there are none. The next step is to determine which candidate has the worst uncancelled mark, i.e., most violates the most highly ranked constraint: it is a , which violates O NSET .Therefore a is the less harmonic. In determining that c b , first cancel the common mark *P ARSE ; c then earns the worst mark of the two, *. When comparing b to d , one F ILL Nuc *P ARSE mark cancels, leaving marks N (b ) = {*P ARSE } and marks N (d ) = {*}. The F ILL Ons worst mark is the uncancelled *P ARSE incurred by b , so b d .

is a language in which all syllables have the overt form .CV.: onsets are required,codas are forbidden. In case of problematic inputs such as /VCVC/ where a faithful parse into CV syllables is not possible, this language uses overparsing to provide missing onsets, and underparsing to avoid codas (it is the language denoted in P&S:§6.2.2.2).

Exchanging the two F ILL constraints in gives the grammar :

F ILL Ons F ILL Nuc (12) Constraint Hierachy for :O NSET >> N O C ODA >> >> P ARSE >> Now the tableau corresponding to (6) becomes (13); the columns have been re-ordered to reflect the constraint reranking, and the candidates have been re-ordered to reflect the new harmonic ordering.

L 2

L 1L 2L 2L 2-CV del,ep L 1L 2(13) Constraint Tableau for

Like , all syllables in are CV; /VCVC/ gets syllabified differently, however. In ,underparsing is used to avoid onsetless syllables, and overparsing to avoid codas ( is P&S’s language ).The relation between and illustrates a principle of Optimality Theory central to learnability concerns:

(14) Typology by Reranking

Systematic cross-linguistic variation is due entirely to variation in language-specific rankings of the universal constraints in Con . Analysis of the optimal forms arising from all possible rankings of Con gives the typology of possible human languages.Universal Grammar may impose restrictions on the possible rankings of Con .

Analysis of all rankings of the CVT constraints reveals a typology of basic CV syllable structures that explains Jakobson’s typological generalizations (Jakobson 1962, Clements and Keyser 1983): see P&S:§6. In this typology, licit syllables may have required or optional onsets, and, independently, forbidden or optional codas.

One further principle of OT will figure in our analysis of learnability, richness of the

base. Discussion of this principle will be postponed until its point of relevance, section 4.3.

1.2 Decomposing the Learning Problem

The results presented in this paper address a particular subproblem of the overall enterprise of language learnability. That subproblem, and the corresponding results, are best understood in the context of an overall approach to language learnability. This section briefly outlines that approach. The nature of and motivation for the approach are further discussed in section 4.2.

To begin, three types of linguistic entities must be distinguished:

(15) Three Kinds of Linguistic Entities

Full structural descriptions: the candidate outputs of Gen, including overt structure and input.

Overt structure: the part of a description directly accessible to the learner.

The grammar: determines which structural descriptions are grammatical.

In terms of CVT, full structural descriptions are exemplified by the descriptions listed in (2). Overt structure is the part of a structural description that actually is realized phonetically. For example, in b = +V,.CV.+C,, the overt structure is CV; the unparsed segments +V, and +C, are not included. Unparsed segments are present in the full structural description, but not the overt structure. The part of the grammar to be learned is the ranking of the constraints, as exemplified in (11).

It is important to keep in mind that the grammar evaluates full structural descriptions; it does not evaluate overt structure in isolation. This is, of course, hardly novel to Optimality Theory; it is fundamental to linguistic theory in general. The general challenge of language acquisition, under any linguistic theory, is that of inferring the correct grammar from overt data, despite the gap between the two arising from the hidden elements of structural

descriptions, absent from overt data.

It is also important to distinguish three processes, each of which plays an important role in the approach to language acquisition proposed here:

(16) Three Processes

Production-Directed Parsing: mapping an underlying form (input) to its optimal description—given a grammar.

Robust Interpretive Parsing: mapping an overt structure to its full structural description, complete with all hidden structure—given a grammar.

