Showing papers on "Formal language published in 1973"
TL;DR: The present purpose is to foster studies which model grammatical transformations as mappings on trees (equivalently, labeled bracketings) and investigating questions of current linguistic interest, such as the recursiveness of languages generated by transformational grammars.
186 citations
TL;DR: It is shown that the quasirational recursion schemes are translatable into strongly equivalent program schemes, and there is a monadic recursion scheme not strongly equivalent to any program scheme with one counter.
107 citations
TL;DR: The first systematic attempt to apply the logician's methods of formal syntax and semantics to natural language was made by Montague as discussed by the authors, whose work on English, as represented in Montague (1970a, (1970b), (1972), represents the first systematic application of the logicians' approach to natural languages.
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.
98 citations
TL;DR: TOL languages form an infinite hierarchy with respect to “natural” complexity measures introduced in this paper, and are contained in the family of context-free programmed languages.
Abstract: We discuss a family of systems and languages (called TOL) which have originally arisen from the study of mathematical models for the development of some biological organisms. From a formal language theory point of view, a TOL system is a rewriting system where at each step of a derivation every symbol in a string is rewritten in a context-free way, but different rewriting steps may use different sets of production rules and the language consists of all strings derivable from the single fixed string (the axiom). The family of TOL languages (as well as its different subfamilies considered here) is not closed with respect to usually considered operations; it is “incomparable” with context-free languages, but it is contained in the family of context-free programmed languages. TOL languages form an infinite hierarchy with respect to “natural” complexity measures introduced in this paper.
84 citations
15 Oct 1973
TL;DR: A class of naturallanguage grammars is formalized and the sentence-recognition problem is shown to be polynomial-hard although the languages are context-sensitive, and new language-theoretic characterizations are given.
Abstract: Complexity of sentence recognition is studied for one-way stack languages, indexed languages, and tree transducer languages The problem is shown to be polynomial-complete in each case A class of naturallanguage grammars is formalized and the sentence-recognition problem is shown to be polynomial-hard although the languages are context-sensitive The proofs give new language-theoretic characterizations of the set of satisfiable propositional formulas and the set of prepositional tautologies
56 citations
TL;DR: A criterion to measure derivational complexity of formal grammars and languages is proposed and discussed and it is shown that for each nonnegative integer k, there exists a context\3-free language whose rank is k.
Abstract: A criterion to measure derivational complexity of formal grammars and languages is proposed and discussed. That is, the associate language and the L-associate language are defined for a grammar such that the former represents all the valid derivations and the latter represents all the valid leftmost derivations. It is shown that for any phrase\3-structure grammar, the associate language is a contex\3-sensitive language and the L\3-associate language is a context\3-free language. Necessary and sufficient conditions for an associate language to be a regular set and to be a context\3-free language are found. The idea in the above necessary and sufficient conditions is extended to the notion of “rank≓ for a measure of derivational complexity of context\3-free grammars and languages. It is shown that for each nonnegative integer k, there exists a context\3-free language whose rank is k. The paper also includes a few solvable decision problems concerning derivational complexity of grammars.
53 citations
Book•
01 Jan 1973
TL;DR: AUTOMATH is a language intended for expressing detailed mathematical thoughts, and can be used to express a large part of mathematics, and admits many ways for laying the foundations.
Abstract: AUTOMATH is a language intended for expressing detailed mathematical thoughts. It is not a programming language, although it has several features in common with existing programming languages. It is defined by a grammar, and every text written according to its rules is claimed to correspond to correct mathematics. It can be used to express a large part (see 1.6) of mathematics, and admits many ways for laying the foundations. The rules are such that a computer can be instructed to check whether texts written in the language are correct. These texts are not restricted to proofs of single theorems; they can contain entire mathematical theories, including the rules of inference used in such theories.
52 citations
TL;DR: The notion of a discrete pattern is formalized and certain properties deduced and a pattern is shown to be a generalization of a formal language.
Abstract: The notion of a discrete pattern is formalized and certain properties deduced. A pattern is shown to be a generalization of a formal language. Algorithms for implementing the kinds of patterns in SNOBOL4 are given. The general approach is to create, in-so-far as possible, a bottom-up parse from a top-down specification.
48 citations
TL;DR: This paper investigates unary developmental systems and languages, which are distinguished by the property that the alphabet involved in their definition has only one symbol in it.
26 citations
01 Jan 1973
TL;DR: It is shown that the grades of membership of desired productions are intensified by choosing an adequate teaching sequence of the sentence set and a concept of ``strongly equivalent,'' in which two grammars are not distinguished by any teaching sequence, is introduced.
Abstract: A learning model of fuzzy formal language is proposed and discussed. We continue training the learning machine by giving sets of sentences sequentially. As a result of parsing of the given teaching sentences, the learning machine reinforces fuzzy grades of membership of productions in an inherent fuzzy grammar of the machine. The convergence of the proposed model is considered, and it is shown that the grades of membership of desired productions are intensified by choosing an adequate teaching sequence of the sentence set. Furthermore, a concept of ``strongly equivalent,'' in which two grammars are not distinguished by any teaching sequence, is introduced.
