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Mojżesz Presburger (* 27. Dezember 1904 in Warschau; † 1943) war ein polnischer Mathematiker, Logiker und Philosoph. Er war Student von Alfred Tarski und erfand 1929 die Presburger-Arithmetik, eine rein additive Arithmetik ohne Multiplikation, für die er einen Vollständigkeitssatz bewies.
Mojżesz Presburger, or Prezburger, (December 27, 1904 – c. 1943) was a Polish Jewish mathematician, logician, and philosopher. He was a student of Alfred Tarski, Jan Łukasiewicz, Kazimierz Ajdukiewicz, and Kazimierz Kuratowski.
Mojżesz Presburger (ur. 1904, Warszawa; zm. 1943 [?]) – polski logik, matematyk i filozof żydowskiego pochodzenia, związany ze szkołą lwowsko-warszawską. Udowodnił rozstrzygalność badania prawdziwości formuł arytmetyki Presburgera .
- Overview
- Properties
- Applications
- Presburger-Definable Integer Relation
- See Also
The language of Presburger arithmetic contains constants 0 and 1 and a binary function +, interpreted as addition. In this language, the axioms of Presburger arithmetic are the universal closuresof the following: 1. ¬(0 = x+ 1) 2. x + 1 = y + 1 → x = y 3. x + 0 = x 4. x + (y + 1) = (x + y) + 1 5. Let P(x) be a first-order formula in the language of...
Mojżesz Presburgerproved Presburger arithmetic to be: 1. consistent: There is no statement in Presburger arithmetic that can be deduced from the axioms such that its negation can also be deduced. 2. complete: For each statement in the language of Presburger arithmetic, either it is possible to deduce it from the axioms or it is possible to deduce i...
Because Presburger arithmetic is decidable, automatic theorem provers for Presburger arithmetic exist. For example, the Coq proof assistant system features the tactic omega for Presburger arithmetic and the Isabelle proof assistant contains a verified quantifier elimination procedure by Nipkow (2010). The double exponential complexity of the theory...
Some properties are now given about integer relationsdefinable in Presburger Arithmetic. For the sake of simplicity, all relations considered in this section are over non-negative integers. A relation is Presburger-definable if and only if it is a semilinear set. A unary integer relation R {\displaystyle R} , that is, a set of non-negative integers...
Die Presburger-Arithmetik ist eine in der Prädikatenlogik erster Stufe formulierte mathematische Theorie der natürlichen Zahlen mit Addition. Sie ist benannt nach Mojżesz Presburger, der sie im Jahre 1929 einführte. Die Signatur der Presburger-Arithmetik enthält nur Addition, nicht jedoch die Multiplikation. Zum Axiomensystem ...
26. Juli 2018 · In formal verification, Presburger arithmetic is the first-choice logic to represent and reason about systems with infinitely many states. This article provides a broad yet concise overview over the history, decision procedures, extensions and geometric properties of Presburger arithmetic.
1. Jan. 1991 · The life and work of Mojżesz Presburger (1904–1943?) are summarised in this article. Although his production in logic was small, it had considerable impact, both his own researches and his...
