Outlines of a model for a grammar of discourse

W. KUMMER

OUTLINES OF A MODEL FOR A GRAMMAR OF DISCOURSE

1. SCOPE AND STRUCTURE

OF THE MODEL

The model for a grammar of discourse outlined below is based on recent developments in the theory of Transformational Grammar and in Intensional Logic and its applications to natural languages. The part of the grammar presented is restricted mainly to the treatment of anaphoric phenomena. The rules are set up to function mainly in the analysis of given texts; a detailed system for generating texts coherent in their anaphoric relations has been given by Bohumil Palek in the monograph Cross-Reference : A Study in Hypersyntax.1 Connections between Palek’s rules for generating texts and the proposed system for analysing texts will not be mentioned in this paper. 1.1 The Structure of the Grammar In accordance with standard views about the tasks of a generative grammar the model has to fulfill at least the following conditions: (a) it has to enumerate all possible wellformed sentences of a language and to mark the types of deviance of not-wellformed sentences (b) it has to assign to every sentence a structural description (c) it must indicate the possible readings of a given sentence Besides these wellknown aims of a generative grammar a discourse grammar is assumed to have to fulfill the following requirements: (a) it has to analyse any given sentence of a language and to assign its possible readings to it (b) it has to explicate the connections between sentences in a given discourse 1 Palek’s method consists basically in deciding which sequences of determiners and other quantifying elements for NPs in a sequence of sentences guarantees a coherent text.

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W. KUMMER

(c) it must allow a definition of ‘coherent text in language L’ and a process of generating coherent texts in language L2 The following parts of the model are assumed to fulfill these tasks: 1.11 A Surface Structure

Grammar

The grammar has to asign labelled bracketings to any given input sentence of a language L, such that every bracketing corresponds to one possible parsing of the sentence. In the process of synthesis the surface structure grammar gives output conditions for strings.

I .I2 A Grammar for Canonical Forms

The grammar gives the formation rules for a language in which the LOGICO-SEMANTIC STRUCTURES or LOGICAL FORM4 of sentences can be represented. This language has the form of a logical calculus, which includes at least a propositional calculus, a functional calculus of first order with identity and a system of modal operators. Besides this it has to include a system of POINTS OF REFERENCES relating sentences to parameters like speaker, time of utterance etc. The axioms for this language include at least all the axioms of the propositional calculus, the functional calculus of first order and the variety of modal logic chosen for the language, as well as the rules of derivation for these parts of logic. Besides these components the grammar specifies the form of rules, which are called MEANING POSTULATES, for the SEMANTIC PART of the dictionary 2 Several definitions of ‘coherent text in language L’ have been proposed, among others by Roland Harweg and Irena Bellert. The definitions are mostly based on the requirement of anaphoric connections between all the sentences in the sequence of sentences forming the text. As this requirement seems to be too strong and no alternative definition can be given under the present approach till a large number of rules of coherence is established, it will not be attempted to frame a definition in this paper. It should be clear that TEXTIJALITY is a concept defined within a theory of discourse grammar and cannot be directly derived from the analysis of given sequences of sentences. s The term was introduced in linguistic literature by Irena Bellert to distinguish canonical forms from DEEPSTRUCrUREs of transformational grammar. 4 The term is generally in use in the fields of logic dealing with the analysis of natural languages and has been adopted specifically from the work of Donald Davidson. 5 A system of intensional logic implying parameters for POINTS OF REFERENCE is called a PRAGMATICAL LANGUAGE by R. Montague. The richest system of POINTSOF REFERENCE as a pairing of a ‘possible’ world with parameters of the speech-situation was proposed by Montague in Universal Grammar; a short explanation of the term is to be found in Dana Scott, Advice in Modal Logic.

A GRAMMAR

OF DISCOURSE

31

entries for lexical items or for relations of implication deducible from syntactic constructions. 1.13 A System of Translation Rules between Surface Structures and Canonical Forms The translation rules have the form of TRANSFORMATIONS mapping labelled bracketings into labelled bracketings. The ordering of the rules is linear and they apply cyclically. 1.14 A Set of Global Derivational Constraints6 Global derivational constraints control the applicability of translation rules in the process of deriving canonical forms from surface structures or surface structures from canonical forms. 1.15 A Lexicon The lexicon specifies the syntactic information for a lexical item needed in the surface structure grammar and the translation rules, and gives the semantic information in the form of MEANING POSTULATES. 1.16 A Set of Rules of Coherence They operate on the canonical forms of sentences of a text specifying the anaphoric relations or other relations between the sentences or parts of sentences involved.7 In the process of generating coherent discourse the rules function as indicators for requirements a successor-sentence or predecessor-sentence must fulfill for a text to be coherent. 1.17 A Semantic Interpretation It maps canonical forms into model structures, which must at least be powerful enough to handle modal contexts and the system of POINTS OF REFERENCE included in the language for the canonical forms. The models constitute POSSIBLE TEXT WORLDS for a given discourse and s The concept was introduced by George Lakoff in a number of papers mentioned in the bibliography. 7 Some of the relations not treated in this paper axe: topic-comment progressions, relations by RELATOR WORDS as conjunctions or implicit relations etc.

