تجزیه وتحلیل الگوریتم های خطی سازی ساختار های اشراف چندگانه: در جستجوی یک تعمیم نظری (مقاله علمی وزارت علوم)
درجه علمی: نشریه علمی (وزارت علوم)
آرشیو
چکیده
ادغام موازی در ساخت همپایگی، منجر به اشتقاق ساختاری می شود که دربرگیرنده رابطه متقارن دوسویه است. در رابطه متقارن مذکور، یک عنصر اشراف چندگانه می شود و در بین دو بند همپایه به اشتراک گذاشته می شود. در این حالت، عنصر مشترک֯ دو گره مادر خواهد داشت و طبیعتاً خطی سازیِ ساختارهای مشتق از ادغام موازی که دارای اشراف چندگانه هستند با مشکل مواجه خواهد شد. هدف از این پژوهش واکاوی و کالبدشکافی الگوریتم هایی بود که تاکنون در ادبیات مربوطه جهت مرتفع شدن چالش خطی سازی ساختارهای اشراف چندگانه مطرح گردیده اند. به طور مشخص، در این پژوهش محتوای الگوریتم های ارائه شده در خصوص خطی سازی ساختار اشراف چندگانه به صورت کیفی و با بهره گیری از ابزارهای گراف و (نظریه) مجموعه تحلیل شد. رویکردهای تجربی و محاسباتی کمّی موجود در رابطه با موجودیت این نوع از ساختار نشان داد که ساختار اشراف چندگانه پیش از اینکه مشخصاً محصول ادغام موازی باشد، برایند طبیعی عملکرد ادغام در فضای کاری است. در ادامه تحلیل، جهت پرتوافکنی بر عملکرد و ماهیت ادغام در فضای کاری، مبحث ترتیب گذاری بر ادغام مجموعه ای مطرح شد تا از این منظر بخشی از خطی سازی، در نحو محض رقم بخورد.Analyzing the Linearization Algorithms of Multidominant Structures: In Search of a Theoretical Generalization
Parallel merge generates a structure that contains a double symmetric relation, in which the shared object has two mother nodes. Naturally, the Linearization of multidominant structures derived from parallel merge will face challenges. The purpose of this study was to analyze and dissect the algorithms that have been proposed in the relevant literature to address the challenge of the linearization of multidominant structures. Specifically, in this research, the content of the proposed algorithms regarding linearization of multidominant structure was qualitatively examined using graph and set notations. The empirical and computational quantitative approaches, in relation to the existence of this type of structure, showed that multidominant structure was the natural result of the function of merge in the workspace rather than the consequences of parallel merge. To shed light on the performance of merge in the workspace, putting order into set merge was raised. Hence, part of the linearization took place in narrow syntax.
Introduction
Parallel merge generates a structure that contains a double symmetric relation, in which the shared object has two mother nodes. Naturally, the Linearization of multidominant structures derived from parallel merge will face challenges. The purpose of this study is to analyze and dissect the algorithms that have been proposed in the relevant literature to address the challenge of the linearization of multidominant structures. Specifically, in this research, the content of the proposed algorithms regarding the linearization of multidominant structures will be qualitatively examined using graphs and set notations. Empirical and computational quantitative approaches, concerning the existence of this type of structure, indicate that multidominant structures are the natural outcome of the merge function in the workspace rather than the result of parallel merge. To shed light on the performance of merge in the workspace, putting order into set merge is raised. Hence, part of the linearization takes place in narrow syntax.
Research Question(s)
This research addresses two fundamental questions. The first question examines how the presented algorithms linearize multidominant structures. The second question explores the possibility of achieving theoretical generalization in the workspace regarding the role of merge as a multidominant constructor, ultimately contributing to the initial linearization process in narrow syntax.
Literature Review
Researchers have aimed to address the linearization of multidominant structures by developing algorithms. Recent algorithms have made significant progress in solving the linearization problem for symmetric multidominant structures.
In the algorithm of Williams (1978), multidominance was a consequence of coordination, not of ATB movement. Wilder (1999) and Grachanen Yuksek (2007) have tried to linearize the multidominant structure by modifying the definition of c-command and movement so this structure is linearized in situ without affecting other parts. Regarding the linearization of multidominant structures, Wilder (1999) ignored some of the nodes in coordinate structures by introducing the notion of full dominance.
