Showing papers on "Formal system published in 1980"

Inductive inference of formal languages from positive data

Abstract: We consider inductive inference of formal languages, as defined by Gold (1967) , in the case of positive data, i.e., when the examples of a given formal language are successive elements of some arbitrary enumeration of the elements of the language. We prove a theorem characterizing when an indexed family of nonempty recursive formal languages is inferrable from positive data. From this theorem we obtain other useful conditions for inference from positive data, and give several examples of their application. We give counterexamples to two variants of the characterizing condition, and investigate conditions for inference from positive data that avoids “overgeneralization.”

On the length of proofs in a formal systems

Abstract: (2) ―pY*-VxA(x) iff there is a k such that (Vn) -p&rAW In thispaper we shallprove an analogue of (2) for systems which have a finitenumber of function symbols and a finitenumber of axiom schemata, and are complete with respect to formulas [in Presburger arithmetici.e. formulas which have only S, +, = other than logicalsymbols. Let T be any one of such systems. By Tk we mean the subsystem of T which has only axioms containingat most k occurrences of bound variablesand critical explicitterms (these willbe definedin §1)' Now our claim is: ~T VxA(x) iff there is a k such that (Vn) I * 1 Tt A(n)

Study of Piron's system of questions and propositions

Abstract: A formal system of “questions” and “propositions” conceived by C. Piron and claimed to yield by interpretation quantum mechanics as well as all other known physical theories is examined. It is proved that the mentioned system is syntactically self-consistent in the sense of the theory of models. However, it is found that the mentioned formal system possesses certain syntactic characteristics in consequence of which qualification of this system as a generator of quantum mechanics by interpretation encounters semantic obstacles so grave that they annihilate any relevance of such a qualification.

A Theoretical Basis for the Systematic Proof Method

Abstract: All redundancies are removed from derivations in a Gentzen-like formal system of first-order logic. The resulting skeleton derivations are characterized in terms of the formulas to be derived. This provides the formal basis for a powerful proof procedure developed earlier by the author.

The representation of communication and concurrency

Abstract: A formal system is described within which we may represent the communication and concurrency features found in systems of interacting computer agents. This formal system may be used both as a model in which to represent the behaviour of existing systems of computing agents or as a language in which to program desired systems. The notion of acceptance semantics is introduced and it is in terms of this that we give meaning to programs constructed in our framework.

Interval Logics with Applications to Study of Tense and Aspect in English

Abstract: Chapter 1: Philosophical Motivation 417 §11: Introduction 417 §12: Temporal Dualism 418 Chapter 2: The Prepositional Logic I 420 §21: Formal Language LI 420 §22: Semantics for I 421 §23: Dl-sequence 423 §24: Formal System I 425 §25: The Soundness and Completeness of I 427 Chapter 3: The Prepositional Logic IM 435 §31: Formal Language LIM 435 §32: Semantics for IM 436 §33: DMI-sequence and DIM-sequence 441 §34: Formal System IM 445 §35: The Soundness and Completeness of IM 450 Chapter 4: Some Applications 450 § 41: Some Interesting Tense Operators Definable within IM 450 §42: Tense and Aspect within IM 455

Independence results in Computer Science? (Preliminary Version)

Abstract: Although there has been considerable additional work discussing limitations of formal proof techniques for Computer Science ([YO-73&77], [HAR-76], [HAR&HO-77], [HAJ-77&79], [GO-79]), these papers show only very general consequences of incompleteness: the stated results hold for all sufficiently powerful formal systems for Computer Science. Only the work of O'Donnell and of Lipton directly addresses the question of just how powerful formal axioms for Computer Science should be, and these two authors make rather radically different suggestions. We investigate this latter question: How powerful should a set of axioms be if it is to be adequate for Computer Science? In particular, in this paper we investigate the adequacy of the system of [LI-78] as a formal system for Computer Science.

Formal properties of one-visit and multi-pass attribute grammars (extended abstract)

Abstract: The purpose of this paper is to study the formal power of certain classes of attribute-grammars (AG). We first consider the class of 1S-AG and extend a result of [DPSS]. Then we compare the formal power of "one-visit" AG with that of related types of AG. Finally, using a partial characterization of the formal power of arbitrary AG we prove some results on deciding whether an AG is (left-to-right) multi-pass.

Application of a Formal Systems Methodology to Civil Defense.

Abstract: : This report contains the studies which treat various problems concerning disaster mitigation and civil defense with the formal methodology of systems, the HOS methodology Included are restricted inquiries concerning transportation, communication and goals analysis The more extensive results present (1) an integrated host and risk area system for relocation, using relocation of industrial personnel as a test bench for the applicability of HOS methodology to a problem which is a general one; (2) a specification of place as a data type and a primitive or basic operation for locating one object in relation to another, which are prerequisites for dynamic mapping, planning, and implementation of mitigation systems The results obtained indicated that the HOS methodology can be employed in the design of systems pertinent to the mitigation environment The most important direct finding, however, is that by employing the HOS methodology, it should be possible to design testable systems for a variety of responses to a variety of crises and disasters The methodology is rigorous enough to deal with the enormous difficulties in terms of complexity and uncertainty and to retain sufficient flexibility to respond in real time to changing situations

Formal methods for classification of complex situations

Abstract: By classification of complex situations, we shall understand the procedure of discriminating to what category a given situation belongs. By formal methods, we understand such methods, which can be realized by computers. If the symptoms used for classification correspond to those on which the classification of situation is based, the actual classification simply consists of determining the truth (or falsity) of a statement that can be represented as a logical (Boolean) function, and the task of discrimination becomes trivial. Much more complicated are cases in which classificatory symptoms cannot be used (if, for instance, they are not yet established, or if they have not yet niade themselves known), and such a classification must be made on the basis of indirect (i.e., nonclassificatory) symptoms. Tasks of this kind appear rather frequently in engineering, medicine, economics, sociology, and in many other areas of contemporary life. Until recently, such tasks were either solved intuitively, on the basis of the experience of experts, o r remained unsolved. But even when the opinion of experts made it possible to assign a given situation t o a given category, the reliability of the decision still left much to be desired. The number of wrong classifications used to be (one may say, still is) too great, with serious consequences: people died, engineering systems failed, and resources or efforts were wasted. I n recent years, however, outlines of formalized classification procedures have begun to appear that promise to bring a more effective solution to the problem of classification of complex situations than was possible in the past. In many cases, such formalized procedures enable us to considerably enhance the reliability of classification and also to classify situations to which intuitive classification was not applicable. The frequency of such tasks in engineering is rather high. They occur in the classification of phenomena associated with an engineering project, that is, performance pattern, proper or defective operation, quality of design, and so on. The tasks of engineering diagnostics include, for instance, checking the performance of an engine by its sound, checking a computer by testing, and establishing the presence of mineral ores on the basis :of a set of geophysical and geologic data. The tasks of medical diagnostics (which is also a classification problem) consist of determining the state of a n animal or human organism o n the basis of accumulated anamnestic and clinical data. The important point is to establish the presence of a disease, type of disease, its stage, pathologic changes in relation to the normal situation, pregnancy, sex of the fetus, and so on. The need for the classification of situations appears in many other fields as well. Although the tasks of classification of complex situations on the basis of the complete set of symptoms are difficult,