Resumen de A formal characterization of fuzzy degrees of grammaticality for natural language
1. HYPOTHESIS This work presents a new approach which combines different interdisciplinary methods to explain fuzziness in a natural language grammar. Since this topic is vast and complex, this work has focused its efforts on dealing with only one fuzzy (or vague) linguistic phenomena: the {\it degrees of grammaticality}. Consequently, fuzziness in natural language comes in this work for one of the most well-known gradient phenomenon in linguistics. The hardest part here is explaining the degrees of grammaticality regarding a natural language grammar (objective formal perspective) without involving degrees of acceptability (a subjective and psycho-linguistic perspective) on the measure of grammaticality. To achieve this objective, as well as to deal with this fuzziness, this new approach has been nourished from different disciplines and points of view such as discrete linguistics, gradience linguistics, grammars with constraints, fuzzy logic reasoning, fuzzy grammars, vagueness in natural language, and so on. Thus, this dissertation deals with different sensitive topics in science, particularly in linguistics. Being our primary aim to study grammaticality from a fuzzy (and not discrete) point of view, we start from threeresearch questions: Is it possible to measure the degrees of grammaticality of a given linguistic input?Which are the best formal tools to calculate the different levels of grammaticality?Can we provide a fuzzy approach to the concept of grammaticality (not acceptability) taking into account competence (not performance)? The hypothesis that emanate from these research questions is the following:
A formal model which combines fuzzy logic and a grammar with constraints can represent fuzzy degrees of grammaticality regarding linguistic competence. In order to test this hypothesis, we will develop a formal model to deal with the degrees of grammaticality.Therefore, the main aim of this work is to introduce a new linguistic model which can both represent and calculate the degrees of grammaticality by considering the notion of grammaticality as a fuzzy phenomenon of the natural language.
In order to achieve our main aim, we take set up the following research objectives:To review and provide a critical analysis of the concept of grammaticality in Linguistics. To review and provide a critical analysis of the models of gradience over the notion of the concept of grammaticality. To propose the bases for the definition of a fuzzy grammar to deal with degrees of grammaticality and its fuzzy features. To extract/determine the linguistic properties that will define the linguistic inputs for taking into account the degrees of grammaticality. To provide a proof-of-concept of a fuzzy grammar with properties for Spanish syntax which can represent the fuzzy degrees of grammaticality.
2. JUSTIFICATION The notion of grammaticality is a must when a natural language grammar is aimed to be defined. As a first step, the linguist discerns between what is in the grammar (grammatical) and what is not (non-grammatical). The categorical view of grammaticality is widely defended in theoretical linguistics. However, the deviations from the norm are inherent to the spontaneous use of language. Hence, either a Natural Language Grammar or the linguistic analysis tools should account for different levels of grammaticality. In linguistics, the degrees of grammaticality are well accepted among some authors (Bolinger, 1961; Ross, 1972; Lakoff, 1973; Keller, 2000; Aarts, 2004c). These authors mainly underpin the degrees of grammaticality under the notion of grammaticality judgments and linguistic gradience (Aarts, 2004b). The most well-known linguistic theories taking into account linguistic gradience are the Optimality Theory and its variations. Keller (1998; 2000; 2006) and his Linear Optimality Theory showed how grammaticality and acceptability judgments are a gradient object. However, these theories together mostly evaluate the degree of acceptability of an input, since they are representing speaker's judgments a formal approach such as Optimality Theory. There is still not in linguistics a grammar framework which can deal with degrees of grammaticality regarding linguistic competence.
Here, it has been defended that the grammaticality can be both an issue as in the competence as in the performance. This work has focused on: reviewing and provide a critical analysis concerning the concept of grammaticality in linguistics, and proposing a fuzzy grammar for representing degrees of grammaticality in natural language.
We recognize a grammar as a system which both produces and recognizes inputs. Besides, we claim that the grammar is a compilation of linguistic constraints which defines the linguistic competence of a speaker. Such an input which violates the constraints of a grammar, it will be associated with the degree of grammaticality concerning to that grammar specific grammar. Therefore, the degree of grammaticality is understood as a vague object which can take into account degrees of membership regarding a linguistic input.
3. METHODOLOGY In order to test our hypothesis and to reach our aims, we have applied the methodology sketched in this section.The first step concerns a deep acknowledgment of the scientific literature regarding both the notion of the degrees of grammaticality and systems which can deal with linguistic gradience and degrees of grammaticality.
We realized that one of the first obstacles for representing the degrees of grammaticality was the distinction of competence and performance which determines the definitions over grammaticality and acceptability. The first solution over this problem was to provide a critical analysis regarding these concepts as well as proposing new definitions and considerations which open the path for calculating the degrees of grammaticality as a fuzzy object.
Gradience and fuzziness seek to show how the relationship between two categorical objects is a question of degree rather than discrete; that is, each word belongs to ``a class in which the transition from membership to non-membership is gradual rather than abrupt'' (Zadeh, 1965). This fuzzy reasoning can be applied to linguistic gradience to determine the grammaticality of an input. Thus, rather than classifying an utterance as non-grammatical if it features some grammatical deviations (discrete reasoning), it can be classified as more or less grammatical according to the constraints that are violated or satisfied 3.1. A Property Grammar for Degrees of Grammaticality Blache and Prost (2008) proposed a framework with algorithms based on a PG for taking into account degrees of grammaticality judgments. PG proposes several algorithms and formulas along its literature in order to calculate weights for properties, degrees of acceptability, ungrammaticality, degrees of grammaticality and degrees of complexity. The formula that we propose for taking into account grammaticality is inspired by the notions developed by PG as well as by some of these formulas.
