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Verification of the Formal Concept Analysis.

José Antonio Alonso, Joaquín Borrego, María José Hidalgo, Francisco Jesús Martín Mateos, José Luis Ruiz Reina (2004)

RACSAM

This paper is concerned with a formal verification of the Formal Concept Analysis framework. We use the PVS system to represent and formally verify some algorithms of this theory. We also develop a method to transform specifications of algorithms based on finite sets into other executable ones, preserving its correctness. We illustrate this method by constructing an executable algorithm to compute an implicational base of the system of implications between attributes of a finite formal context.

Very small sets

Haim Judah, Amiran Lior, Ireneusz Recław (1997)

Colloquium Mathematicae

Very true operators on MTL-algebras

Jun Tao Wang, Xiao Long Xin, Arsham Borumand Saeid (2016)

Open Mathematics

The main goal of this paper is to investigate very true MTL-algebras and prove the completeness of the very true MTL-logic. In this paper, the concept of very true operators on MTL-algebras is introduced and some related properties are investigated. Also, conditions for an MTL-algebra to be an MV-algebra and a Gödel algebra are given via this operator. Moreover, very true filters on very true MTL-algebras are studied. In particular, subdirectly irreducible very true MTL-algebras are characterized...

Vitali sets and Hamel bases that are Marczewski measurable

Arnold Miller, Strashimir Popvassilev (2000)

Fundamenta Mathematicae

We give examples of a Vitali set and a Hamel basis which are Marczewski measurable and perfectly dense. The Vitali set example answers a question posed by Jack Brown. We also show there is a Marczewski null Hamel basis for the reals, although a Vitali set cannot be Marczewski null. The proof of the existence of a Marczewski null Hamel basis for the plane is easier than for the reals and we give it first. We show that there is no easy way to get a Marczewski null Hamel basis for the reals from one...

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