In Citko's (2005) algorithm, movement is regarded as a key factor in the linearization of multidominant structures. In her algorithm, traces are not pronounced since they do not belong to the computational component and result from the derivation process.
In the representation of a multidominant structure, in addition to complete dominance and precedence relations, there are syntactic dependencies in more than one place. It seems that the merge behavior within the proposed algorithms can bring us closer to a theoretical generalization about the nature of merge as a multidominant constructor.
Methodology
In this study, we are undertaking descriptive-analytical research. To begin with, theoretical information regarding various types of merges in the minimalist program as well as algorithms for linearizing multidominant structures was gathered. These concepts were then discussed and analyzed using set notations and graph notations.
Discussion
The noteworthy point is that a multidominant structure is not just a product of parallel merge; rather, it is the fundamental characteristic of merge in the workspace. From this perspective, shown in Diagram 17, the internal merge of XP leads to the formation of an asymmetric multidominant structure. In this case, XP simultaneously merges into two positions. One of the occurrences of XP is under the dominance of YP and the other occurrence is under the dominance of ZP. Therefore, we can consider merge as an operation that naturally creates a multidominant structure.
Diagram 17. The workspace resulting from the set merge
According to Chomsky (2020: 38), parallel merge does not have legitimacy and it is necessary to eliminate parallel merge from computational component. As shown in diagram 21, we consider the symmetric multidominant structure in the form of two floating trees in the derivation. The result of this event is diagram 22, in which the original structure segregates into two asymmetric multidominant structures and hence the parallel merge is removed.
Diagram 21. symmetric multidominant structure (Gračanin-Yuksek, 2013: 269)
Diagram 22. Two floating trees in derivation
The existence of two floating trees within the minimalist program in derivation can be a channel for theoretical and empirical discussions. The possibility of placing an order on the set merge can help some part of linearization to take place in narrow syntax.
The authors contend in Chomsky (1995: 244) implicitly applying order to the unordered two-membered set {α, β} in {α,{α,β}}.
{α, β} = {α,{α,β}}
According to Langendoen (2003: 310), the hypothetical set E′ is the same as the set E, and the set E′ is the ordered pair < α, β>, and this point is also mentioned in the research of Kuratovsky (1921:171).
E= {α, {α, β}}
E′= {{α}, {α, β}}
If α≠β → < α, β> = {{α} , {α, β}}
If the product of the set merge is considered from this perspective,
it assumes that set merge produces a set of ordered pairs.
If α is head in the set merge, the workspace created in this relationship is called ¥ 1 , and the reflection of the desired relationship will be:
1= {{α},{α, β}}¥
And if β is the head, the reflection of the desired relationship in the new workspace will be ¥ 2:
2= {{ β },{ β, α }}¥
If we want to provide a schematic view of the simultaneous existence of symmetry and asymmetry along with the multidominance structure in 11.b, perhaps we can present diagram 24 in which parallel merge is not involved, and linearization of the existing relations may be proposed in situ.
(11. b) Mary wrote and John reviewed an article on Bo. (Gračanin-Yuksek, 2013: 269)
Diagram 24. Linearization of the multidominant structure, in situ
Conclusion
In this research, initially, various algorithms for linearizing multidominant structures were examined. Subsequently, workspaces resulting from the operation of different merges were investigated within the target tree graph, categorized as "symmetric" and "asymmetric" spaces. Later on, the merge was introduced as a multidominant constructor. It was noted that multidominant structures, prior to being explicitly the result of the parallel merge, exhibit key characteristics of the merge within the workspace.
The authors believed that Chomsky (1995: 244) implicitly applied an order to the unordered two-membered set {α,β} in {α,{α,β}}. Perhaps a theoretical generalization can emerge by introducing an initial order to the elements of the binary set in merge. In this perspective, both external and internal merges gain the capability to generate ordered pairs. Furthermore, in a general conceptual view, a tree graph was presented in which both hierarchical and adjacency relationships were simultaneously evident and the linearization of multidominant structure was suggested in situ.
It seems that despite the simultaneous presence of symmetry and asymmetry relationships in the tree diagram and the performance of various types of merge, revisiting, and defining a new workspace in the linearization of multiple dominance structures is not out of reach with Citko (2011a: 211).
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