Learning the Grammar: determining a grammar from full grammatical descriptions. Production-directed parsing is the computation of that structural description, among those candidates produced by Gen containing a given input, which is optimal with respect to a given ranking. Production-directed parsing takes a part of a structural description, the underlying form, and fills in the rest of the structure. Robust interpretive parsing also takes a part of a structural description and fills in the rest, but it starts with a different part, the overt structure. Robust interpretive parsing is closer to what many readers probably associate with the word “parsing.” “Robustness” refers to the fact that an overt structure not generated by the grammar currently held by the learner is not simply rejected: rather, it is assigned the most harmonic structure possible. The learner can, of course, tell that the assigned parse is not grammatical by her current grammar (by comparing it to the description her grammar assigns to the same underlying form); in fact, the learner will exploit that observation during learning. Both production-directed parsing and robust interpretive parsing make use of the same harmonic ordering of structural descriptions induced by the constraint ranking. They differ in the part of the structure they start from: production-directed parsing starts with an underlying form, and chooses among candidates with the same underlying form, while robust

interpretive parsing starts with an overt structure, and chooses among candidates with the same overt structure.

These entities and processes are all intimately connected, as schematically shown in (17).

(17) Decomposition of the Learning Problem

Any linguistic theory must ultimately be able to support procedures which are tractable performance approximations to both parsing and learning. Ideally, a grammatical theory should provide sufficient structure so that procedures for both parsing and grammar learning can be strongly shaped by grammatical principles.

In the approach to learning developed here, full structural descriptions bear not just a logical relationship between overt structures and grammars: they also play an active role in the learning process. We propose that a language learner uses a grammar to interpret overt forms by imposing on those overt forms the best structural descriptions, as determined by her current ranking. She then makes use of those descriptions in learning.

Specifically, we propose that a learner starts with an initial ranking of the constraints. As overt forms are observed, the learner uses the currently hypothesized ranking to assign

structural descriptions to those forms. These hypothesized full structures are treated by the grammar learning subsystem as the target parses to be assigned by the correct grammar: they are used to change the hypothesized ranking, yielding a new grammar. The new ranking is then used to assign new full descriptions to overt forms. This process continues, back and forth, until the correct ranking is converged upon. At that point, the ranking will assign the correct structural descriptions to each of the overt structures, and the overt structures will indicate that the ranking is correct, and should not be changed.

The process of computing optimal structural descriptions for underlying forms (production-directed parsing) has already been addressed elsewhere. Algorithms which are provably correct for significant classes of OT grammars have been developed, based upon dynamic programming (Tesar 1994, 1995ab, in press). For positive initial results in applying similar techniques to robust interpretive parsing, see Tesar, in preparation a.

At this point, we put aside the larger learning algorithm until section 4.2, for the present paper is devoted to the subproblem in (17) labelled “grammar learning”: inferring constraint rankings from full structural descriptions. The next two sections develop an algorithm for performing such inference. This algorithm has a property important for the success of the overall learning approach: when supplied with the correct structural descriptions for a language, it is guaranteed to find the correct ranking. Furthermore, the number of structural descriptions required by the algorithm is quite modest, especially when compared to the number of distinct rankings.

2. Constraint Demotion

Optimality Theory is inherently comparative; the grammaticality of a structural description is determined not in isolation, but with respect to competing candidates. Therefore, the learner is not informed about the correct ranking by positive data in isolation; the role of the competing candidates must be addressed. This fact is not a liability, but an

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Tesar & Smolensky Learnability in Optimality Theory

advantage: a comparative theory gives comparative structure to be exploited. Each piece of positive evidence, a grammatical structural description, brings with it a body of implicit negative evidence in the form of the competing descriptions. Given access to Gen and the underlying form (contained in the given structural description), the learner has access to these competitors. Any competing candidate, along with the grammatical structure, determines a data pair related to the correct ranking: the correct ranking must make the grammatical structure more harmonic than the ungrammatical competitor. Call the observed grammatical structure the winner, and any competing structure a loser. The challenge faced by the learner is then, given a suitable set of such loser/winner pairs, to find a ranking such that each winner is more harmonic than its corresponding loser. Constraint Demotion solves this challenge, by demoting the constraints violated by the winner down in the hierarhy so that they are dominated by the constraints violated by the loser. The main principle is presented more precisely in this section, and an algorithm for learning constraint rankings from grammatical structural descriptions is presented in section 3.

2.1 The Basic Idea

In our CV language , the winner for input /VCVC/ is .~V.CV.+C,. Table (6) gives the marks incurred by the winner (labelled d) and by three competing losers. These may be used to form three loser/winner pairs, as shown in (18). A mark-data pair is the paired lists of constraint violation marks for a loser/winner pair.

