S Emi - Sentences , S Emi - Strings and S Emi - Grammatical R Ules in P Rolog

The aim of this work is to analyse the concept of semi-sentence from a linguistic, formal and computational point of view. A semi-sentence can be characterised as a sentence which, from a grammatical perspective, is neither absolutely correct nor incorrect (in the sense that a speaker-listener of the language in which it is uttered understands it). This study focuses on: a characterisation of the semi-sentences in the setting of the grammar of a language. This study will help to analyse in depth the concept of grammaticality [3]; the correlate of semi-sentences in formal languages, i.e., semi-strings, which arise from applying productions that deviate from that which is strictly permitted by the rules of grammar [6]; a Prolog program for handling semi-grammaticality in a computational manner [2]. These aspects are dealt with in an introductory way, and the purpose of this paper is not to treat them generically, rather they are adapted to specific examples. 1. Linguistic vagueness and grammatical vagueness The most common type of linguistic vagueness, and also the one that is most alluded to, is the referential one; that is, vagueness that arises by way of which a word signifies an object. This type of linguistic vagueness is referred to more specifically as semantic vagueness. From this point of view, it is said that a word is vague when it does not denote its referent in a precise and unmistakable manner; that is, when there are objects for which it is doubtful that they are significantly well represented by this word. When this word refer to collections or classes of objects, they give rise to a fuzzy set. Semantic vagueness has been treated in a formal way in the setting of fuzzy formal semantics [7]. A. SOBRINO, J. A. OLIVAS, S. FERNÁNDEZ 118 There are other topics of linguistic vagueness which are less common than semantic vagueness, such as: • phonological vagueness, present, for example, in the phonic recognition of dialectal usage of a language; • morphologic vagueness, which accompanies the deficient characterisation of classes of words by virtue of their endings; • syntactic vagueness, which refers, for example to the absence of regularities in the format of dative clauses, or; • grammatical vagueness, present in grammatical classifications, in which the categories are grouped in a “squishy” manner [4] rather than a precise one, as will be seen subsequently. This paper deals with topics that are related to grammatical vagueness; it will specifically deal with the study of semi-sentences, sentences which from a grammatical point of view are neither totally correct, nor incorrect; i.e., sentences which are more grammatical than ungrammatical. The study of semi-sentences is relevant: • in the field of natural language, in order to analyse in depth the concept of an almost grammatically correct sentence, as well as the understanding that a speaker-listener of a language has of these sentences, in spite of their relative malformation. In this context the distinction between grammaticality and acceptability will be useful • in the area of formal languages, in order to lay the foundations for the development of grammars which enable the generation of strings which deviate from that which the production rules strictly permit • from a computational point of view, processing semi-sentences leads to natural language man-machine interfaces that are flexible, not rigid. 2. Notes for a semi-sentence theory A study of grammatical vagueness is to a great extent an investigation into whether linguistic objects may be grouped into grammatical categories with crisp boundaries, or whether, on the contrary, there are objects which are susceptible to belonging to more than one category, or to being a member of one category more clearly than of another. If the latter holds, then one would have to accept the existence of grammatical categories with fuzzy boundaries, to which linguistic objects would belong to a certain degree. SEMI-SENTENCES, SEMI-STRINGS AND SEMI-GRAMMATICAL RULES IN PROLOG 119 English grammar has this peculiarity [4]. Written in Italics are some of the categories that are central to this grammar and in normal text the categories of transition between the central categories, Verb > Present participle > Perfect participle > Passive participle > Adjective > Preposition (?) > “Adjectival noun” (e. g. fun, snap) > Noun Ross verifies a gradation amongst these. In the prototypical categories, oppositions work in a binary manner; a linguistic fact either belongs or does not belong to the category being considered. In the transition categories, facts are evaluated according to their distance from the prototypical category. This is the case of the participle. If it is the present participle, it exceeds certain grammatical tests typical of verbs; but if it is the past participle, it shares more characteristics with the “adjective” category than the “verb” one. These examples leads us to distinguish in grammatical classifications between: • central elements, with genuine membership, and • peripheral elements, with degree of membership to the category. A grammatical model which enables this flexible, non rigid grouping of linguistic facts will take on notions such as unstable syntactic constructions, loosely fitting morphological units, semi-productive morphological schemes or semi-sentences. We will now go on to discuss some characteristics of semi-sentences. The characterisation of the semi-sentence presupposes, with respect to grammaticality, an alternative to the dichotomic grammatical/non grammatical opposition. In this context, the internal or external character of negation enables a three-way distinction: • grammatically correct sentences • grammatically non correct sentences, and • grammatically