Tarski's influence on computer science

  title={Tarski's influence on computer science},
  author={S. Feferman},
  journal={20th Annual IEEE Symposium on Logic in Computer Science (LICS' 05)},
  • S. Feferman
  • Published 2005
  • Computer Science, Mathematics
  • 20th Annual IEEE Symposium on Logic in Computer Science (LICS' 05)
Summary form only given. The great logician Alfred Tarski played one of the leading roles in the development of mathematical logic in the twentieth century, as much for the programs he promoted and the conceptual organization of the subject as for his many important results. Except for his fixed-point theorem, Tarski's influence on computer science has been largely indirect but nevertheless substantial. The author surveys this influence through his work in the areas of decision procedures… Expand

Paper Mentions

Contribution of Warsaw Logicians to Computational Logic
The newly emerging branch of research of Computer Science received encouragement from the successors of the Warsaw mathematical school: Kuratowski, Mazur, Mostowski, Grzegorczyk, and Rasiowa, where ukasiewicz’s landmark idea of many-valued logic found its continuation in various approaches to incompleteness and uncertainty. Expand
A relation-algebraic approach to the "Hoare logic" of functional dependencies
  • J. Oliveira
  • Computer Science, Mathematics
  • J. Log. Algebraic Methods Program.
  • 2014
This paper shows how a relation-algebraic rendering of both database dependency theory and Hoare programming logic purports one such unification, in spite of the latter being an algorithmic theory and the former a data theory. Expand
Pointfree foundations for (generic) lossless decomposition
This report presents a typed, “pointfree” generalization of relational data dependency theory expressed not in the standard set-theoretic way, “a la Codd”, but in the calculus of binary relationsExpand
Functions as types or the "Hoare logic" of functional dependencies
This paper shows how the algebraic treatment of standard data dependency theory equips relational data with functional types and an associated type system which is useful for type checking database operations and for query optimization. Expand
Logic for physical space
From the initial axiomatic efforts of Euclid, this work revisits the major milestones in the logical representation of space and investigates current trends by considering classical logic from the perspective of Logic. Expand
Alloy Meets the Algebra of Programming: A Case Study
This paper puts Alloy and the Algebra of Programming together in a case study originating from the Verifiable File System mini-challenge put forward by Joshi and Holzmann: verifying the refinement of an abstract file store model into a journaled data model catering to wear leveling and recovery from power loss. Expand
Automated deduction for verification
Some of the basic deduction techniques used in software and hardware verification are introduced and the theoretical and engineering issues in building deductive verification tools are outlined. Expand
Minkowski Games
A natural representation of boundedness games yields coNP-completeness, whereas the safety games are undecidable; a general characterizations of which player can win such games are provided. Expand
Performance of a Quaternary Logic Design
The performance of the logic circuit as a quaternary difference calculator is described and functional operation of the circuit is shown and propagation delay and power consumption are determined. Expand
Design of High Performance Quaternary Adders
Two types of multiple-valued full adder circuits, implemented in Multiple-Valued voltage-Mode Logic (MV-VML), designed using one hot encoding and barrel shifter and implemented by converting the quaternary logic in to unique code. Expand


Applications of Alfred Tarski's Ideas in Database Theory
Many ideas of Alfred Tarski - one of the founders of modern logic - find application in database theory, and Topics discussed include the genericity of database queries; the relational algebra, the Tarskian definition of truth for the relational calculus, and cylindric algebras. Expand
The axiom of elementary sets on the edge of Peircean expressibility
The main achievement of this paper is the proof that the ‘kernel’ set theory whose postulates are extensionality, E, and single-element adjunction and removal, cannot be axiomatized by means of three-variable sentences. Expand
Alfred Tarski: Life and Logic
1. The two Tarskis 2. Independence and university Interlude I. The Banach-Tarski paradox, set theory and the axiom of choice 3. Polot! The Polish attribute Interlude II. The completeness andExpand
Little engines of proof
  • N. Shankar
  • Computer Science
  • Proceedings 17th Annual IEEE Symposium on Logic in Computer Science
  • 2002
This work argues for a modem reinterpretation and reappraisal of Hao Wang's hitherto neglected ideas on inferential analysis by describing some of the "little engines of proof" and a few of the ways in which they can be combined. Expand
Quantifier elimination for real closed fields by cylindrical algebraic decomposition
Tarski in 1948, ( Tarski 1951) published a quantifier elimination method for the elementary theory of real closed fields, which provides a decision method, which enables one to decide whether any sentence of the theory is true or false. Expand
Logic, Semantics, Metamathematics: Papers from 1923 to 1938
This edition of The Concept of Truth in Formalized Languages includes a new preface and a new analytical index for use by philosophers and linguists as well as by historians of mathematics and philosophy. Expand
Quantifier elimination for real closed fields by cylindrical algebraic decomposition--preliminary report
Tarski in 1948, published a quantifier elimination method for the elementary theory of real closed fields, which provides a decision method, which enables one to decide whether any sentence of the theory is true or false. Expand
Lower bounds are established on the computational complexity of the decision problem and on the inherent lengths of proofs for two classical decidable theories of logic: the first-order theory of theExpand
A 2^2^2^pn Upper Bound on the Complexity of Presburger Arithmetic
  • D. Oppen
  • Computer Science, Mathematics
  • J. Comput. Syst. Sci.
  • 1978
The decision problem for the theory of integers under addition, or “Presburger Arithmetic,” is proved to be elementary recursive in the sense of Kalmar and it is proved that a quantifier elimination decision procedure for this theory determines the truth of any sentence of length n within deterministic time. Expand
Three-variable statements of set-pairing
Abstract The approach to algebraic specifications of set theories proposed by Tarski and Givant inspires current research aimed at taking advantage of the purely equational nature of the resultingExpand