Publication

The Definition of Transitive Closure with OCL - Limitations and applications

2003
Reports

Abstract

The Object Constraint Language (OCL) is based on rst- order logic and set theory. As the most well-known application, OCL is used to formulate well-formedness rules in the UML metamodel. Here, the transitive closure of a relationship is de ned in terms of an OCL invariant, which seems to contradict classical results on the expressive power of rst-order logic. In this paper, we give su cient justi cation for the correctness of the def- inition of transitive closure. Our investigation reinforces some decisions made in the semantics of UML and OCL. Currently, there is a lively debate on the same issues in the semantics of the upcoming UML 2.0.

Official source

https://infoscience.epfl.ch/entities/publication/68e83e25-f53c-4c14-818e-5d26309bd8db

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2003
Reports

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/68e83e25-f53c-4c14-818e-5d26309bd8db

About this result

Related concepts (30)

Set theory

Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory, as a branch of mathematics, is mostly concerned with those that are relevant to mathematics as a whole. The modern study of set theory was initiated by the German mathematicians Richard Dedekind and Georg Cantor in the 1870s. In particular, Georg Cantor is commonly considered the founder of set theory.

Naive set theory

Naive set theory is any of several theories of sets used in the discussion of the foundations of mathematics. Unlike axiomatic set theories, which are defined using formal logic, naive set theory is defined informally, in natural language. It describes the aspects of mathematical sets familiar in discrete mathematics (for example Venn diagrams and symbolic reasoning about their Boolean algebra), and suffices for the everyday use of set theory concepts in contemporary mathematics.

Zermelo–Fraenkel set theory

In set theory, Zermelo–Fraenkel set theory, named after mathematicians Ernst Zermelo and Abraham Fraenkel, is an axiomatic system that was proposed in the early twentieth century in order to formulate a theory of sets free of paradoxes such as Russell's paradox. Today, Zermelo–Fraenkel set theory, with the historically controversial axiom of choice (AC) included, is the standard form of axiomatic set theory and as such is the most common foundation of mathematics.

Related publications (3)

The Definition of Transitive Closure with OCL - Limitations and applications

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