(18) Mark-data pairs ()

To make contact with more familiar OT constraint tableaux, the information in (18) will also be displayed in the format of (19).

(19) Initial data

At this point, the constraints are unranked; the dotted vertical lines separating constraints in (19) conveys that no relative ranking of adjacent constraints is intended. The winner is indicated with a T; L will denote the structure that is optimal according to the current grammar, which may not be the same as the winner (the structure that is grammatical in the target language). The constraint violations of the winner, marks(winner), are dis-tinguished by the symbol ?. Diagonal shading denotes mark cancellation, as in tableau (9).

Now in order that each loser be less harmonic than the winner, the marks incurred by the former, marks(loser), must collectively be worse than marks(winner). According to (8), what this means more precisely is that loser must incur the worst uncancelled mark, compared to winner. This requires that uncancelled marks be identified, so the first step is to cancel the common marks in (18).

L1

(20) Mark-data pairs after cancellation ()

The cancelled marks have been struck out. Note that the cancellation operation which transforms marks to marks N is defined only on pairs of sets of marks; e.g., *P ARSE is cancelled in the pairs b d and c d, but not in the pair a d. Note also that cancellation of marks is done token-by-token: in the row b d, one but not the other mark *P ARSE in marks(b) is cancelled.

The table (20) of mark-data after cancellation is the data on which Constraint Demotion operates. Another representation in tableau form is given in (19), where common marks in each loser/winner pair of rows are indicated as ‘cancelled’ by diagonal shading. This table also reveals what successful learning must accomplish: the ranking of the constraints must be adjusted so that, for each pair, all of the uncancelled winner marks ? are dominated by at least one loser mark *. Using the standard tableau convention of positioning the highest-ranked constraints to the left, the columns containing uncancelled ? marks need to be moved far enough to the right (down in the hierarchy) so that, for each pair, there is a column (constraint) containing an uncancelled * (loser mark) which is further to the left (dominant in the hierarchy) than all of the columns containing uncancelled ? (winner marks).

The algorithm to accomplish this is based upon the principle in (21).

(21) The Principle of Constraint Demotion: for any constraint ÷ assessing an uncancelled

winner mark, if ÷ is not dominated by a constraint assessing an uncancelled loser mark, demote ÷ to immediately below the highest-ranked constraint assessing an

uncancelled loser mark.

Constraint Demotion works by demoting the constraints with uncancelled winner marks down far enough in the hierarchy so that they are dominated by an uncancelled loser mark, ensuring that each winner is more harmonic than its competing losers.

Notice that it is not necessary for all uncancelled loser marks to dominate all uncancelled winner marks: one will suffice. However, given more than one uncancelled loser mark, it is often not immediately apparent which one needs to dominate the uncancelled winner marks (the pair a d above is such a case). This is the challenge successfully overcome by Constraint Demotion.

2.2 Stratified Domination Hierarchies

Optimality Theory grammars are defined by rankings in which the domination relation between any two constraints is specified. The learning algorithm, however, works with a larger space of hypotheses, the space of stratified hierarchies. A stratified domination hierarchy has the form:

(22) Stratified Domination Hierarchy

÷1÷2÷3÷4÷5÷6÷7÷8÷9

{, , ..., } >> {, , ..., } >> ... >> {, , ..., }

÷1÷2÷3

The constraints , , ..., comprise the first stratum in the hierarchy: they are not ranked with respect to one another, but they each dominate all the remaining constraints.

÷4÷5÷6

Similarly, the constraints , , ..., comprise the second stratum: they are not ranked with respect to one another, but they each dominate all the constraints in the lower strata. In tableaux, strata will be separated from each other by solid vertical lines, while constraints within the same stratum will be separated by dotted lines, with no relative ranking implied.

The original notion of constraint ranking, in which a domination relation is specified for every pair of candidates, can now be seen as a special case of the stratified hierarchy,

where each stratum contains exactly one constraint. That special case will be labeled here a

total ranking. Henceforth, ‘hierarchy’ will mean stratified hierarchy; when appropriate,

hierarchies will be explicitly qualified as ‘totally ranked.’

