On Cloning Context-Freeness
نویسنده
چکیده
A first-order language is called monadic if its non-logical vocabulary lacks both function symbols and relation symbols of arity greater than one. Formulas of this kind of language can be mechanically tested for validity but its expressive power seems to be too restricted to be of any interest for linguistics. Monadic second-order languages on the other hand extend the language of (full) first-order logic by providing for quantifiable monadic second-order variables. These languages increase the definitional resources of first-order logic substantially but they still retain many metamathematical properties which make them a ‘good source of expressive and manageable theories.’ (Gurevich 1985) In the paper from which the preceding remark is taken Gurevich gives a detailed account of two strong decidability techniques which were developed in connection with monadic second-order theories. One of these techniques is based on games and automata while the other employs generalized products. The applicability of these methods to certain secondorder theories where quantification is restricted to variables ranging over subsets of the domain of discourse underlines the fact that formalizations couched in this linguistic framework are supported by a manageable underlying logic. In sharp contrast with the situation exemplified by monadic first-order logic the decidability of applied forms of its secondorder counterpart detracts nothing from its value as a flexible expressive means for the presentation of theories which embody interesting parts of either mathematics or the empirical sciences. This is not the proper place to substantiate this last claim as far as mathematical theories are concerned. The interested reader is referred to the paper by Gurevich where she can find a wealth of examples. The development which brought linguistics into the picture was initiated by
منابع مشابه
About Graph and Hypergraph Context Free Grammars
The main idea of this paper is to show some important differences between graph grammars and hypergraph grammars in context of freeness. On the other hand, we give a possibility to transform the planar structure of a hypergraph into a linear one with concern of determinism. This can create a path to transform a pushdown automaton into a generative grammar equivalent. Key-Words: Hyperedge Replac...
متن کاملPartial Freeness of Random Matrices
We investigate the implications of free probability for random matrices. From rules for calculating all possible joint moments of two free random matrices, we develop a notion of partial freeness which is quantified by the breakdown of these rules. We provide a combinatorial interpretation for partial freeness as the presence of closed paths in Hilbert space defined by particular joint moments....
متن کاملCriteria to Disprove Context-Freeness of Collage Languages
Collage grammars generate picture languages in a context-free way. The generating process is based on the replacement of atomic nonterminal items and can be seen as an adaptation of the notion of hyperedge replacement known from the area of context-free graph generation. While a pumping lemma holds for hyperedge replacement graph grammars and is quite useful to show that certain graph languages...
متن کاملMaking Finite-State Methods Applicable to Languages Beyond Context-Freeness via Multi-dimensional Trees
We provide a new term-like representation for multi-dimensional trees as defined by Rogers [8,9] which establishes them as a direct generalization of classical trees. As a consequence these structures can be used as input for finite-state applications based on classical tree language theory. Via the correspondence between string and tree languages these applications can then be conceived to be ...
متن کاملSeparations of Matroid Freeness Properties
Properties of Boolean functions on the hypercube that are invariant with respect to linear transformations of the domain are among some of the most well-studied properties in the context of property testing. In this paper, we study the fundamental class of linear-invariant properties called matroid freeness properties. These properties have been conjectured to essentially coincide with all test...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- CoRR
دوره cmp-lg/9707013 شماره
صفحات -
تاریخ انتشار 1997