32

W. KUMMER

explicate the MEANING of the sentences involved by specifying the truthconditions in a model structure.8 1.2 Motivation for the Apparatus It is impossible to give a detailed defense of all the types of rules required

in the model, but some intuitive arguments for setting up the different parts of the system are in order. Probably there will be no doubts as to the necessity of a surface structure grammar assigning structural descriptions to sentences of a language, and the requirement that a grammar should be able to account for all possible sentences of a language. A major difference between classical Transformational Grammar and the Grammar of Discourse proposed here is the status of SENTENCEas a descriptive term. Because it is claimed that it is impossible to analyse sentences without having recourse to parameters of context and cotext, SENTENCE in this model means ‘possible part of an utterance having the form of a well-formed formula’ or shorter ‘utterance-type having the form of a well-formed formula’. The claim, that the component of a grammar specifying the readings of surface sentences should have the form of a logical calculus is relatively new in linguistic theory, but generally acknowledged in the fields of logic dealing with the analysis of the logical form of sentences. In order to validate this claim for linguistic theory it must be shown that the systems of semantic interpretation proposed in the linguistic literature are equivalent to some form of some logical calculus proposed for the grammar of canonical forms.g If it is true that the so-called “semantic interpretation” of surface strings can be handled by a logical grammar for canonical forms it can be shown that such a system has some definite advantages over any of the systems of semantic interpretation proposed up to now. It involves no claim that there exists a syntactic level of DEEP STRUCTUREfunctioning as a device generating strings which can be interpreted semantically, but instead puts the generative capacity of the system directly into the * The connections between MEANING and truth-conditions have been stated most clearly in Donald Davidson, Truth and Meaning, and an application to natural languages can be found in Edward Keenan, A Logical Base for a Transformational Grammar of

English. g It is easy to show this for a Katz-Fodor type of semantics; more recent systems

for semantics like the one proposed by Klaus Brockhaus and Arnim v. S&how are already based on a logical system.

A GRAMMAR OF DISCOURSE

33

SEMANTIC COMPONENT, which

seems intuitively to be more satisfactory.10 Secondly a system of the proposed kind can take advantage of the rich tradition of logical analysis of natural languages.11 Besides this it allows a characterization of relations between sentences like ‘consequence of’, ‘presupposition of’, ‘synonymous with’, ‘hyponymous with’, ‘equivalent to’, ‘analytic’ etc., which are generally assumed to be relations which have to be explicated by a theory of meaning, in terms of well-known operations on canonical forms.12 Another advantage of a model with a logical base is a natural treatment of what has traditionally been called the THEORY OF REFERENCEas against the THEORY OF MEANING. The major problem for an application of the THEORY OF REFERENCE to natural languages has always been, that the notion of ‘existing individual’ is irrelevant to natural languages, while the important concept for natural languages is ‘possible individual’. Since the development of intensional logics powerful enough to handle PRAGMATICAL LANGUAGES the reconstruction of the notion ‘possible individual’ poses no major problems. The THEORY OF REFERENCE can be handled by model structures for canonical forms, and the THEORY OF MEANING is based on the truthconditions of sentences in models for intensional logics.13 Another feature of the development of INTENSIONAL LOGIGS relevant to linguistic theory is the definition of truth and related notions for types of sentences traditionally believed to be incapable of treatment in the framework of truth-functional logic. By now there exists a well-developed branch of logic dealing with definitions of truth-conditions for questions,

10 This does not identify the proposed model as a variant of a system of GENERATIVE of the basic tenets of GENERATIVE SEMANTICS is not accepted: the derivation of lexical items via transformations. In this model lexical items which are not LOGICAL WORDSand so don’t control processes in the translation from surface structures to canonical forms are kept unanalyzed by the translation rules and are only analysed by help of the meaning postulates. Such a treatment does not have to claim an equivalence between a lexical item and the result of its analysis, as it is necessary for GENERATIVE SEMANTICS, if transformations don’t change meaning, but only a relation of implication between lexical item and result of analysis is assumed. This approach makes the canonical form of the proposed model a DEEP STRIJ~~~RE in the technical sense of Chomsky’s, Empirical Issues in the Theory of Transformational Grammar, because all lexical items (with the exception of LWICALWORDS)are introduced at this level. 11 The most important result of this tradition are available in some recently edited collections of papers (ed. Davis, Rescher, Lambert, Logic and Lunguage). 12 Definitions of these relations in a framework similar to the one proposed here are to be found in E. Keenan’s LogicaI Base. l3 Cf. Montague, Vragmatics” and “English as a Formal Language”. SEMANTICS, because one

