A topological study of phrase-structure languages

It is proposed that structural equivalence of phrase-structure languages be defined by means of introducing, for each such language, a class of topological structures on the language. More specifically, given a phrase-structure language (either as a set of trees or as a set of strings), we introduce a class of topological spaces associated with finite sets of “phrases.” A function from one language to another, where both are equipped with such classes of topological spaces, is said to be structurally continuous, if for any topological space belonging to the first, there is a space belonging to the second such that the function is continuous with respect o these spaces. Then phrase-structure languages, or grammars that generate such languages, may be classified into structurally homeomorphic types in the obvious way. Two different methods of topologizing phrase-structure languages (one dependent on the other) are considered, and it is shown that for the class of context-free languages, one method provides a finer classification of languages (or grammars) than the other. In Part 2 we apply the general theory to a particular subclass of context-free languages, the class of tree language counterparts of regular languages

On Folding and Twisting (and whatknot): towards a characterization of workspaces in syntax

Syntactic theory has traditionally adopted a constructivist approach, in which a set of atomic elements are manipulated by combinatory operations to yield derived, complex elements. Syntactic structure is thus seen as the result or discrete recursive combinatorics over lexical items which get assembled into phrases, which are themselves combined to form sentences. This view is common to European and American structuralism (e.g., Benveniste, 1971; Hockett, 1958) and different incarnations of generative grammar, transformational and non-transformational (Chomsky, 1956, 1995; and Kaplan & Bresnan, 1982; Gazdar, 1982). Since at least Uriagereka (2002), there has been some attention paid to the fact that syntactic operations must apply somewhere, particularly when copying and movement operations are considered. Contemporary syntactic theory has thus somewhat acknowledged the importance of formalizing aspects of the spaces in which elements are manipulated, but it is still a vastly underexplored area. In this paper we explore the consequences of conceptualizing syntax as a set of topological operations applying over spaces rather than over discrete elements. We argue that there are empirical advantages in such a view for the treatment of long-distance dependencies and cross-derivational dependencies: constraints on possible configurations emerge from the dynamics of the system.Comment: Manuscript. Do not cite without permission. Comments welcom

グラフ リロン ト シゼン ゲンゴ トウゴ ブンセキ

This paper argues for Kayne\u27s (1984) Connectedness Condition which is aimed at accounting for the island effect first discovered by Ross (1967). An island is a structure out of which an element cannot escape. A variable which is confined in an island is not related to the operator outside the island. The study of islands, or the boundary condition for structures that allow operator-variable relations, is important, because the displacement builds operator-variable relations and because displacement is a characteristic of human natural language. Displacement is a phenomenon in which the actual position of an element in a sentence is distinct from the position where it is interpreted.The island effect is a long-standing formidable problem that resists a simple and elegant explanation. Linguists have tried hard and proposed various conditions and principles to explain the island effect, such as the Subjacency Condition, the ECP (Empty Category Principle), the CED (Condition on Extraction Domain), barriers, Relativized Minimality, the MLC (Minimal Link Condition), the PIC (Phase Impenetrability Condition), etc. Various factors have been considered;(a) the nature of empty category e (trace t or original) that has been left by movement (of the copy),e. g. , whether e is a sister of a lexical category L, or whether e is properly governed , (b) the structure of islands, e. g. , whether islands contain adjunction structure, or whether the specifier position is occupied, (c) the position of islands, e. g. , whether the island is a sister of L, (d) the manner of movement, e. g. , whether the movement crosses more than two bounding nodes (barriers) at a time, whether each step in a movement is the shortest possible, whether the movement is internal Merge, whether the movement takes place cyclically, whether the movement takes place within the same structure-building space, or takes place between distinct spaces (sideward movement), (e) the timing of movement, e. g. , whether the movement takes place before Spell-Out, etc.Kayne\u27s (1984) take on islands is new and insightful: the language system in the human brain is solving a legibility problem of classic topology, i. e. , is it possible from e to reach the antecedent by drawing with one stroke of the brush? A legibility problem is posed by external systems (the thought system and the perception-motor system) which are connected to the language system, which the language system must solve in order for it to be identified by external systems. An example of classic topological problems is Euler\u27s path : is it possible to cross seven bridges by passing each bridge once?, a hard problem posed by a citizen of the then Konigsberg in1736 (now Kaliningrad in Russia), which is the origin of graph theory in mathematics.Euler\u27s Path (Can one draw this with one stroke of the brush? If not, prove it. )Euler proved that it is not possible to draw it with one stroke, providing necessary and sufficient (iff) conditions for the path solution.Kayne\u27s (1984) Connectedness Condition is a legibility problem that the language system solves in the optimal way. An acceptable sentence is the optimal solution to the Connectedness Condition, topological in nature