The definition of harmonic ordering (8) needs to be elaborated slightly for stratified

÷1÷2÷1÷2 hierarchies. When and are in the same stratum, two marks * and * are equally

weighted in the computation of Harmony. In effect, all constraints in a single stratum are

collapsed together, and treated as though they were a single constraint, for the purposes of

determining the relative Harmony of candidates. Minimal violation with respect to a stratum

is determined by the candidate incurring the smallest sum of violations assessed by all

constraints in the stratum. The tableau in (23) gives a simple illustration.

÷1÷2÷3÷4

(23) Harmonic ordering with a stratified hierarchy: >> {, } >>

Here, all candidates are compared to the optimal one, p. In this illustration, parses p and

32

p violate different constraints which are in the same stratum of the hierarchy. Therefore, 3

these marks cannot decide between the candidates, and it is left to the lower-ranked constraint

to decide in favor of p. Notice that candidate p is still eliminated by the middle stratum

34

because it incurs more than the minimal number of marks to constraints in the middle stratum.

(The symbol *! indicates a mark fatal in comparison with the optimal parse.)

With respect to the comparison of candidates, marks assessed by different constraints

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1简介2 2.4.3中文数字转换 (7) 2.5高级设置 (8) 2.5.1章节标题设置 (9) 2.5.2部分修改标题格式 (12) 2.5.3附录标题设置 (12) 2.5.4其他标题设置 (13) 2.5.5其他设置 (13) 2.6配置文件 (14) 3版本更新15 4开发人员17 1简介 这个宏包的部分原始代码来自于由王磊编写cjkbook.cls文档类,还有一小部分原始代码来自于吴凌云编写的GB.cap文件。原来的这些工作都是零零碎碎编写的,没有认真、系统的设计,也没有用户文档,非常不利于维护和改进。2003年,吴凌云用doc和docstrip工具重新编写了整个文档,并增加了许多新的功能。2007年,oseen和王越在ctex宏包基础上增加了对UTF-8编码的支持,开发出了ctexutf8宏包。2009年5月,我们在Google Code建立了ctex-kit项目1,对ctex宏包及相关宏包和脚本进行了整合,并加入了对XeT E X的支持。该项目由https://www.wendangku.net/doc/965805676.html,社区的开发者共同维护,新版本号为v0.9。在开发新版本时,考虑到合作开发和调试的方便,我们不再使用doc和docstrip工具,改为直接编写宏包文件。 最初Knuth设计开发T E X的时候没有考虑到支持多国语言,特别是多字节的中日韩语言。这使得T E X以至后来的L A T E X对中文的支持一直不是很好。即使在CJK解决了中文字符处理的问题以后,中文用户使用L A T E X仍然要面对许多困难。最常见的就是中文化的标题。由于中文习惯和西方语言的不同,使得很难直接使用原有的标题结构来表示中文标题。因此需要对标准L A T E X宏包做较大的修改。此外,还有诸如中文字号的对应关系等等。ctex宏包正是尝试着解决这些问题。中间很多地方用到了在https://www.wendangku.net/doc/965805676.html,论坛上的讨论结果,在此对参与讨论的朋友们表示感谢。 ctex宏包由五个主要文件构成:ctexart.cls、ctexrep.cls、ctexbook.cls和ctex.sty、ctexcap.sty。ctex.sty主要是提供整合的中文环境,可以配合大多数文档类使用。而ctexcap.sty则是在ctex.sty的基础上对L A T E X的三个标准文档类的格式进行修改以符合中文习惯,该宏包只能配合这三个标准文档类使用。ctexart.cls、ctexrep.cls、ctexbook.cls则是ctex.sty、ctexcap.sty分别和三个标准文档类结合产生的新文档类,除了包含ctex.sty、ctexcap.sty的所有功能,还加入了一些修改文档类缺省设置的内容(如使用五号字体为缺省字体)。 1https://www.wendangku.net/doc/965805676.html,/p/ctex-kit/