34

W. KUMMER

commands, epistomological contexts etc.14 A linguistic model with a base grammar in the form of a logical calculus can take advantage of these developments. All the arguments presented up to now can only show that a logical base can handle at least all the data a traditional transformational grammar can handle in its semantic component, and that the adoption of a logical base leads to certain desirable results in the treatment of some refractory areas of description of natural languages. But the arguments cannot prove that it is necessary to adopt a logical base for a grammar. The major arguments for the necessity of a logical base come from the needs of a discourse grammar. Any discourse grammar which is powerful enough to explicate the coherence between sentences in a text needs a strong component allowing inferences on the material presented in the sentences of the text. The coherence between the sentences can in many cases not directly be read from the morphological material of the text, but has to be inferred from this material. Some examples for types of inference needed even in the simplest parts of a grammar of discourse will be presented below. Since no system of semantic interpretation developed so far within linguistics has a strong inferential component it is necessary to use the rules of inference available in logical theory. This does not mean that no new rules of inference need to be set up which are specific for what has been called NATURAL LOGIC or the LOGIC OF DISCOURSE. But most of the examples for the LOGIC OF DISCOURSEknown to the author can be treated as operations on base forms of sentences which are equivalent to logical inference rules. It shall not be claimed that all LOGICAL SI-RUCTURES of discourse are reducible to known rules of inference, but that rules of inference can be set up on logical base structures allowing their treatment. That the translation rules between canonical forms and surface structures map labelled bracketings into labelled bracketings and not simply give a direct mapping between two levels of structure15 is based on the fact that there does not exist a one-one correspondence between surface structures and canonical forms. An ambiguous surface structure must be assigned different canonical forms, and a canonical form can correspond to a variety of surface structures. There is a large body of 14 Truth-conditions for questions are deiined in Lennart Aquist, A New Approach to the Logical Theory of Interrogatives, for commands in Rescher’s Logic of Commands and for epistemological contexts e.g. in Hintikka’s Knowledge and Belief. 16 Such a mapping is proposed by Bohnert and Becker in Automatic-English-to-logic Translation and as an isomorphism between two algebras in Montague, Universal Grammar.

A GRAMMAR OF DISCOURSE

35

known principles and rules of translation available in the literature on generative grammar, and other rules of translation can be modelled on them. The basic problem in the process of translation is the fact, that the metalanguage for the syntactical description of the surface structures and the metalanguage for the ‘semantic’ canonical forms are categorically different. It is therefore either necessary to develop a regimented DEEP STRUCTURE for syntax and to translate it by a mapping directly into the canonical form, or to give a step-by-step procedure of translation which uses the transformations mapping labelled bracketings into labelled bracketings to translate successively parts of the surface structure into canonical form. In the present model the second method is used, although it is by no means clear how workable it is for a general treatment of natural languages. The proposed discourse grammar requires that all translation rules should be able to function in the direction of analysis. At the present stage of linguistic knowledge it is an open question whether the rules used for analysis can also be used in the process of synthesis, or if the grammar for analysis has to be completely or partially distinct from the grammar for synthesis.ls Recent developments in transformational grammar suggest, that simple transformations are not enough to control the translation process between surface forms and canonical forms and led to the proposal of global derivational constraints predicting certain features of canonical forms directly from surface forms by a control of a whole set of transformations.17 In the examples presented below MEANING POSTULATES of only the simplest form, similar to those proposed by Carnaprs are used. As a connector the simple sign of implication is taken, although a more detailed account has to differentiate between LEXICAL PRESUPPOSITIONS,~~ simple implications and other relations for implicative terms like those proposed by Karttunen.20

16 A solution of the question depends on a prior solution of the formal treatment of transformations, which is barely under way. 17 Lakoff’s notation for global derivational constraints is adopted in this paper. 1s Cf. Rudolf Camap, Meaning Postulates. 19 A classification into “lexical” and “non-lexical” presuppositions was proposed by Ference Kiefer in On Presuppositions. 20 Cf. Lauri Karttunen, On the Semantics of Complement Sentences.

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W. KUMMER

2. THE FUNCTIONING

OF THE MODEL

Some examples will be given for the types of rules involved in the model and for their functioning in derivations.

2.1 The Grammar for Canonical Forms No fully specified rules of formation for the grammar are presented, but some tentative features of the grammar are informally discussed. The system is presented in the form of a many-sorted language, but well-known processes could be used to reduce it to a language with just one sort of variables. The language has different sorts of constants and variables ; all constants and variables stand for SETS of items of the respective sorts:21 thing constants: a, b, c... fact constants: ar, br, cf... event constants: ae, be, ce.. . property constants: ap, bp, cp.. . and corresponding

variables :

thing variables : x, y, z.. . event variables: Xe, Ye, Ze.. . fact variables : xi, yf, zf . . . property variables: xp, yp, zp.. . Other sorts of constants and variables are: constants for time-points: COnstantS for space-points variables for time-points: variables for space-points

at, bt, ct.. . : p&, plb,pk

tr, tz, rs. . . : p11, plz, pk.. .