01 Oct 1973
TL;DR: A syntax-directed approach is proposed for the extraction of pattern features from one-dimensional spatial or temporal series of events using formal and ad hoc methods for recognition of carotid pulse waves.
Abstract: : A syntax-directed approach is proposed for the extraction of pattern features from one-dimensional spatial or temporal series of events The approach is offered as a synthesis of formal and ad hoc methods Existing techniques in the parsing of formal languages are shown to apply to the problem of analyzing series which exhibit certain structure An example is given detailing this approach as applied to the recognition of carotid pulse waves (Author)
TL;DR: This paper claimed that this system is strong enough to precisely state the formative and deductive rules of formal languages, and supported this claim by formulating, in a very precise way, the rule of procedure of Leśniewski’s Protothetic.
Abstract: Part I of this paper presented an axiomatized theory of general syntax, defined the usual notions of general syntax, and proved some typical theorems of general syntax. We claimed that this system is strong enough to precisely state the formative and deductive rules of formal languages. In Part II we support this claim by formulating, in a very precise way, the rule of procedure of Leśniewski’s Protothetic. Section 1 is an informal introduction to Protothetic and its rule of procedure. Our metalogical system is extended there to a theory MP which is concerned explicitly with the syntax of Protothetic. This section is intended to motivate the Terminological Explanations of Section 2 which culminate in the statement of the rule of Protothetic. In Section 3 we sketch a proof that our formulation of the rule is equivalent to that given by Leśniewski (1929). This proof shows that our system is strong enough to conduct certain metalogical investigations.
09 Jul 1973
TL;DR: W: Proceeedings of the Conference on Automata and Formal Languages, Bonn, (1973), volume 2 of Lecture Notes in Computer Science, pages 24-37.
Abstract: W: Proceeedings of the Conference on Automata and Formal Languages, Bonn, (1973), volume 2 of Lecture Notes in Computer Science, pages 24-37
01 Jan 1973
TL;DR: In this paper, a suitable mathematical environment for future Logic for Computable Functions (LCF) experiments and its axiomatic basis is described, consisting of a large body of theorems from the areas of integer arithmetic, list manipulation and finite set theory.
Abstract: LCF (Logic for Computable Functions) is being promoted as a formal language suitable for the discussion of various problems in the Mathematical Theory of Computation (MTC). To this end, several examples of MTC problems have been formalised and proofs have been exhibited using the LCF proof-checker. However, in these examples, there has been a certain amount of ad-hoc-ery in the proofs; namely, many mathematical theorems have been assumed without proof and no axiomatisation of the mathematical domains involved was given. This paper describes a suitable mathematical environment for future LCF experiments and its axiomatic basis. The environment developed, deemed appropriate for such experiments, consists of a large body of theorems from the areas of integer arithmetic, list manipulation and finite set theory.
TL;DR: It is shown how the system can be used to build composite data types out of simpler ones with the operations of rowing, structuring, and uniting and that completely new primitive types can be introduced into languages through the mechanism of singleton data types.
Abstract: A formal system is presented which abstracts the notions of data item, function, and relation. It is argued that the system is more suitable than set theory (or its derivatives) for the concise and accurate description of program semantics. It is shown how the system can be used to build composite data types out of simpler ones with the operations of rowing, structuring, and uniting. It is also demonstrated that completely new primitive types can be introduced into languages through the mechanism of singleton data types.Both deterministic and nondeterministic functions are shown to be definable in the system. It is described how the local environment can be modeled as a data item and how imperative statements can be considered functions on the environment. The nature of recursive functions is briefly discussed, and a technique is presented by which they can be introduced into the system. The technique is contrasted with the use of the paradoxical combinator, Y. The questions of local and global environments and of various modes of function calling and parameter passing are touched upon.The theory is applied to the proof of several elementary theorems concerning the semantics of the assignment, conditional, and iterative statements.An appendix is included which presents in detail the formal system governing webs and fen, the abstractions used informally in the body of the paper.
Proceedings Article•
01 Jan 1973
TL;DR: A method for forming a negative image comprising imagewise exposing a photographic material to provide exposed areas and unexposed areas and a substance which renders said grains less soluble by adsorbing thereto.
Abstract: A method for forming a negative image comprising imagewise exposing a photographic material to provide exposed areas and unexposed areas, said material comprising, on a support, (1) an emulsion layer containing a light-sensitive silver halide, (2) unsensitized silver halide metallic salt grains which are more soluble in a developer than the light sensitive silver halide, and (3) nuclei for physical development, processing said material in the presence of a reducing agent and a solvent for said grains with said developer containing a substance which renders said grains less soluble by adsorbing thereto, said developer rendering said grains in said exposed areas and not in said unexposed areas soluble in said solvent, whereby metal ions are released and deposited on said nuclei.
TL;DR: An extension for the concept of the finite index of context-free grammars is introduced and regular control languages are derived for the resulting family of languages generated by ordered Context-free Grammars.