In general terms, Property Grammars are the ideal theory to account for the gradual phenomenon of language such as grammaticality. They are highly descriptive. Likewise, their constraints are entirely autonomous which enables them to be independently weighed. On the other hand, PG collects much linguistic information regardless of whether the input is grammatical or ungrammatical. This differentiates them from the other grammars insofar as, those grammars which successfully describe canonical inputs but which offer very little information about the elements that trigger violations. Therefore, PG is an excellent tool to build syntactic models that tolerate different degrees of grammaticality.
3.2. Using fuzzy logic for a fuzzy grammar. Grammaticality is acknowledged as a vague concept. Since fuzzy logic is the right tool to capture vague objects, we state that fuzzy logic can represent a grammar which can deal with the degrees of grammaticality.
We are showing the application of Fuzzy Natural Logic (FNL) from Novák in order to define a grammar which can capture the vague notion of grammaticality. We show our proposal for evaluating grammaticality in a fuzzy grammar.
Finally, we claim that FNL is a very suitable tool for a Property Grammars for dealing with degrees of grammaticality.
The application of fuzzy logic to the property grammar has been supervised by members of the Institute for Research and Applications of Fuzzy Modeling (IRAFM) Center of Excellence IT4 Innovations of Ostrava (Czech Republic). The fuzzy logic model used in our formal grammar is Fuzzy Natural Logic by Novák which is a variation of a fuzzy type theory.
There are many different approaches in order to formalize fuzzy logic as well as different theories. For our work, we have chosen Fuzzy Natural Logic a high-order fuzzy logic; fuzzy type theory (FTT) with Lukasiewicz algebra. This theory is highly suitable for modeling natural language and other linguistic concepts. This theory is genuinely linguistic motivated and highly influenced by Lakoff (1970).
3.3. Extracting a Property Grammar from Universal Dependency Treebank}. A Spanish Property Grammar and its extraction will be presented. This Property Grammar is determined by the basis of Blache (2016) together with the fuzzy logic from Novák (2015) and original evaluative bases from this work. This method provides a new perspective since a grammar has never been able to define their bases from a gradient grammaticality perspective before. This new framework might be called Fuzzy Property Grammars, and it can represent the degrees of grammaticality that are found in the different constructions, regarding linguistic competence.
The syntactic properties have been extracted automatically by applying the MarsaGram tool to the Corpus Universal Dependency Spanish Treebank. This corpus is obtained from the Universal data set Google dataset (version 2.0). It consists of 16,006 tree structures and 430,764 tokens. It is built from newspaper articles, blogs, and consumer reviews.
4. CONCLUSIONS We conclude that it is essential to highlight two characteristics regarding the concept of grammaticality:
Grammaticality is the value that represents how much satisfied is an input according to the linguistic knowledge that defines the competence of a natural language grammar. Consequently, it is not a value which needs from the judgment of a speaker; it is a value which can be calculated within a grammar.
Grammaticality is a fuzzy-gradient value which must be explained in terms of degrees. The value is fuzzy given its vague nature because of all the criteria that are involved into it. It is a melting pot of linguistic constraints and linguistic modules in interaction which needs precise tools to separate everything in order to be able to calculate the value of every piece before the estimation of the final value.
A fuzzy grammar (FGr) is considered as a fuzzy set on the whole set of linguistic rules or constraints. These constraints are the linguistic knowledge of the fuzzy grammar in every module (linguistic domain). Therefore, a fuzzy grammar is multi-modal. We provide a formal representation of how a module from a fuzzy grammar takes into account degrees regarding the linguistic competence and grammaticality, not performance. The linguistic competence is understood as all the constraints which take part in the fuzzy grammar. The fuzzy grammar matches every constraint from the grammar with every constraint from a linguistic input. From this relation, both the constraints on the module and the constraints on the input match a degree of membership of being grammatical.
We have presented three constraint behaviors. These are necessary for adapting both fuzzy notions and a Property Grammar towards a Fuzzy Property Grammar: {Syntactic Canonical Properties}: These are the properties which define the gold standard of the Fuzzy Grammar; {Syntactic Violated Properties}: These properties are canonical properties which have been violated regarding a linguistic input or a dialect; and Syntactic Variability Properties: these are borderline cases in-between a violation and a canonical. They explain linguistic variability concerning a fuzzy grammar. When a variability property is satisfied, it triggers a new value over the violated constraint improving its degree of grammaticality.
We have provided the notion of a xCategory which is a feature that specifies that a specific category is displaying a {syntactic fit} from another category. This concept is necessary for a fuzzy property grammar; it describes the fuzzy idiosyncrasy of some linguistic categories which can acquire different properties depending on its context in an utterance.
Finally, we have verified our hypothesis. We can affirm that a formal model which combines fuzzy logic and grammar with constraints can represent fuzzy degrees of grammaticality regarding linguistic competence. The concept of grammaticality is a theoretical one, therefore, with a formal tool such as Fuzzy Natural Logic we would be able to define grammaticality regarding a grammar; without involving any acceptability trait on the formal definition.