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中排布。年份、序号用阿拉伯数字标识,年份用全称,用六角括号“〔〕”括入。序号不用虚位,不用“第”。发文字号距离红色反线4mm。 (六)签发人 上行文需要标识签发人,平行排列于发文字号右侧,发文字号居左空一字,签发人居右空一字。“签发人”用3号方正仿宋_GBK,后标全角冒号,冒号后用3号方正楷体_GBK标识签发人姓名。多个签发人的,主办单位签发人置于第一行,其他从第二行起排在主办单位签发人下,下移红色反线,最后一个签发人与发文字号在同一行。 二、主体部分 (一)标题 由“发文机关+事由+文种”组成,标识在红色反线下空两行,用2号方正小标宋_GBK,可一行或多行居中排布。 (二)主送机关 在标题下空一行,用3号方正仿宋_GBK字体顶格标识。回行是顶格,最后一个主送机关后面用全角冒号。 (三)正文 主送机关后一行开始,每段段首空两字,回行顶格。公文中的数字、年份用阿拉伯数字,不能回行,阿拉伯数字:用3号Times New Roman。正文用3号方正仿宋_GBK,小标题按照如下排版要求进行排版:

tabularx宏包中改变弹性列的宽度

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2-1论文写作要求与格式规范(2009年修订)

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4.对本研究课题有创造性见解,并取得显著的科研成果。 5.学位论文必须是作者本人独立完成,与他人合作的只能提出本人完成的部分。 6.论文字数不少于5万字,中、英摘要3000字;详细中文摘要(单行本)1万字左右。 (四)临床专业学位博士论文要求 1.要求论文课题紧密结合中医临床或中西结合临床实际,研究结果对临床工作具有一定的应用价值。 2.论文表明研究生具有运用所学知识解决临床实际问题和从事临床科学研究的能力。 3.论文字数一般不少于3万字,中、英文摘要2000字;详细中文摘要(单行本)5000字左右。 二、学位论文的格式要求 (一)学位论文的组成 博士、硕士学位论文一般应由以下几部分组成,依次为:1.论文封面;2. 原创性声明及关于学位论文使用授权的声明;3.中文摘要;4.英文摘要;5.目录; 6.引言; 7.论文正文; 8.结语; 9.参考文献;10.附录;11.致谢。 1.论文封面:采用研究生处统一设计的封面。论文题目应以恰当、简明、引人注目的词语概括论文中最主要的内容。避免使用不常见的缩略词、缩写字,题名一般不超过30个汉字。论文封面“指导教师”栏只写入学当年招生简章注明、经正式遴选的指导教师1人,协助导师名字不得出现在论文封面。 2.原创性声明及关于学位论文使用授权的声明(后附)。 3.中文摘要:要说明研究工作目的、方法、成果和结论。并写出论文关键词3~5个。 4.英文摘要:应有题目、专业名称、研究生姓名和指导教师姓名,内容与中文提要一致,语句要通顺,语法正确。并列出与中文对应的论文关键词3~5个。 5.目录:将论文各组成部分(1~3级)标题依次列出,标题应简明扼要,逐项标明页码,目录各级标题对齐排。 6.引言:在论文正文之前,简要说明研究工作的目的、范围、相关领域前人所做的工作和研究空白,本研究理论基础、研究方法、预期结果和意义。应言简

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(公文写作)毕业论文写作要求和格式规范

中国农业大学继续教育学院 毕业论文写作要求和格式规范 壹、写作要求 (壹)文体 毕业论文文体类型壹般分为:试验论文、专题论文、调查方案、文献综述、个案评述、计算设计等。学生根据自己的实际情况,能够选择适合的文体写作。 (二)文风 符合科研论文写作的基本要求:科学性、创造性、逻辑性、实用性、可读性、规范性等。写作态度要严肃认真,论证主题应有壹定理论或应用价值;立论应科学正确,论据应充实可靠,结构层次应清晰合理,推理论证应逻辑严密。行文应简练,文笔应通顺,文字应朴实,撰写应规范,要求使用科研论文特有的科学语言。 (三)论文结构和排列顺序 毕业论文,壹般由封面、独创性声明及版权授权书、摘要、目录、正文、后记、参考文献、附录等部分组成且按前后顺序排列。 1.封面:毕业论文(设计)封面(见文件5)具体要求如下: (1)论文题目应能概括论文的主要内容,切题、简洁,不超过30字,可分俩行排列; (2)层次:高起本,专升本,高起专; (3)专业名称:现开设园林、农林经济管理、会计学、工商管理等专业,应按照标准表述填写; (4)密级:涉密论文注明相应保密年限; (5)日期:毕业论文完成时间。 2.独创性声明和关于论文使用授权的说明:(略)。

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