The sorts of individuals assumed are linguistically motivated and have ontological import only in this relativized sense. To the different sorts of individual terms correspond different categories of predicates; thing predicates, event predicates, fact predicates, property predicates etc. In the examples a specific form for fact predicates and 21 A similar treatment is proposed in W. Quine’s Mathematical Logic.

A GRAMMAR

OF DISCOURSE

event predicates will be used, corresponding splitting’ and ‘event splitting’+

PWl+ 0-b)

to Reichenbachs

37 ‘fact

P’Wl+ (Ad

‘P’ is a metalinguistic name for predicates of any category; if the category has to be specified, subscripts analogous to those used for the individual terms are used. ‘A’, ‘B’ etc. are metalinguistic names for individual terms of the category marked by the subscript. Examples for ‘event splitting’ and ‘fact splitting’ are: The murder of Caesar took two hours The murder of Caesar was unexpected

(1) (2)

Besides the individual terms mentioned there are individual functions mapping individuals into individuals like : the father of -

(3)

There are some marked predicates in the calculus like the following: identity: ‘=’ forming a formula when used between two terms zero predicate : ‘ 0 ’ used for pronominal forms name predicates: used for predicates equivalent to ‘is called A’; name predicates are marked by the subscript ‘n’. number predicates: give the cardinal number of set@; they can be definite like the natural numbers or indefinite like the ‘higher predicates’ which have been called ‘quantifiers’ in linguistic literature+ ‘an’, ‘the’, ‘many’, etc. (‘an’ and ‘the’ get the number predicate ‘1’ if not used in the plural or in a generalized sense) There

are marked individual constants specifying the POINTS OF for the semantic interpretation of the base language:

REFERENCE SPi

rei tsi

speakerr (the subscript is used, if more than one speaker is involved in a text) = receiver(s) = time of utterance of sentence i =

22 Reichenbach’s proposal was worked out in further detail by Christian Rohrer in Funktionelle Sprachwissenschaft und Tranqformationelle Grammatik; it probably has to be modified according to the criticism presented in Donald Davidson’s LogicaI Form of Action Sentences. 29 The analysis of number predicates proposed is by no means clear and probably has to be modified in radical ways. 24 The analysis of quantifiers as higher predicates was proposed by G. Lakoff and G. Carden and attacked by B. Partee; see also L&off’s reply in “Repartee”.

38

W.

KUMMER

pl,i = place of utterance of sentence i pl,~i = point of perspective in the visual field There are the usual quantifiers for existence and universality, the logical connectors, negation, and a set of relators between well-formed formulae specifying relations like causality etc. Besides this there is a class of operators including the well-known markers for the aesthetic modalities, deontic modalities etc.25 For the following examples it is enough to assume as axioms the axioms of the propositional calculus, the axioms of quantification and the axioms specified by the meaning postulates. The rules of inference are modus ponens and the rules of quantification. No inference rules for modalities will be used. The POINTS OF REFERENCE are involved in nearly all types of sentences in natural languages: tensed discourse involves tSi as a point of reference, local deixis involves pldi and p&i. Each canonical form of a sentence consists of two parts which are headed ‘P’ and ‘A’ respectively; i.e. PRESUPPOSITION and ASSERTION. The test for factoring out presuppositions is the wellknown negation test: a sentence as well as its negation imply the truth of a presupposition.ss In the derivation from surface structures to canonical forms presuppositions are factored out by specific translation rules. The distinction between constants and variables is used to differentiate ‘new’ information, which is represented by variables, from information assumed to be known to the receiver, which is represented by constants. The difference turns up e.g. in the distinction between definite and indefinite descriptions.27 It is important to distinguish between this difference and the difference between presupposition and assertion. Not every presupposed information is assumed to be known to the receiver, e.g.: (4)

Why are you sorry? I am sorry,

BECAUSE MARY

presupposes: Mary is here In the system proposed here the distinction

IS HERE

between variables and

2s A good introduction to the systems of modal operators proposed in the literature is to be found in the collection of papers on Modal and Many-valued Logics. 26 The definition is probably due to Frege and is given in full in E. Keenan’s Logical Base and F. Kiefer’s On Presuppositions. 17 A similar treatment is proposed by F. Kiefer in On Presuppositions although it is not embedded in the framework of a grammar of discourse.

