Showing papers on "Formal grammar published in 1975"

Deterministic parsing of ambiguous grammars

Abstract: Methods of describing the syntax of programming languages in ways that are more flexible and natural than conventional BNF descriptions are considered. These methods involve the use of ambiguous context-free grammars together with rules to resolve syntactic ambiguities. It is shown how efficient LR and LL parsers can be constructed directly from certain classes of these specifications.

Some transformational extensions of montague grammar

Abstract: Richard Montague’s work on English, as represented in Montague (1970a), (1970b), (1972), represents the first systematic attempt to apply the logician’s methods of formal syntax and semantics to natural language. With few exceptions,1 linguists and logicians had previously been agreed, although for different reasons, that the apparatus developed by logicians for treating the syntax and semantics of artificially constructed formal languages, while obviously fruitful within its restricted domain, was not in any direct way applicable to the analysis of natural languages. Logicians seem to have felt that natural languages were too unsystematic, too full of vagueness and ambiguity, to be amenable to their rigorous methods, or if susceptible to formal treatment, only at great cost.2 Linguists, on the other hand, emphasize their own concern for psychological reality, and the logicians’ lack of it, in eschewing the logicians’ approach: linguists, at least those of the Chomskyan school, are searching for a characterization of the class of possible human languages, hoping to gain thereby some insight into the structure of the mind, and the formal languages constructed by logicians appear to depart radically from the structures common to actual natural languages.

The restriction language for computer grammars of natural language

Abstract: Over the past few years, a number of systems for the computer analysis of natural language sentences have been based on augmented context-free grammars: a context-free grammar which defines a set of parse trees for a sentence, plus a group of restrictions to which a tree must conform in order to be a valid sentence analysis. As the coverage of the grammar is increased, an efficient representation becomes essential for further development. This paper presents a programming language designed specifically for the compact and perspicuous statement of restrictions of a natural language grammar. It is based on ten years' experience parsing text sentences with the comprehensive English grammar of the N.Y.U. Linguistic String Project, and embodies in its syntax and routines the relations which were found to be useful and adequate for computerized natural language analysis. The language is used in the current implementation of the Linguistic String Parser.

Stochastic Syntax-Directed Translation Schemata for Correction of Errors in Context-Free Languages

Abstract: A formal method of correcting errors of changed, deleted, and inserted terminals in the strings of a context-free language is considered. Grammars generating strings containing these errors are first constructed from a known grammar for the language; these new grammars are then used to specify simple syntax-directed translation schemata which can parse both correct strings and strings with errors and simultaneously produce output strings in the original language. Stochastic aspects of productions and of errors are incorporated into the correction model to assign probabilities to translations produced.

Sentence paraphrasing from a conceptual base

Abstract: A model of natural language generation based on an underlying language-free representation of meaning is described. A program based on this model is able to produce sentence paraphrases which demonstrate understanding with respect to a given context. This generator operates in conjunction with a natural language analyzer and a combined memory and inference model. In generating sentences from meaning structures, the program employs both the information retrieval and deduction capabilities of the memory model.The model encompasses several diverse classes of linguistic knowledge, which include: (1) executable tests of conceptual properties stored in discrimination nets; (2) information relating conceptual to syntactic roles, stored in a word-sense dictionary, and (3) surface grammatical knowledge, stored in a formal grammar.

Generating hierarchical semantic networks from natural language discourse

Abstract: The following paper contains a description of a computer program that constructs hierarchical semantic networks from natural language texts in simulating completely and precisely the meaning of the input text. The program works with a formal grammar describing sentences syntactically and a formal semantic stransducing texts to networks dependent on their syntactic description. The networks' nodes have concepts or again networks, as their values. The networks' edges are many-place relations among the concepts respectively networks. They are realized as reference structures. The program in its fietual state works on domains which art to comprehend sematically rather well: A network has been constructured automatically for the area of general topology from a compendi urn's definitions (N. Bourbaki. E lenient s of Mathcmatics. General topology). Another one is being constructed for the area of computer science.

Formal semantics of Natural Language: Model theory and linguistics

Abstract: Model theory is a mathematical technique for investigating certain properties of formal systems: properties such as consistency, completeness, the finite model property and having a decision procedure. Instead of looking for proofs based directly upon the formal system being studied, the method is to relate it to other formal systems whose properties are already known, by defining a translation from the former to the latter. Where this can be carried through, the systems thus related to the one under investigation are termed ‘models’ of it and known properties of the models can then be extrapolated to the new system. If a natural language or a fragment of a natural language constitutes a formal system, then the technique can be applied to it also, for the same purposes. There is now a prevalent impression among linguists, however, that model theory can provide a theory of meaning for natural language. The thesis of this paper is that any such hope will certainly be disappointed and that the mistake has arisen from confusion among mathematicians about the correct description of their own procedure. This confusion is illustrated by the following descriptions of model theory from a recent book on mathematical logic: ‘Model theory is the study of the relations between languages and the world, or more precisely between formal languages and the interpretations of formal languages' (Crossley et al. (1972:20)). The idea which links these two descriptions is that interpretations of formal languages are not, as I have claimed, other formal languages, but structures , ‘the world’ being the structure which interprets a natural language.

The dimension of a formal language

Abstract: A connection is established between formal language theory and mathematical analysis by associating the symbols of strings of a language with the digits of expansions of points in the unit interval. A language is made to correspond to a particular subset of the unit interval, and the dimension of a language is defined as the Hausdorff dimension of this subset. It is shown that the dimension of a language is less than or equal to its channel capacity, and it is shown that a statement involving the dimension of a language can be added to a list of criteria developed by Brainerd and Knode (1972) for determining that a language is not recognizable by a finite automaton.

An algebraic theory of formal languages

Abstract: : X ÷ A. This map extends to a homomorphism (uniquely) ~ : W~(X) ÷ A by induction as follows: (i) ~(x) = ~(x) for each xEX (2) ~(~(e I ..... en)) = ~A(~(e l) ..... ~(en)). We can use this idea to define composition of assignments. Let XI, X 2, X 3 ~ X and ~i : Xl ÷ W~(X2) and ~2 : X2 ÷ W~(X3) then we define ~2 o el(X) : ~2(~l(X)). Because of the unique extension property it is not difficult to verify that "o" is associative.