5 research outputs found
Automated Reasoning and Presentation Support for Formalizing Mathematics in Mizar
This paper presents a combination of several automated reasoning and proof
presentation tools with the Mizar system for formalization of mathematics. The
combination forms an online service called MizAR, similar to the SystemOnTPTP
service for first-order automated reasoning. The main differences to
SystemOnTPTP are the use of the Mizar language that is oriented towards human
mathematicians (rather than the pure first-order logic used in SystemOnTPTP),
and setting the service in the context of the large Mizar Mathematical Library
of previous theorems,definitions, and proofs (rather than the isolated problems
that are solved in SystemOnTPTP). These differences poses new challenges and
new opportunities for automated reasoning and for proof presentation tools.
This paper describes the overall structure of MizAR, and presents the automated
reasoning systems and proof presentation tools that are combined to make MizAR
a useful mathematical service.Comment: To appear in 10th International Conference on. Artificial
Intelligence and Symbolic Computation AISC 201
A trajectory-based strict semantics for program slicing
We define a program semantics that is preserved by dependence-based slicing algorithms. It is a natural extension, to non-terminating programs, of the semantics introduced by Weiser (which only considered terminating ones) and, as such, is an accurate characterisation of the semantic relationship between a program and the slice produced by these algorithms.
Unlike other approaches, apart from Weiser’s original one, it is based on strict standard semantics which models the ‘normal’ execution of programs on a von Neumann machine and, thus, has the advantage of being intuitive. This is essential since one of the main applications of slicing is program comprehension. Although our semantics handles non-termination, it is defined wholly in terms of finite trajectories, without having to resort to complex, counter-intuitive, non-standard models of computation. As well as being simpler, unlike other approaches to this problem, our semantics is substitutive. Substitutivity is an important property becauseit greatly enhances the ability to reason about correctness of meaning-preserving program transformations such as slicing
A Real Semantic Web for Mathematics Deserves a Real Semantics
Contains fulltext :
72735.pdf (author's version ) (Open Access)SemWiki 2008, 2 juni 200
A real semantic web for mathematics deserves a real semantics
Mathematical documents, and their instrumentation by computers, have rich structure at the layers of presentation, metadata and semantics, as objects in a system for formal mathematical logic. Semantic Web tools [2] support the first two of these, with little, if any, contribution to the third, while Proof Assistants [17] instrument the third layer, typically with bespoke approaches to the first two. Our position is that a web of mathematical documents, definitions and proofs should be given a fully-edged semantics in terms of the third layer. We propose a "Math- Wiki" to harness Web 2.0 tools and techniques to the rich semantics furnished by contemporary Proof Assistants
Position paper: A real Semantic Web for mathematics deserves a real semantics
Abstract. Mathematical documents, and their instrumentation by computers, have rich structure at the layers of presentation, metadata and semantics, as objects in a system for formal mathematical logic. Semantic Web tools [2] support the first two of these, with little, if any, contribution to the third, while Proof Assistants [17] instrument the third layer, typically with bespoke approaches to the first two. Our position is that a web of mathematical documents, definitions and proofs should be given a fully-fledged semantics in terms of the third layer. We propose a “Math-Wiki ” to harness Web 2.0 tools and techniques to the rich semantics furnished by contemporary Proof Assistants. 1 Background and state of the art We can identify four worlds of mathematical discourse available on the Web: – Traditional mathematical practice: a systematic body of knowledge, organised around documents written by experts, most often in L ATEX, to varying degrees of sophistication. The intended audience is an expert readership, an