39

A GRAMMAR OF DISCOURSE

constants is handled by the translation rules; ambiguities can be eliminated partially by the rules of coherencess 2.2 The Meaning Postulates In the following examples these meaning postulates will be needed: (x) (x) (x) (x)

(Peter,(x) 2 miinnlich(x)) (M&khen(x) 3 weiblich(x)) (Blondine(x) 3 weiblich (x))

(Junge(x) 3 mSinnlich(x))

(Pl) (P2) (P3) (P4)

2.3 The Translation Rules

The following ordered set of rules is assumed for the translation process between surface forms and canonical forms. The rules specify only a part of the whole translation process starting at a level corresponding approximately to a syntactic DEEP smucwm of a transformational grammar and leading to the canonical forms. The part of the translation process from the surface structures to the starting point of the set of rules specifically given below corresponds to wellknown syntactic transformations and need not be written out in detail. (Rl)

(a) NPi + NPi xi (b) (s x (NPi (s)) I> 123

(R2) (R3)

1 y> -+ 12 {$

4

(IQ (up,= (a (NPrXk x)))) + 1 i2 3 ‘4 5 67 (NP (S da# X>> -+

Izr, 2

}, 324

OBL 1,2,1,2,0,2,7 OBL OBL

1 2 (R4)

(R5)

(s {V, NP+Nom, NP+Gen, NP+Dat, NP+Akk}) + 1,2,3,4,5 2 5 1 3 4 explanation : “I” is used to mark a set; 2, 3, 4,5 are optional OBL (a) NPI xi+Def+ P 1 1 I xfX3”’ @) (s NPi

+ PI,233 OBL

SEIn this respect the rules proposed in the paper are still too powerful as they allow the detection of ambiguities which are not recognized by a native speaker of a language.

W.

40

KUMMER

W) OBL

OBL 1 W)

(NPI 1

(9) --t 0,2,

Xei xii

[31+

3

ad

Iafi I 2

OBL

1 2 3 where: “Lex” = lexical items under NP (sV+Lex, y)-+ 0, 0,3,4 VW 12 3 4) where: “Lex” = lexical items under V (RI 0 Lex. ..x.. . --t (Ex) Lex (...x. ..) VW 1

2

OBL

OBL OBL

OBL 2.4 The Global Derivational Constraints

These constraints specify conditions which a surface structure or a canonical form must meet given certain features of the canonical form or surface structure respectively, from which it is derived. One global derivational constraint needed for the examples is the constraint on identities in complex sentences known as the Langacker-Ross constraint on backwards pronominalization :29 Cl ca:

A=B NP(A) commands NP(B) NP(A) precedes NP(B)

c4:

N-W9

c2:

-

Constraint:

Pro P&I

1

(P&2

. P&3

. P&4)

29 The constraint was formulated in R. Langacker’s Pronominalization and the and recast in J. Ross, Constraints on Variables in Syntax.

Chain of Command

A GRAMMAR

OF DISCOURSE

41

The constraint specifies for the conditions Cl - Cd that an identity in the canonical form (PI) is incompatible with a surface structure (P,) in which a nonpronominal NP is preceded and commanded by another NP.30 2.5 The Rules of Coherence The component of the grammar dealing with the coherence of sentences in a discourse consists of a set of rules and a set of rule schemata applicable to all of the rules. For the application of the rules of coherence the canonical forms of sentences have to be transformed into PROCESSUAL NORMAL

FORMS.

2.51 Processual Normal Forms The processual normal form gives the information, which part of the canonical ‘form for a sentence is assumed to be known to the receiver or has deictic function, and which part of the canonical form consists of information available for future sentences in the discourse after the sentence has been uttered. The rules for transforming canonical forms into the processual normal form are the following: (1) Copy all wellformed formulas in the presupposition the arguments of which contain at least one individual constant of some sort into AI (Anfangsinformation) and EI (Endinformation) (2) Substitute for any variable bound by an existential quantifier a constant which is not identical with one of the constants in AI. Substitute for any variable bound by a universal quantifier a constant which is not identical with one of the constants in AI, or, if the quantification has as its domain one of the constants in AI, substitute the respective constant. Copy the information so obtained into EI. 2.52 Ruie Schemata The following rule schemata are assumed to be valid: (RSl) AI: P(A) EI: Pi(B)

EI: Pj(A)

A n B = I

Condition: PI 2 N Pi 3o The sign ‘ 4 ’ is used for incompatibility.

0

W.

42

(RS2)

(RS3) (RS4)

(RS5)

KUMMER

The first line specifies AI and EI of the sentence under investigation, the second line specifies the EI of the sentence the coherence of which with the sentence under investigation is tested by a rule of coherence. (RSl) specifies that an identity is impossible to derive given incompatible predications about the respective sets, AI: (EX) (...X...) A (EX) (...;...) EI: (EY) (...Y...) i Condition: P(X) = P(Y) The schema specifies that given identical predicates for two variables, a constant substitutable for the variable in the EI of the compared sentence can be substituted for the variable in the AI of the sentence under investigation. (A = B) E P(A) = P(B) (Identity of indiscernibles for texts) For any tsr and ter and any rule of coherence, the rule is applied to tsi before it is applied to tsj if i .c j, where ‘tsi’ and ‘rsj’ are used as indices for the ordering of the sentences in a text (‘left to right convention’ for rule application). (EPr) (Pi c Consqu(Pr)) . (- Pi c Consqu (Ps)) . PI(A) . P2(B)