Abstract: An extension for the concept of the finite index of context-free grammars is introduced and regular control languages are derived for the resulting family of languages generated by ordered context-free grammars.
Proceedings Article•
01 Jan 1973
TL;DR: The present invention relates to novel 1-azaxanthone-3-carboxylic acid and its derivatives usable for effective medicines for the treatment of allergic diseases.
Abstract: The present invention relates to novel 1-azaxanthone-3-carboxylic acid and its derivatives usable for effective medicines for the treatment of allergic diseases, which are shown by the following formula (I) (I) wherein R1 is hydrogen, alkyl, phenyl, carboxyl, hydroxyl, alkoxy or amino group which may be unsubstituted or substituted by one alkyl, m is 0, 1 or 2 and R2 is alkyl, alkoxy, halogen, nitro, hydroxy, carboxyl, butadienylene (-CH=CH-CH=CH-) which forms a benzene ring with any adjacent carbon atoms or amino group which may be unsubstituted or substituted by at least one alkyl, and their physiologically acceptable salts.
TL;DR: Some basic concepts and some aspects of the technology and methodology of these modes of theory evaluation for theory evaluation in political science are discussed.
Abstract: Mathematical languages and computer algorithms are becoming important modes of analysis for theory evaluation in political science. Typically, the process involves (I) translating the major theoretical relationships into a 'formal' language for the logical analysis of internal consistency, or, (2) empirically interpreting the formal language in order to make specific predictions, which, in turn, allow evaluation of external consistency with theoretically significant real world phenomena. In this paper I wish to discuss, first, some basic concepts and, second, some aspects of the technology and methodology of these modes of theory evaluation.
01 Jan 1973
TL;DR: A general factorization of the social choice process is given and it is shown that the formal language model has the power to include mathematical axiomatic characterizations as a special case.
Abstract: This paper defines concepts of grammar, language and automata and their application to both structural and axiomatic representations of the social choice process. A general factorization of the social choice process is given and it is also shown that the formal language model has the power to include mathematical axiomatic characterizations as a special case. In addition, the general model can be extended to explicitly describe uncertainty in the social decision process.
27 Aug 1973
TL;DR: A general framework in which the language of predicate logic of first-order can be used to describe the syntax of an object language and the development of the recursive mechanism in the form of definition of semantic functions by cases is presented.
Abstract: In the recent years there is an intensive search for a rigorous and explicit semantics in the theory of natural languages (and in the field of computer languages). In this paper we want to present a general framework in which all these ideas and results can be stated and related in a unified and systematic way, and at the same time, by the using of the language of predicate logic, eventually of higher order, to reformulate and improve the different semantical systems: the system discussed by Scott and Strachey in their development of the theory of mathematical semantics for computer languages, the set-theoretic semantics for context-free fragments of natural languages proposed by Suppes and, finally, Lewis's iutensional semantics for a categorial grammar. In § 1, mainly by the example of context-free grammar, we show that the language of predicate logic of first-order can be used to describe the syntax of an object language. We obtain then in § 2 a logical characterization of structural descriptions associated with each reformulated syntactic rule. This leads to the development of the recursive mechanism in the form of definition of semantic functions by cases. This general principle will be then applied in § 3--5 to treat the concrete semantical systems mentioned above.
01 Jan 1973
TL;DR: The paper describes a suitable mathematical environment for future LCF experiments and its axiomatic basis, which consists of a large body of theorems from the areas of integer arithmetic, list manipulation and finite set theory.
Abstract: : LCF (Logic for Computable Functions) is being promoted as a formal language suitable for the discussion of various problems in the Mathematical Theory of Computation (MTC). To this end, several examples of MTC problems have been formalised and proofs have been exhibited using the LCF proof-checker. However, in these examples, there has been a certain amount of ad-hoc-ery in the proofs: namely, many mathematical theorems have been assumed without proof and no axiomatisation of the mathematical domains involved was given. The paper describes a suitable mathematical environment for future LCF experiments and its axiomatic basis. The environment developed, deemed appropriate for such experiments, consists of a large body of theorems from the areas of integer arithmetic, list manipulation and finite set theory.
01 Jan 1973
TL;DR: In dealing with a complicated pattern, it is essential to analyse the pattern into subpatterns, to which some information measure is to be assigned, to decide whether the corresponding sub-pattern is not worth being maintained for further processing or how detailed it should be described or how itShould be transformed.
Abstract: In dealing with a complicated pattern it is essential to analyse the pattern into subpatterns, to which some information measure is to be assigned. According to this information measure which is generated by a certain mechanism, it is decided whether the corresponding sub-pattern is not worth being maintained for further processing or how detailed it should be described or how it should be transformed. The mechanism which generates the information measures to be assigned to the subpatterns functions depending upon the mission for which the given pattern is being processed.
01 Jan 1973
TL;DR: A formal language for the description of linguistic data is discussed and possible ways of further restricting that formal language are discussed to finally lead to the construction of a linguistic theory.
Abstract: The aim of this article is to discuss a formal language for the description of linguistic data and to discuss possible ways of further restricting that formal language. These restrictions should finally lead to the construction of a linguistic theory.