scholarly journals Exploring the Jungle of Intuitionistic Temporal Logics

2021 ◽  
pp. 1-34
Author(s):  
JOSEPH BOUDOU ◽  
MARTÍN DIÉGUEZ ◽  
DAVID FERNÁNDEZ-DUQUE ◽  
PHILIP KREMER
Keyword(s):  
Programming Languages ◽  
Type Theory ◽  
Proof Theory ◽  
Order Relation ◽  
Point Of View ◽  
Temporal Logics ◽  
Functional Programming Languages ◽  
Order Relations ◽  
Theory Point ◽  
Axiomatic Systems

Abstract The importance of intuitionistic temporal logics in Computer Science and Artificial Intelligence has become increasingly clear in the last few years. From the proof-theory point of view, intuitionistic temporal logics have made it possible to extend functional programming languages with new features via type theory, while from the semantics perspective, several logics for reasoning about dynamical systems and several semantics for logic programming have their roots in this framework. We consider several axiomatic systems for intuitionistic linear temporal logic and show that each of these systems is sound for a class of structures based either on Kripke frames or on dynamic topological systems. We provide two distinct interpretations of “henceforth”, both of which are natural intuitionistic variants of the classical one. We completely establish the order relation between the semantically defined logics based on both interpretations of “henceforth” and, using our soundness results, show that the axiomatically defined logics enjoy the same order relations.

Special issue on Dependent Type Theory Meets Programming Practice CALL FOR PAPERS

2001 ◽  
Vol 11 (4) ◽  
pp. 437-437
Author(s):  
Gilles Barthe ◽  
Peter Dybjer ◽  
Peter Thiemann
Keyword(s):  
Programming Languages ◽  
Type Theory ◽  
Type System ◽  
Type Systems ◽  
Point Of View ◽  
Theoretical Point ◽  
Special Issue ◽  
Dependent Type Theory ◽  
The Impact ◽  
Dependent Type

Modern programming languages rely on advanced type systems that detect errors at compile-time. While the benefits of type systems have long been recognized, there are some areas where the standard systems in programming languages are not expressive enough. Language designers usually trade expressiveness for decidability of the type system. Some interesting programs will always be rejected (despite their semantical soundness) or be assigned uninformative types.There are several remedies to this situation. Dependent type systems, which allow the formation of types that explicitly depend on other types or values, are one of the most promising approaches. These systems are well-investigated from a theoretical point of view by logicians and type theorists. For example, dependent types are used in proof assistants to implement various logics and there are sophisticated proof editors for developing programs in a dependently typed language.To the present day, the impact of these developments on practical programming has been small, partially because of the level of sophistication of these systems and of their type checkers. Only recently, there have been efforts to integrate dependent systems into intermediate languages in compilers and programming languages. Additional uses have been identified in high-profile applications such as mobile code security, where terms of a dependently typed lambda calculus to encode safety proofs.A special issue of the Journal of Functional Programming will be devoted to the interplay between dependent type theory and programming practice. We welcome technical contributions in the field, as well as position papers that:[bull ] make researchers in programming languages aware of new developments and research directions on the theory side;[bull ] point out to theorists practical uses of advanced type systems and urge them to address theoretical problems arising in emerging applications.Authors who are concerned about the appropriateness of a topic are welcome to contact the guest editors. Manuscripts should be unpublished works and not submitted elsewhere. Revised and enhanced versions of papers published in conference proceedings that have not appeared in archival journals are eligible for submission. All submissions will be reviewed according to the usual standards of scholarship and originality.Submissions should be sent to Gilles Barthe ([email protected]), with a copy to Nasreen Ahmad ([email protected]). Submitted articles should be sent in postscript format, preferably gzipped and uuencoded. In addition, please send, as plain text, title, abstract and contact information.The submission deadline is December 1st, 2001.

Chemical analysis: Information contribution of results

1991 ◽  
Vol 56 (3) ◽  
pp. 505-559 ◽  
Author(s):  
Karel Eckschlager
Keyword(s):  
Analytical Chemistry ◽  
Information Theory ◽  
Set Theory ◽  
Fuzzy Set Theory ◽  
Information Gain ◽  
Analytical Signal ◽  
Point Of View ◽  
System A ◽  
Review Analysis ◽  
Theory Point

In this review, analysis is treated as a process of gaining information on chemical composition, taking place in a stochastic system. A model of this system is outlined, and a survey of measures and methods of information theory is presented to an extent as useful for qualitative or identification, quantitative and trace analysis and multicomponent analysis. It is differentiated between information content of an analytical signal and information gain, or amount of information, obtained by the analysis, and their interrelation is demonstrated. Some notions of analytical chemistry are quantified from the information theory and system theory point of view; it is also demonstrated that the use of fuzzy set theory can be suitable. The review sums up the principal results of the series of 25 papers which have been published in this journal since 1971.

scholarly journals Dynamic game semantics

2020 ◽  
pp. 1-60
Author(s):  
Norihiro Yamada ◽  
Samson Abramsky
Keyword(s):  
Programming Languages ◽  
Functional Programming ◽  
Operational Semantics ◽  
Dynamic Game ◽  
Standard Interpretation ◽  
Functional Programming Languages ◽  
Game Semantics ◽  
Wide Range ◽  
Cartesian Closed Categories ◽  
Cartesian Closed