=

A

f

B

where ‘Consqu’ stands for the consequences derivable from Pr and PZ respectively via the meaning postulates and the rules of inference. (Identity is impossible if the consequences of applying one predicate to an individual are inconsistent with the consequences of applying another predicate to the individual.) (RS6) (1 I+>(xd = ([I:l+@dl+>Ord in EI or AI (a fact is equivalent to the existence of a corresponding event) (RS7) EI: I’@) = ([[Pe(B)I+(Ae)l+ (Ad (any event predication in EI can be transformed into ‘fact splitting)’ 2.53 Rules of Coherence The rules of coherence

specify the AI and/or EI of a sentence under investigation (first line of the rule), the EI of the sentence the coherence of which with the one under investigation is to be tested, a specification of the scope of application of the rule given in terms of a numbering of the sentences in a text using their times of utterance as an index, and a series of conditions which must be fulfilled for a rule to apply. If the

A GRAMMAR OF DISCOURSE

43

conditions are in a hierarchical order and the scope of the rule covers more than one sentence, it is understood that the order of application is the following: start with the condition highest in the hierarchy and work beginning from the sentence within the scope closest to the one under investigation, working to the end of the scope step by step. If the highest condition is not applicable, take the second in the hierarchy etc. @Cl) AI: PI(A) A _ B EI: P2(B) I scope: rsi_n and for all j between i and n EIj # AI, &I+1 Conditions : NF’(Pl), NP(Ps), AI: l(A) and EI : 1(B) or AI: N Pnum(A) and ,“:,:,

““p’, and r;(z]

(2) Pl c Ps and r;PJ

~rz] r;YP;j]

(3) Consqu (PI) c Consqu (Pz) and NP(PI), NP(Ps) (4) @PI) ((Pi c Consqu (IQ. (Pi c Consqu (WN wm

NJv2)

The rule specifies that two sets are identical only if their syntactic correlates are NPs and the number predicates are either ‘one’ for EI and AI or there is no number predicate (notation for plurals without quantifiers) in the AI and a number predicate differing from ‘one’ in EI. These conditions exclude identities in cases like: (5)

*a man . . . the men Isome of the men 1

They allow identities in cases like: (6)

the men some of the men many of the men etc.

In cases like (6) there is a presupposed set of men in the AI for the second occurrences, over which the assertion of the respective sentences quantifies. The identity applies to this presupposed set, and no special treatment of subset-formation or the relation of membership is necessary in the rule of coherence. Cases in which the first occurrence marks a

W. KUMMER

44

subset or membership in a set given by the second occurrence are treated by a special rule of coherence called GENERALIZATION. The numbered conditions are hierarchically ordered and require either identity of predicates (e.g. a man . . . the man) and genus identity or subset relation of the predicates, which can be tested using the meaning postulates (e.g. a bachelor . . . the man . . . he) or subset relation between the consequences of the respective predicates without requirement of genus identity (e.g. eine Frau . . . das hiljiose Geschiipf) or the existence of at least one common predicate derivable by the meaning postulates from the given predicates (e.g. Lola . . . die Serviererin). The scope of the rule goes as far back in the text as no EI is met that is identical to the AI or goes one sentence to the right (e.g. this girl: . . . she). (RC2) AI: PI(A) EIi: P2(B) A = )Bu Cu . . . WI} . .. . .. .. . .. . EL: P2(I) I scope : tsi._n Conditions : N l(A) otherwise as in RCl (example: a cow . . . two cows . . . some cows . . . the cows 1some of the animals1) (RC3) AI: P&W Ae = Be EI: h(Be) I scope: tsi-1 Conditions : NP(Pr), S(P2)

other conditions as in RCl The rules of coherence given so far are needed for the analysis of the examples below; for a full analysis of a language it is necessary to find many more. All rules of coherence are optional, i.e. it is always possible to give an interpretation to a sequence of sentences, in which no identities are assumed, but such an interpretation violates the definition of a coherent text. 2.54 Analysis of Examples Consider the following short discourse: Peter ki@te das Mfidchen, das er liebte. Daj der Junge das tat, (7) freute die Blondine The following

structures,

approximately

corresponding

to syntactic

A GRAMMAR

45

OF DISCOURSE

deep structures, are assumed to be given for the two sentences of the discourse : (74

G’b)

a!

Def

The translation rules assign the following-derivations

I

to these structures :

W.

46

KUhlMER

(7a)

I I

[""I

II”1 CL”“” I

(R4)

S

A GRAMMAR (R5)

OF DISCOURSE

47

s

‘-------NP P

r

i kiissen -,

I

N PI

cI Pefer

CR@ S

(R7)

pj& NPQ

V

NP.

W.

48

KUMhfER

CR9) S

kiissen

Peter

al

0

Miidchen

a2

(R12) P: Peter al. Miidehen az. 0 as. lieben a5az A: kicssen ala2 (7b)

(RI)

Lieben

@

as

a-z

A GRAMMAR

OF DISCOURSE

(W

Xe?