Context-Free Grammars: Covers, Normal Forms, and Parsing

This monograph develops a theory of grammatical covers, normal forms and parsing. Covers, formally defined in 1969, describe a relation between the sets of parses of two context-free grammars. If this relation exists then in a formal model of parsing it is possible to have, except for the output, for both grammars the same parser. Questions concerning the possibility to cover a certain grammar with grammars that conform to some requirements on the productions or the derivations will be raised and answered. Answers to these cover problems will be obtained by introducing algorithms that describe a transformation of an input grammar into an output grammar which satisfies the requirements. The main emphasis in this monograph is on transformations of context-free grammars to context-free grammars in some normal form. However, not only transformations of this kind will be discussed, but also transformations which yield grammars which have useful parsing properties

ゲンゴ システム イコール ギソウ ウイルス チェック システム シゼン ゲンゴ ジョウホウ ショリ ニオケル ヘンスウ ショウキョ キョスウ ソクチセン マツナガ トシオ キョウジュ タイニン キネンゴウ

This paper argues for the following. a. The natural language system is a disguised virus-check system. It self-organized in the brain of the human ancestor as the result of a self-organizing mutation that took place about two million years ago. b. The language system generates information that is discrete and infinite. Discrete infinity is an indication that the language system has become cancerous. The language system disguised itself as an immune system. The brain is a typical immune system. c. The evidence for the disguise exists in the natural language computation. d. The structural informations (formal features) in Case particles and finite Tense inflection are variables. e. The variables are checked and eliminated. The Variable-elimination is the driving force of structure building. f. A sentence structure has a self-part and non-self part. A formal (structural) feature is checked off at the non-self part. The parasitic language system mimics the prominent characteristic of the host brain, which is the immunity. That is to say, the language system creates viruses = antigens (= structural features = variables of NPs), and the antibodies (structural features of the heads such as V, T, and C) check and eliminate those variables. This variable elimination is the driving force of the growth of bifurcating sentence structure. g. A Head movement extends the minimal domain MinD (the non-self part of the sentence structure). The MinD extension brings about the infinite increase of the shortest root. The head movement induces a non-Euclidean geometrical change of a sentence structure. That is, without head movement, a sentence structure is a flat plane, but with head movement, the sentence structure becomes a curved surface. On a curved surface, geodesic lines appear, increasing the number of the shortest root for NP movement (virus checking and elimination). h. The group theory can be an effective tool for studying the scrambling problem in CHL. i. The computational system of human natural language (CHL) includes a distinction between real time and imaginary time. The CHL contained the imaginary number i when Mother Nature created the CHL about two million years ago. The imaginary number i is not a modern invention of mathematicians. j. A sentence is an equation with constants and variables. The human brain solves one-dimensional simultaneous equations with multiple variables (= Case features). But linguistic simultaneous equations consist of a single equation, which is not solvable in mathematics. A sentence is an equation. Therefore, a sentence can be paraphrased into a mathematical equation. Interesting results obtain when we draw the graphs and the vector spaces of the linguistic equations. k. Points of breakdown of the operation of variable elimination exist both in linear algebra and in the CHL. l. Sequential voicing (rendaku) obeys the least effort (energy) principle