incorrect or ungrammatical sentences The grammatically non correct sentences are referred to as semisentences (SemiS). An example of a SemiS is: An idea occurred me or A sandwich I ate. The lack of total grammaticality can be given by: • a deficient syntactic organisation • a insufficient semantic analysis A. SOBRINO, J. A. OLIVAS, S. FERNÁNDEZ 120 In the above examples it can be observed that the malformation is brought about by deficient syntactic organisation. But not all semisentences arise from syntactic problems. Irregularities in the semantic stratum explain, as can be seen below, the absence of complete grammaticality, such as in the sentence The trial runs fast. A semi-sentence theory should explain how the knowledge that the speaker has of the language enables him to understand utterances which are neither totally grammatical, nor ungrammatical. If we consider the knowledge that a speaker has of his grammar and the capability to categorize every linguistic fact, a SemiS generates a double perplexity: • if the SemiS is not generated, then the grammar is incomplete, • if the SemiS is generated, the grammar fails. This perplexity should be solved in a non dichotomic manner by a theory that deals with these linguistic entities. One way of classifying sentences produced by semantic irregularities is to distinguish different levels of structural description of a sentence [3]. Let us call each one of these levels formatives [1]. Let us suppose then that we have m levels of formatives f, f, ..., f each one with n index f1, f 1 2, ..., f 1 n in such a manner that the sub-index 1, 2, ..., n indicate a greater degree of specificity in the structural description. Let the sentence be the one already quoted: The trial runs fast (S1) This is a sentence that is syntactically well ordered, but about which it cannot be said that it is as grammatically correct as the sentence: The athlete runs fast. The anomaly is to be found in the semantic component. Let us now go on to specify different levels of formatives with reference to the type of linguistic actions that they describe. Let us accept that, in level one 1, f1. represents words. In level 2, f 2 1 represents nouns, f2 verbs, f 2 3 adverbs and f 2 4 articles. Lastly, in level 3 classes of formatives which are subclasses of those presented in 2 are represented: f1 represents the names of inanimate objects, f 3 2 verbs of action f 3 3, adverbs of mode and f4 definite articles. Thus (S1) has three possible levels of structural representation (according to the formatives distinguished): SEMI-SENTENCES, SEMI-STRINGS AND SEMI-GRAMMATICAL RULES IN PROLOG 121 • In level 1, f1, repeated as many times as the number of words there are. • In level 2, f4 + f1 + f2 + f3, which is the equivalent of Art + N + V + Adv. • Lastly, in level 3, f4d + f1i + f2a+ f3mod, where d, i, a and mod represent the sub-categorisations determinate, inanimate, ..., of the categories differentiated in level 2. Given a grammar that has two descriptive levels, it is possible to say something about the grammaticality of (S1): • In level 1, the description is very generic, and will give any series of words as being grammatical, including, for example, (S1). • Levels 2 and 3 constitute successive refinements of 1. Level 2 reveals an initial structure of (S1): Art + N + V + Adv. As represents good syntactical ordering, according to English grammar it is possible to generate (S1). In spite of sharing the structural description of (S1) with level 2, level 3 impedes the generation of this sentence. There is a structural rule of the constituents, which indicates that a verb of motion only accompanies nouns marked as “animate”, as in the sentence “the athlete runs fast”. Level 2 permits the generation of the semi-sentence (S1), as its level of grammatical analysis is not sufficiently fine. In level 2 (S1) does not contravene the rule that it transgresses in level 3. In agreement with this form of grammatical description, it can be said that a semi-sentence is a sentence that is at the same time both grammatical (level 1 and 2) and non-grammatical (level 3). Nevertheless, even within the same level of structural description, there are sentences that are not totally grammatical with respect to others which are so. These are deviations that are characterised in the syntactic stratum. Such is the case with A sandwich I ate (in comparison with the grammatical sentence I ate a sandwich). A common way of explaining a SemiS from a syntactic point of view contemplates three forms of deviation from what can be considered as being prototypical sentences, obtained from standard syntactic derivations. The most simple types of variant are: • inversion • addition • deletion A. SOBRINO, J. A. OLIVAS, S. FERNÁNDEZ 122 which can be summarised in the following typical format, Format Name ...AB...→ ...BA... Inversion ...AB...→ ...A... Deletion ...A... → ...BA... Addition Examples (in the same order): I ate a sandwich → A sandwich I ate I ate a sandwich → I ate sandwich I ate a sandwich → I ate a sandwich big Note that on the left side of the productions there is a totally grammatical sentence, whilst on the right there are semi-sentences. In a paradigmatic way, the property known as deletion shows that, for a given class of words, no universal rule can be put forward as regards the possibility of (non) deletion in sentences without the grammaticality (vagueness) or meaning (ambiguity) of the sentence being altered [5]. The following examples show cases of grammatical ambiguity. (The symbol (*) will be used for “can be deleted” and *( ) for “cannot be deleted”.) Following Ross [4], we show the deletion of three classes of words: prepositions, adjectives and nouns. • Deletion of prepositions. -Your perfume surprised(*to) me -It was surprising, your perfume *(for) me. • Deletion of