(R4)

W. KUMMFS

50 (R5)

CR71

hp. \

-NPS

P

mlLa*l

J-

i\ LB*Odinel

S

P

P--------

NP -pi]+ I

NP7 \ae7

51

A GRAMMAR OF DISCOURSE

K

--P

I\

LBlondin’3

/,a*l

a6

APT p------q+ \

V

a7

a6

COJ (RIO)

[ra

LJuweJ

Junge aa [@I+ ae71+of1 Blondine as

(R12) P: Junge a6 [a]+ ae7 [0 (as, ae7)]+ an A: jieuen (an, as)

Blondine as

The canonical forms derived are: (7a) (7b)

P: A: P: A:

Peter u1 . itflidchen a2 . o a5 . lieben a5 a2 kiissen al a2 Junge utj . [a]+ ae7 . [ @ (as, a.# at1 . Blondine as freUf?n of1 a8

Next the canonical forms are translated into processual normal forms: (7a) (7b)

AI: EI: AI: EI:

Peter al . Mridchen a2 . o a5 . lieben a5 a2 Peter al . Mlidchen a2 . (ZI a5 . lieben as a2 . kiissen al

02

Junge a6 . [ 0]+ Ue7 . [ 0 (as, &7>]+ an . Blondine a8 Junge a6 . [ 0]+ Ue7 . [ 0 (a& a,$]+ ai1 . Blondine US . j?euen aila8

Applying (RCl) to (7a) condition 2 in accordance with the global derivational constraint on backwards pronominalization guarantees under one interpretation: ‘a5 = al’. For the following this interpretation will be a88UUIed.

W.

52

KUMMER

(RS4) specifies that the first application of rules of coherence has to be used between the EI of (7a) and the AI of (7b): AI: Junge ~6 . [a]+ ae7 . [ 0 (ae, ae7)]* ~1 . Blondine as El: Peter 01 . MBdchen us . lieben al us . kfissen ui us Using the meaning postulates given in 2.2 the following derivations can be formed for AI and EI: Junge ug (x) (Junge(x) I mPnnlich us Peter al (x) (Petern(x) 3 mlnnlich al Blondine ag (x) (BZondine(x) weiblich us Mgdchen us (x) (Miidchen(x) weiblich us

(AI) mlnnlich(x))

m&mlich(x))

2 weiblich(x))

13 weiblich(x))

(P4) (axiom of quantification) (EI) (Rl) (axiom of quantification) (AI) P3) (axiom of quantification) @I) (P2) (axiom of quantification)

Using these derivations condition 4 of (RCl) is fulfilled and the following identities can be inferred: ‘Us = al’, ‘UZ = us’. (RS5) guarantees that the appositive material involved in this identity is factored out. Next (RS7) can be applied to EI resulting in: EI: [[Zieben(~1, US)]+aez]+up.2 [[kiissen (Ul, Uz)]+ be]+ bf (RC3) is applicable under condition 2 and the following identities are derivable: ‘ai1 = uf2’ and ‘an7 = ae2' or ‘ari = bt’ and ‘ae7 = be’. Translating the results obtained by the rules of coherence back into the processual normal forms we get the following two interpretations for the coherence of (7): I: (7a) AI: Peter at . MGdchen u2 . lieben al a2 EI: Peter al . MGdchen u2 . lieben ul a2 . kiissen 01 u2 (7b) Junge al . [[Ziebenal u2]+ ae2]+ ufl . Blondine u2 EI: Junge (11 . [[lieben ul a~]+ ue2]+ ml . Blondine u2

.

aflu

II: (7a) AI : Peter al . Mtidchen u2 . Zieben al (12 EI: Peter 01 . Miidchen a2 . lieben al ~72. kiissen al LIZ

freuen

GRAMMAR

OF DISCOURSE

53

(7b) AI: Junge al . [[kiissen al az]+ be]+ afl . Blondine a2 EI: Junge al . [[kiissen al a~]+ be]+ ail . Blondine 02 . freuen ai1

a2

It is easy to translate these processual normal forms back into canonical forms and to use translation rules to translate the canonical forms back into surface forms. The two resulting versions of the discourse are: (8) 69

Peter kiipte das Mlidchen, dus Peter liebte. DuJ Peter dus MZdchen liebte, freute das Miidchen, das eine Blondine wur. Peter kiijte das Miidchen, dus Peter liebte. DuJ Peter das Miidchen kiipte, freute dus Miidchen, dus eine Blondine war.