Abstract The present work achieves a mathematical, in particular syntax-independent, formulation of dynamics and intensionality of computation in terms of games and strategies. Specifically, we give game semantics of a higher-order programming language that distinguishes programmes with the same value yet different algorithms (or intensionality) and the hiding operation on strategies that precisely corresponds to the (small-step) operational semantics (or dynamics) of the language. Categorically, our games and strategies give rise to a cartesian closed bicategory, and our game semantics forms an instance of a bicategorical generalisation of the standard interpretation of functional programming languages in cartesian closed categories. This work is intended to be a step towards a mathematical foundation of intensional and dynamic aspects of logic and computation; it should be applicable to a wide range of logics and computations.

Real-time MLton: A Standard ML runtime for real-time functional programs

2021 ◽  
Vol 31 ◽  
Author(s):  
BHARGAV SHIVKUMAR ◽  
JEFFREY MURPHY ◽  
LUKASZ ZIAREK
Keyword(s):  
Programming Languages ◽  
Real Time ◽  
Concurrency Control ◽  
General Purpose ◽  
Functional Languages ◽  
Control Mechanisms ◽  
Real Time Systems ◽  
Functional Programming Languages ◽  
Standard Ml ◽  
Time Systems

Abstract There is a growing interest in leveraging functional programming languages in real-time and embedded contexts. Functional languages are appealing as many are strictly typed, amenable to formal methods, have limited mutation, and have simple but powerful concurrency control mechanisms. Although there have been many recent proposals for specialized domain-specific languages for embedded and real-time systems, there has been relatively little progress on adapting more general purpose functional languages for programming embedded and real-time systems. In this paper, we present our current work on leveraging Standard ML (SML) in the embedded and real-time domains. Specifically, we detail our experiences in modifying MLton, a whole-program optimizing compiler for SML, for use in such contexts. We focus primarily on the language runtime, reworking the threading subsystem, object model, and garbage collector. We provide preliminary results over a radar-based aircraft collision detector ported to SML.

scholarly journals A TORSIONAL TOPOLOGICAL INVARIANT

2007 ◽  
Vol 22 (29) ◽  
pp. 5237-5244 ◽  
Author(s):  
H. T. NIEH
Keyword(s):  
Affine Connection ◽  
Euler Class ◽  
Christoffel Symbol ◽  
Space Time ◽  
Topological Invariant ◽  
Point Of View ◽  
Underlying Space ◽  
Recent Developments ◽  
Theory Point ◽  
Curvature And Torsion

Curvature and torsion are the two tensors characterizing a general Riemannian space–time. In Einstein's general theory of gravitation, with torsion postulated to vanish and the affine connection identified to the Christoffel symbol, only the curvature tensor plays the central role. For such a purely metric geometry, two well-known topological invariants, namely the Euler class and the Pontryagin class, are useful in characterizing the topological properties of the space–time. From a gauge theory point of view, and especially in the presence of spin, torsion naturally comes into play, and the underlying space–time is no longer purely metric. We describe a torsional topological invariant, discovered in 1982, that has now found increasing usefulness in recent developments.

The axiomatic systems from the methodological point of view

Studia Logica ◽  
1960 ◽  
Vol 9 (1) ◽  
pp. 205-220 ◽  
Author(s):  
Kazimierz Ajdukiewicz
Keyword(s):  
Point Of View ◽  
Axiomatic Systems

scholarly journals COMPUTER PROOFS PRACTICE AND HUMAN UNDERSTANDING: EPISTEMOLOGICAL ISSUES

2021 ◽  
pp. 5-19
Author(s):  
Lev D. Lamberov ◽  
Keyword(s):  
Type Theory ◽  
Point Of View ◽  
Foundations Of Mathematics ◽  
Traditional Concept ◽  
New Approach ◽  
Informal Mathematics ◽  
Computer Proofs ◽  
Number Of Publications ◽  
Univalent Foundations ◽  
Epistemological Point

In recent decades, some epistemological issues have become especially acute in mathematics. These issues are associated with long proofs of various important mathematical results, as well as with a large and constantly increasing number of publications in mathematics. It is assumed that (at least partially) these difficulties can be resolved by referring to computer proofs. However, computer proofs also turn out to be problematic from an epistemological point of view. With regard to both proofs in ordinary (informal) mathematics and computer proofs, the problem of their surveyability appears to be fundamental. Based on the traditional concept of proof, it must be surveyable, otherwise it will not achieve its main goal — the formation of conviction in the correctness of the mathematical result being proved. About 15 years ago, a new approach to the foundations of mathematics began to develop, combining constructivist, structuralist features and a number of advantages of the classical approach to mathematics. This approach is built on the basis of homotopy type theory and is called the univalent foundations of mathematics. Due to itspowerful notion of equality, this approach can significantly reduce the length of formalized proofs, which outlines a way to resolve the epistemological difficulties that have arisen

Sign in / Sign up

Export Citation Format

Share Document