adjectives -Sarah is like (*to) a doll -Sarah is [near *(a) doll • Deletion of nouns -I'm sorry (*(about) the fact) that you didn't come yesterday -(The fact )remains that they accused you The deletion property shows how some grammatical elements such as “to” and “the fact” can sometimes be suppressed (or not) in sentences without loss of grammaticality. SEMI-SENTENCES, SEMI-STRINGS AND SEMI-GRAMMATICAL RULES IN PROLOG 123 Up until now, some forms of classifying or generating semisentences have been shown. Nevertheless, a theory of semi-sentences should give a measurement of the degree of the good formation of a sentence, an evaluation of its degree of grammatical deviation. A plausible proposal should make it depend on the degree of addition/deletion and the degree of inversion of the element or elements that give rise to the grammatical deviation. The degree of accessibility is the degree of mobility of the element or linguistic action inside the sentence (the element under consideration is written in italics). 1 i. It is possible that George will sign up for French next year. ii. Next year it is possible that George will sign up for French. 2 i. The man with the moustache whom I saw yesterday is the cousin of the inspector. ii. The man with the moustache is the cousin of the inspector whom I saw yesterday In 1. the sentence has the maximum degree of accessibility for the expression “next year”. Hence the sense and reference for the sentences (1.i) and (1.ii) do not change in spite of the fact that the ordering of the lexical elements being different. In 2, on the other hand, the degree of accessibility in the sentence of the relative clause “whom I saw yesterday” is minimum; by changing the position the sense of the sentence it changed, as is shown by a comparison of (2.i) and (2.ii). The degree of addition is the degree of possibility of encrustation of an element in the sentence, for example, Base sentence: It may rain. 3 (i). It may rain tomorrow. (ii). Tomorrow it may rain. Base sentence: I’m sorry that John is like that. 4 (i). I’m always sorry that John is like that. (ii). I’m sorry that John is always like that. In 4, the possibility that the sense of the phrase may change significantly by altering the position of the word in Italics is maximum, A. SOBRINO, J. A. OLIVAS, S. FERNÁNDEZ 124 which is not true of 3. Note how in these examples, the words in Italics do not give rise to cases of grammatical vagueness, but rather of grammatical ambiguity, which it possible to recognise immediately if a tree is drawn up for each of the sentences. They simply change the meaning of the sentences and not their grammaticality. If the encrustation and the mobility of an element do not give rise to an alteration in the meaning (in this case the sentence will still be in accordance with the grammatically established rules) but lead to the transgression of these rules, then we will have a case of grammatical vagueness. The smaller the degree of encrustation and mobility, the greater the transgression will be, so that a semi-sentence will be less grammatical the closer the product of these factors approaches zero. Lastly, we deal with a methodological matter. It is interesting to analyse whether the comprehension of a semi-sentence can be explained as it entails a small deviation with respect to a grammatical regularity, or whether it is due to our cognitive ability. In other terms, if the semisentences are not grammatical, but are acceptable as sentences, as they enable communication with a good part of the speakers of a language, or if they allow communication, as they bear a resemblance to totally grammatical sentences. Whilst “grammaticality” is a term that belongs to the sphere of linguistics and refers to a normative conception, acceptability is a term that belongs to the sphere of sociolinguistics, and has to do with the description of language. Acceptability enables us to think about evaluating a sentence as a semi-sentence, and even a degree depending on the acceptability that the sentence has in the linguistic community. This evaluation would not be possible for a totally grammatical sentence, which in such a way is independent of its acceptation. This links up with an important theoretical matter, but one which will not be discussed in this work: whether grammar should be normative or, on the contrary, it should respond to linguistic actions just as they appear, and thus, to their deviations as well. Up until now we have given no more than an outline of some elements for a semi-sentence theory. Due to the complexity of natural languages, the construction of this is beyond the scope of this work. 3. Semi-grammaticality and semi-strings The objective of this section is to define cases of grammatical vagueness in the context of a language generated by a Chomsky’s formal grammar. SEMI-SENTENCES, SEMI-STRINGS AND SEMI-GRAMMATICAL RULES IN PROLOG 125 Given a formal grammar, G = <ΣT, ΣNT, S, P>, where ΣNT is the non-terminal vocabulary ΣT is the terminal vocabulary S is the initial symbol or axiom P is the set of production rules, It is considered that imprecise strings (semi-strings) can be produced in the same manner as semi-sentences are formed; that is, by: • Inversion. A string that is similar to a grammatical string is produced, the difference being that the elements are in a different order (if the elements are terminal or non-terminal will be indicated by the type of grammar that is being defined -context sensitive, context free, ..., etc.-) • deletion. A string that is similar to a grammatical string is produced, except that it has less terminal symbols than the grammatical string with which it is compared. • A string that is similar to a grammatical string is produced, except that it has more terminal symbols than the grammatical string with which it is compared.