Showing papers on "Formal system published in 1977"

Lucid, a nonprocedural language with iteration

Abstract: Lucid is a formal system in which programs can be written and proofs of programs carried out. The proofs are particularly easy to follow and straightforward to produce because the statements in a Lucid program are simply axioms from which the proof proceeds by (almost) conventional logical reasoning, with the help of a few axioms and rules of inference for the special Lucid functions. As a programming language, Lucid is unconventional because, among other things, the order of statements is irrelevant and assignment statements are equations. Nevertheless, Lucid programs need not look much different than iterative programs in a conventional structured programming language using assignment and conditional statements and loops.

A language for formal problem specification

Abstract: A language for specifying the intended behavior of communicating parallel processes is described. The specifications are constraints on the order in which events of a computation can occur. The language is used to write specifications of the readers/writers problem and the writer priority of the second readers/ writers problem.

A practical formal semantic definition and verification system for typed lisp.

Abstract: : Despite the fact that computer scientists have developed a variety of formal methods for proving computer programs correct, the formal verification of a non-trivial program is still a formidable task. Moreover, the notion of proof is so imprecise in most existing verification systems, that the validity of the proofs generated is open to question. With an aim toward rectifying these problems, the research discussed in this dissertation attempts to accomplish the following objectives: 1. To develop a programming language which is sufficiently powerful to express many interesting algorithms clearly and succintly, yet simple enough to have a tractable formal semantic definition. 2. To completely specify both proof theoretic and model theoretic formal semantics for this language using the simplest possible abstractions. 3. To develop an interactive program verification system for the language which automatically performs as many of the straightforward steps in a verification as possible.

Set-Theoretic Semantics

Abstract: Publisher Summary This chapter focuses on set-theoretic semantics. Two fundamental acquisitions of modern logic are the notion of formal system and that of interpretation. These two notions somehow complement each other; when a formal language is constructed, the meanings of the symbols, in order to deal with their syntactic relations, are abandoned. The two semantics may have to be used concurrently;first, because a sentence may contain both count terms and mass terms, and second, because the quasi-individual terms obtained from mass terms by a variety of linguistic means, require individuals for their interpretation. There is also, with mass terms, the problem of mixtures, both on the syntactic and on the semantic plane. Because quantifiers cannot be interpreted except in a discrete domain, the proper treatment of mass terms requires a variable-free system. The chapter introduces model theory that has bloomed into an extensive science. But this new discipline does not seem to care much about what was the original object of semantics.

On Equivalence and Containment Problems for Formal Languages

Abstract: Sufficient but general conditions on a family of formal languages ~ and a language L~ m ~ are given such that ( l) \"'= L0\" is as hard as \"= {0, 1}*\" for,~', (2) \"_~ Lo\" is as hard as \"= {0, 1}*\" for if', and (3) \"= L0\" and \"C_ Lo\" are as hard as \"= ~ \" lor ~: For many interesting families such as the regular sets and contextfree languages, a sufficient condmon for (1) is that Lo has an unbounded regular subset; a sufficient condinon for (2) is that Lo has an unbounded context-free subset, and a sufficient condition for (3) is that L0 has no unbounded regular subsets Numerous applications of these results to specific families of languages are hsted Many context-free languages are shown to contain unbounded regular subsets

Formal properties of phonological rules

Abstract: One of the salient features of generative phonology has been the emphasis put on formal questions. The study of abstract properties of grammars has been the distinctive concern of work carried out in the field and most of the research has been aimed at discovering formal universals. The fundamental methodological assumption has been that the investigation of formal properties of grammars would eventually lead to significant discoveries. At the same time, however, generative linguists have been aware that phonological theory, as a part of a general theory of language, should concern itself with substantive universals as well. In particular, it was apparent that the evaluation measure would have to incorporate an elaborate system of substantive constraints. For example, in The Sound Pattern of English (SPE),1 the basic theoretical work of generative phonology, Chomsky and Halle remark that the formal evaluation procedures and the associated notational devices defined in the early chapters of their book give wrong results in many instances and that they must be supplemented by a set of conventions which takes into account the intrinsic content of phonological features and of phonological rules.2 Of course, there is no contradiction in undertaking investigations of both types of universals, formal and substantive. The open, and empirical, question, however, is how greatly substantive conditions limit the class of grammars available to the language-learner: if very greatly, formal properties have little interest. In this paper I would like to provide a partial answer to this question, and to argue that the fundamental methodological assumption of generative phonology, as stated at the beginning of this introduction, is correct. I will suggest that phonological theory contains a rich core of formal. constraints. In particular, I will present some striking results from Halle et al. (1975).

An approach to describing a data link level protocol with a formal language

Abstract: A method approaching the formal description of protocols is presented. The method -based on formal languages - utilises the relationship between the formal languages and automata and allows the dialogue between two partners/stations, units of equipments, processes, etc./ to be defined in a formal way. The paper considers a data link level protocol, the High Level Data Link Control Procedure. Two basic models are given: the first is for the description of the operation of the stations in half-duplex, the other for the full-duplex transmission mode. A number of other improved models are introduced taking into consideration the effect of time-out, unknown frame, sequence numbering and the request for retransmission frames with a sequence number. It is shown that the models can follow the way of avoiding the deadlock situation, and the formal grammars are more advantageous for modelling complicated systems than are automata. The advantages and limitations of the approach is emphasized by comparing it with approaches elaborated by other authors.

