Displaying similar documents to “Representation Theorem for Stacks”

Free Interpretation, Quotient Interpretation and Substitution of a Letter with a Term for First Order Languages

Marco Caminati (2011)

Formalized Mathematics

Similarity:

Fourth of a series of articles laying down the bases for classical first order model theory. This paper supplies a toolkit of constructions to work with languages and interpretations, and results relating them. The free interpretation of a language, having as a universe the set of terms of the language itself, is defined.The quotient of an interpreteation with respect to an equivalence relation is built, and shown to remain an interpretation when the relation respects it. Both the concepts...

Relational Formal Characterization of Rough Sets

Adam Grabowski (2013)

Formalized Mathematics

Similarity:

The notion of a rough set, developed by Pawlak [10], is an important tool to describe situation of incomplete or partially unknown information. In this article, which is essentially the continuation of [6], we try to give the characterization of approximation operators in terms of ordinary properties of underlying relations (some of them, as serial and mediate relations, were not available in the Mizar Mathematical Library). Here we drop the classical equivalence- and tolerance-based...

The Vector Space of Subsets of a Set Based on Symmetric Difference

Jesse Alama (2008)

Formalized Mathematics

Similarity:

For each set X, the power set of X forms a vector space over the field Z2 (the two-element field {0, 1} with addition and multiplication done modulo 2): vector addition is disjoint union, and scalar multiplication is defined by the two equations (1 · x:= x, 0 · x := ∅ for subsets x of X). See [10], Exercise 2.K, for more information.MML identifier: BSPACE, version: 7.8.05 4.89.993

Preliminaries to Classical First Order Model Theory

Marco Caminati (2011)

Formalized Mathematics

Similarity:

First of a series of articles laying down the bases for classical first order model theory. These articles introduce a framework for treating arbitrary languages with equality. This framework is kept as generic and modular as possible: both the language and the derivation rule are introduced as a type, rather than a fixed functor; definitions and results regarding syntax, semantics, interpretations and sequent derivation rules, respectively, are confined to separate articles, to mark...

Abstract Reduction Systems and Idea of Knuth-Bendix Completion Algorithm

Grzegorz Bancerek (2014)

Formalized Mathematics

Similarity:

Educational content for abstract reduction systems concerning reduction, convertibility, normal forms, divergence and convergence, Church- Rosser property, term rewriting systems, and the idea of the Knuth-Bendix Completion Algorithm. The theory is based on [1].

Pseudo-Canonical Formulae are Classical

Marco B. Caminati, Artur Korniłowicz (2014)

Formalized Mathematics

Similarity:

An original result about Hilbert Positive Propositional Calculus introduced in [11] is proven. That is, it is shown that the pseudo-canonical formulae of that calculus (and hence also the canonical ones, see [17]) are a subset of the classical tautologies.

Formalization of the Advanced Encryption Standard. Part I

Kenichi Arai, Hiroyuki Okazaki (2013)

Formalized Mathematics

Similarity:

In this article, we formalize the Advanced Encryption Standard (AES). AES, which is the most widely used symmetric cryptosystem in the world, is a block cipher that was selected by the National Institute of Standards and Technology (NIST) as an official Federal Information Processing Standard for the United States in 2001 [12]. AES is the successor to DES [13], which was formerly the most widely used symmetric cryptosystem in the world. We formalize the AES algorithm according to [12]....

Sequent Calculus, Derivability, Provability. Gödel's Completeness Theorem

Marco Caminati (2011)

Formalized Mathematics

Similarity:

Fifth of a series of articles laying down the bases for classical first order model theory. This paper presents multiple themes: first it introduces sequents, rules and sets of rules for a first order language L as L-dependent types. Then defines derivability and provability according to a set of rules, and gives several technical lemmas binding all those concepts. Following that, it introduces a fixed set D of derivation rules, and proceeds to convert them to Mizar functorial cluster...