3. CONCLUSION

The analyses and rules presented are highly tentative, but it is assumed that a grammar of discourse has to be based on a model of the form outlined if it shall be powerful enough to analyse the coherence between sentences in a text. Freie Universita”t,Berlin

BIBLIOGRAPHY

Aquist, Lennart 1965 A New Approach to the Logical Theory of Interrogatives, Part 1 (Uppsala). Bohnert, H.C. and P.O. Becker 1967 Automatic English-to-Logic Translation in a Simplified Model, IBM Research Paper RC-1744 Brockhaus, Klaus turd Arnim v. Stechow 1970 “Formale Semantik”, in: Beitr&e zur generativen Grammatik (Braunschweig). Bellert, Irena 1970 “A Condition on the Coherence of Texts”, Semiotica 2. Catnap, Rudolf 1947 “Meaning Postulates”, in: Mean& and Necessity (Chicago), 222ff. Carden, Guy 1968 “English Quantifiers”, in: Mathematical Linguistics and Automatic Translation, Report NSF 20, Computation Laboratory Harvard Univ. Chomsky, Noam 1970 “Some Empirical Issues in the Theory of Transformational Grammar”, mimeo. Davidson, Donald 1969 “Truth and Meaning”, in: Philosophical Logic, ed. J.W. Davis et ai. (Dordrecht).

54 1966

W. KUMMER

“The Logical Form of Action Sentences”, in: The Logic of Decision and Action, ed. Nicholas Rescher (Pittsburgh). Davis, J.W. et al. (eds.) 1969 Philosophical Logic (Dordrecht). Harweg, Roland 1968 Pronomina und Textkonstitution (Miinchen). Hintikka, Jaakko 1962 Knowledge and Belief (Cornell UP). Hall-Partee, Barbara 1968 “Negation, Conjunction and Quantifiers”, Foundations of Language. Keenan, Edward 1969 “A Logical Base for a Transformational Grammar of English”, TDAP. Kiefer, Ferenc 1971 On Presuppositions, preliminary draft. Karttunen, Lauri 1970 “On the Semantics of Complement Sentences”, Papers from the Sixth Regional Meeting of the Chicago Linguistic Society 1970. Lakoff, George 1968 “Repartee”, Founaiations of Language. 1969 “Generative Semantics”, rnimeo. 1970a “Linguistics and Natural Logic” (Univ. Michigan). 1970b “Global Rules”, Language 46. Lambert, Karel (ed.) 1970 Philosophical Problems in Logic (Dordrecht). Langacker, Ronald 1969 “Pronominalization and the Chain of Command”, in: Modern Studies in English, eds. D. Reibel and S. Schane (Englewood Cliffs). Logic and Language, Studies dedicated to Rudolf Carnap 1962 (Dordrecht). Modal and Many-valued Logics 1963 Proceedings of a Conference, Helsinki 1962, Acta Philosophica Fennica, Fax. XVI. Montague, Richard “Pragmatics”, in: Contemporary Philosophy, ed. R. Klibanski (Firenze). 1969 “English as a Formal Language”, mimeo, Grammatik”, hbersetzt und mit einem Kornmentar von 1971 “Universale H. Schnelle (Berlin). Palek, Bohumil 1969 Cross-Reference : A Study in Hypersyntax (Prague). Quine, W.V.O. 1968 Mathematical Logic (Cambridge, Mass.). Rescher, Nichols (ed.) 1966a l7ze Logic of Decision and Action (Pittsburgh). 1966b Z?te Logic of Commands (London). 1968 Topics in Philosophical Logic (Dordrecht). Reichenbach, Hans 1947 Elements of Symbolic Logic (New York). Rohrer, Christian 1971 Funktionelle Sprachwissenschaft und Transformationelle Grammatik (Miinthen). Ross, John Robert 1967 “Constraints on Variables in Syntax” (MIT) mimeo.

A GRAMMAR OF DISCOURSE

55

Schnelle, Helmut 1971 “Mbglichkeiten und Grenzen der Automatisierung der Sprachverwendungsprozesse”, in : Grammatik Kybernetik Kommunikation, Festschrif Hoppe. Scott, Dana 1970 “Advice on Modal Logic” 7, in: Philosophical Problems in Logic, ed. K. Lambert (Dordrecht).

W. Kummer (b. 1943) took degrees in Anglistik, Germanistik at the University of Graz, M.A. in Linguistics at the University of California, San Diego, is presently assistant professor for linguistics at the FU Berlin, published: “Sprechsituation, Satztyp und Aussagecharakter”, Beitree zur Linguistik und Informationsverarbeitung 1411968; “Neue Methoden der Sprachbeschreibung in den Vereinigten Staaten”, Studium Generale, 22/1969; “On Deriving Axioms from Texts”, L.unguges (1971), “Referenz, Pragmatik und zwei miigliche Textmodelle”, in: Probleme und Fortschritte der Transformationsgrammatik, 1971; “Quantifikation und Identitlt in Texten”, in: Beitriige zur generativen Grammatik, 1971; “Typen, Inhaltfunktionsklassen und Subklassifizierungsregeln” in: Grammatik, Kybernetik Kommunikation (1971); Grundlagen einer Textgrammatik des Deutschen (Habilschrift, to appear with Athen&nu Verlag); Textstrukturen (to appear in rowohlts deutscher enzyklop%lie).