Andrew M. Pitts. Interpolation and conceptual completeness for pretoposes via category theory. Mathematical logic and theoretical computer science, edited by Kueker David W., Lopez-Escobar Edgar G. K. and Smith Carl H., Lecture notes in pure and applied mathematics, vol. 106, Marcel Dekker, New York and Basel1987, pp. 301–327. - Andrew M. Pitts. Conceptual completeness for first-order intuitionistic logic: an application of categorical logic. Annals of pure and applied logic, vol. 41 (1989), pp. 33–81.

1995 ◽  
Vol 60 (2) ◽  
pp. 692-694
Author(s):  
Marek Zawadowski
Keyword(s):  
New York ◽  
Mathematical Logic ◽  
Intuitionistic Logic ◽  
Category Theory ◽  
Applied Mathematics ◽  
Theoretical Computer Science ◽  
Theoretical Computer ◽  
Applied Logic ◽  
First Order ◽  
Categorical Logic

Vaughan R. Pratt. Semantical considerations on Floyd–Hoare logic. 17th Annual Symposium on Foundations of Computer Science, Institute of Electrical and Electronics Engineers, New York1976, pp. 109–121. - Michael J. Fischer and Richard E. Ladner. Propositional dynamic logic of regular programs. Journal of computer and system sciences, vol. 18 (1979), pp. 194–211. - Krister Segerberg. A completeness theorem in the modal logic of programs. Universal algebra and applications. Papers presented at Stefan Banach International Mathematical Center at the semester “Universal algebra and applications” held February 15–June 9, 1978, edited by Tadeuz Traczyk, Banach Center Publications, vol. 9, PWN—Polish Scientific Publishers, Warsaw1982, pp. 31–46. - Rohit Parikh. The completeness of propositional dynamic logic. Mathematical foundations of computer science 1978, Proceedings, 7th symposium, Zakopane, Poland, September 4–8, 1978, edited by J. Winkowski, Lecture notes in computer science, vol. 64, Springer-Verlag, Berlin, Heidelberg, and New York, 1978, pp. 403–415. - Dexter Kozen and Rohit Parikh. An elementary proof of the completeness of PDL. Theoretical computer science, vol. 14(1981), pp. 113–118.

1986 ◽  
Vol 51 (1) ◽  
pp. 225-227 ◽  
Author(s):  
Robert Goldblatt
Keyword(s):  
New York ◽  
Computer Science ◽  
Universal Algebra ◽  
Dynamic Logic ◽  
Completeness Theorem ◽  
Theoretical Computer Science ◽  
Propositional Dynamic Logic ◽  
Theoretical Computer ◽  
Mathematical Foundations ◽  
Scientific Publishers

scholarly journals Outline of an Introduction to Mathematical Logic I

1958 ◽  
Vol 1 (1) ◽  
pp. 41-54
Author(s):  
Abraham Robinson
Keyword(s):  
New York ◽  
Mathematical Logic ◽  
English Translation ◽  
First Order ◽  
The Subject ◽  
Formed Part

This is the first of (presumably) three articles on the subject mentioned in the title. The exposition is based on a course of fifteen lectures which formed part of the Edmonton (1957) Seminar of the Canadian Mathematical Congress. Limitations of space (and, originally, of time) compel us to be selective in two directions. First, while we shall refer to other branches of logic in passing, we shall be concerned principally with the two fundamental calculi - of propositions and of predicates (of the first order). Thus, except for a number of modern developments which are included here, our exposition will be similar in scope, though not in detail, to the first and third chapters of the well-known "Principles of Mathematical Logic" by D. Hilbert and W. Ackermann (English translation, Chelsea, New York, 1950) and this was in fact the recommended text for the Edmonton course. However, there exists a growing number of other good introductions to the field and some of these will be listed later.

Modern statistical estimation via oracle inequalities

Acta Numerica ◽  
2006 ◽  
Vol 15 ◽  
pp. 257-325 ◽  
Author(s):  
Emmanuel J. Candès
Keyword(s):  
Statistical Estimation ◽  
Applied Mathematics ◽  
Theoretical Computer Science ◽  
Efficient Estimation ◽  
Oracle Inequalities ◽  
Theoretical Computer ◽  
Survey Paper ◽  
Applied Harmonic Analysis ◽  
Potential Applications ◽  
History Of

A number of fundamental results in modern statistical theory involve thresholding estimators. This survey paper aims at reconstructing the history of how thresholding rules came to be popular in statistics and describing, in a not overly technical way, the domain of their application. Two notions play a fundamental role in our narrative: sparsity and oracle inequalities. Sparsity is a property of the object to estimate, which seems to be characteristic of many modern problems, in statistics as well as applied mathematics and theoretical computer science, to name a few. ‘Oracle inequalities’ are a powerful decision-theoretic tool which has served to understand the optimality of thresholding rules, but which has many other potential applications, some of which we will discuss.Our story is also the story of the dialogue between statistics and applied harmonic analysis. Starting with the work of Wiener, we will see that certain representations emerge as being optimal for estimation. A leitmotif throughout our exposition is that efficient representations lead to efficient estimation.

Preface to Special Issue devoted to the memory of Sauro Tulipani

2008 ◽  
Vol 18 (1) ◽  
pp. 1-4 ◽  
Author(s):  
FLAVIO CORRADINI ◽  
CARLO TOFFALORI
Keyword(s):  
Mathematical Logic ◽  
Computer Science ◽  
Crucial Role ◽  
Recursion Theory ◽  
Theoretical Computer Science ◽  
Special Issue ◽  
Nineteen Thirties ◽  
Theoretical Computer ◽  
The Subject ◽  
The Church

2006 was a special year for both mathematical logic and computer science, as it celebrated Gödel's centenary. Although Gödel's work was mainly concerned with mathematics and metamathematics, the crucial role it had in the foundation of modern theoretical computer science is undeniable: for instance, one only has to remember Gödel's contributions to the birth of recursion theory as well as his part in the debate in the nineteen thirties on the subject of the Church Thesis.

scholarly journals Introduction: special issue ICICTA 2012

2014 ◽  
Vol 24 (5) ◽  
Author(s):  
ZHIXIANG HOU
Keyword(s):  
Computer Science ◽  
Software Design ◽  
Category Theory ◽  
Theoretical Computer Science ◽  
Special Issue ◽  
Theoretical Computer ◽  
Mathematical Structures ◽  
And Mathematics

Mathematical Structures in Computer Science bridges the gap between theoretical computer science and software design. By publishing original perspectives from all areas of computing, the journal stresses applications from logic, algebra, geometry, category theory and other areas of logic and mathematics. Through issues such as this special issue, the journal also plans to play an occasional, but important role in the fields of intelligent computation and automation.

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