Basic Concepts of Formal Methodology of Empirical Sciences

Abstract: Taking as the starting point some concepts of mathematical logic, especially those of logical semantics (theory of models), I will try to elaborate and adjust them to the needs of the methodology of empirical sciences. Proceeding along these lines, I will aim at constructing a set-theoretic model of the relationships which connect the formal components of an empirical theory (its language and the set of asserted statements) with the empirical systems that the theory is to describe. The discussion will result in producing two such models. The second one will be devised in such a manner as to conform with the approximative nature of empirical inquiry. Inside this conceptual framework there will be defined and discussed several notions, among others some types of regularities (determinism, some correlation regularities) and the notion of approximative truth.

Continuity and comprehension in intuitionistic formal systems

Abstract: Within the framework of a formal system, we can ask if one can find any necessary relations between the answers to the two questions posed above. We show that, within the language of second-order arithmetic, one cannot find any such relations; even if one includes Church's thesis, which says that every constructive function is recursive. In earlier work, we have proved independence results related to question (1) in the context of the language of arithmetic. The main tool of the present paper is an extension of our earlier methods to second-order comprehension principles. It is fairly easy to prove the consistency of strong principles of set existence with the continuity of extensional functions, even in the presence of Church's thesis (see discussion in [3]). And, as mentioned, the case where one does not have strong set existence principles has been dealt with in [1]. The main problem, then, is the independence of the continuity of extensional functions from strong set existence principles. Of course, if all the formal axioms considered are classically true, this independence is trivial; but we are interested in the independence in an axiomatic framework including nonclassical principles. Foremost among such principles is Church's thesis, which (in a suitable formulation) will reduce members of NN to recursive indices, and functions from NN to N to effective operations, which compute the function value recursively from an index of the argument. Thus, under Church's thesis CT, the statement "all functions are continuous" reduces to an arithmetical proposition about effective operations. This proposition (for the case of NN) is called KLS, after Kreisel, Lacombe, and Shoenfield, who gave a classical proof of it [5]. It also happens that this sentence KLS lies in a syntactic class for which CT is conservative (over all the theories we will consider; see discussion in the text). Thus the difficult part of our problem is to prove the independence of KLS from various principles of set existence.

Strategies for mechanizing structural induction

Abstract: A theorem proving system has been programmed for automating mildly complex proofs by structural induction. One purpose was to prove properties of simple functional programs without loops or assignments. One can see the formal system as a generalization of number theory: the formal language is typed and the induction rule is valid for all types. Proofs are generated by working backward from the goal. The induction strategy splits into two parts: (1) the selection of induction variables, which is claimed to be linked to the useful generalization of terms to variables, and (2) the generation of induction subgoals, in particular, the selection and specialization of hypotheses. Other strategies include a fast simplification algorithm. The prover can cope with situations as complex as the definition and correctness proof of a simple compiling algorithm for expressions.

The formal system for various 3-valued logics II

Abstract: We gave the Gentzen-type formal system of Kleene’s 3-valued logic and McCarthy’s 3-valued logic interpreted into the system in [3]. In this paper we shall give the Gentzen-type formal system of McCarthy’s logic itself. After that, we shall give the formal system in which McCarthy’s and Kleene’s are joined. In this system, serial or parallel evaluation is mixed. We shall use the same terminology in [3]. Especially we use the symbols

Lucid, a Nonprocedural with

Abstract: Lucid is a formal system in which programs can be written and proofs of programs carried out. The proofs are particularly easy to follow and straightforward to produce because the statements in a Lucid program are simply axioms from which the proof proceeds by (almost) conventional logical reasoning, with the help of a few axioms and rules of inference for the special Lucid functions. As a programming language, Lucid is unconventional because, among other things, the order of statements is irrelevant and assignment statements are equations. Nevertheless, Lucid programs need not look much different than iterative programs in a conventional structured programming language using assignment and conditional statements and loops. Key Words and Phrases: program l~roving, formal systems, semantics, iteration, structured programming CR Categories: 5.21, 5.24

On the formal definition of VDL-objects.

Abstract: Originally the VDL (Vienna Definition Language) was designed for defining programming languages [1], [2], [3], but recently it has been used as a general technique of defining data structures and algorithms [4]. The VDL is a definition system? This system consists of objects, a machine operating on objects and a programming language. The VDL-objects are abstractions of data structures of a certain type. \"In this paper we deal with the objects and the basic operators of VDL manipulating on objects. * The VDL-objects form a set with the elements of which there are associated selection and construction operators. The basic properties of the operators are taken as axioms and their main properties are proved. A complet formal system of VDL-objects is given, -which can be regarded as a detailed elaboration of the axiomatic definition of VDL data structures given in [4] and [5].

On certain theorems of analysis in the formal system Kleene-Vesley

Abstract: It is proven that in the Kleene-Vesley formal system of intuitionistic analysis, theorems on upper bounds and on mean values of functions can neither be deduced nor verified.