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Mechanised Proof Systems for Relation Algebras Jeremy E. Dawson
"... This project involves implementing Display Logic, and the Display Logic system for relation algebras, in Isabelle, and looking at the relationship between this and other proof systems for relation algebras. ..."
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This project involves implementing Display Logic, and the Display Logic system for relation algebras, in Isabelle, and looking at the relationship between this and other proof systems for relation algebras.
A Mechanised Proof System for Relation Algebra using Display Logic
 In Proc. JELIA98, LNAI
, 1997
"... . We describe an implementation of the Display Logic calculus for relation algebra as an Isabelle theory. Our implementation is the first mechanisation of any display calculus, but also provides a useful interactive proof assistant for relation algebra. The inference rules of Display Logic are coded ..."
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Cited by 16 (10 self)
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algebraic theorems proved using our system can be put in the form of structural rules of Display Logic, facilitating later reuse. We then show how the implementation can be used to prove results comparing alternative formalizations of relation algebra from a prooftheoretic perspective. Keywords: logical
Homological Algebra of Mirror Symmetry
 in Proceedings of the International Congress of Mathematicians
, 1994
"... Mirror Symmetry was discovered several years ago in string theory as a duality between families of 3dimensional CalabiYau manifolds (more precisely, complex algebraic manifolds possessing holomorphic volume elements without zeroes). The name comes from the symmetry among Hodge numbers. For dual Ca ..."
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Cited by 529 (3 self)
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Mirror Symmetry was discovered several years ago in string theory as a duality between families of 3dimensional CalabiYau manifolds (more precisely, complex algebraic manifolds possessing holomorphic volume elements without zeroes). The name comes from the symmetry among Hodge numbers. For dual
Using Linear Algebra for Intelligent Information Retrieval
 SIAM REVIEW
, 1995
"... Currently, most approaches to retrieving textual materials from scientific databases depend on a lexical match between words in users' requests and those in or assigned to documents in a database. Because of the tremendous diversity in the words people use to describe the same document, lexical ..."
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Cited by 672 (18 self)
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Currently, most approaches to retrieving textual materials from scientific databases depend on a lexical match between words in users' requests and those in or assigned to documents in a database. Because of the tremendous diversity in the words people use to describe the same document, lexical methods are necessarily incomplete and imprecise. Using the singular value decomposition (SVD), one can take advantage of the implicit higherorder structure in the association of terms with documents by determining the SVD of large sparse term by document matrices. Terms and documents represented by 200300 of the largest singular vectors are then matched against user queries. We call this retrieval method Latent Semantic Indexing (LSI) because the subspace represents important associative relationships between terms and documents that are not evident in individual documents. LSI is a completely automatic yet intelligent indexing method, widely applicable, and a promising way to improve users...
Hierarchical correctness proofs for distributed algorithms
, 1987
"... Abstract: We introduce the inputoutput automaton, a simple but powerful model of computation in asynchronous distributed networks. With this model we are able to construct modular, hierarchical correctness proofs for distributed algorithms. We de ne this model, and give aninteresting example of how ..."
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Cited by 439 (66 self)
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Abstract: We introduce the inputoutput automaton, a simple but powerful model of computation in asynchronous distributed networks. With this model we are able to construct modular, hierarchical correctness proofs for distributed algorithms. We de ne this model, and give aninteresting example
Learning probabilistic relational models
 In IJCAI
, 1999
"... A large portion of realworld data is stored in commercial relational database systems. In contrast, most statistical learning methods work only with "flat " data representations. Thus, to apply these methods, we are forced to convert our data into a flat form, thereby losing much ..."
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Cited by 619 (31 self)
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A large portion of realworld data is stored in commercial relational database systems. In contrast, most statistical learning methods work only with "flat " data representations. Thus, to apply these methods, we are forced to convert our data into a flat form, thereby losing much
PVS: A Prototype Verification System
 CADE
, 1992
"... PVS is a prototype system for writing specifications and constructing proofs. Its development has been shaped by our experiences studying or using several other systems and performing a number of rather substantial formal verifications (e.g., [5,6,8]). PVS is fully implemented and freely available. ..."
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Cited by 654 (16 self)
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. It has been used to construct proofs of nontrivial difficulty with relatively modest amounts of human effort. Here, we describe some of the motivation behind PVS and provide some details of the system. Automated reasoning systems typically fall in one of two classes: those that provide powerful
Automating the Design of Graphical Presentations of Relational Information
 ACM Transactions on Graphics
, 1986
"... The goal of the research described in this paper is to develop an applicationindependent presentation tool that automatically designs effective graphical presentations (such as bar charts, scatter plots, and connected graphs) of relational information. Two problems are raised by this goal: The codi ..."
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Cited by 550 (7 self)
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exploits the capabilities of the output medium and the human visual system. A wide variety of designs can be systematically generated by using a composition algebra that composes a small set of primitive graphical languages. Artificial intelligence techniques are used to implement a prototype presentation
Term Rewriting Systems
, 1992
"... Term Rewriting Systems play an important role in various areas, such as abstract data type specifications, implementations of functional programming languages and automated deduction. In this chapter we introduce several of the basic comcepts and facts for TRS's. Specifically, we discuss Abstra ..."
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Cited by 613 (18 self)
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Term Rewriting Systems play an important role in various areas, such as abstract data type specifications, implementations of functional programming languages and automated deduction. In this chapter we introduce several of the basic comcepts and facts for TRS's. Specifically, we discuss
The empirical case for two systems of reasoning
, 1996
"... Distinctions have been proposed between systems of reasoning for centuries. This article distills properties shared by many of these distinctions and characterizes the resulting systems in light of recent findings and theoretical developments. One system is associative because its computations ref ..."
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Cited by 631 (4 self)
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reflect similarity structure and relations of temporal contiguity. The other is “rule based” because it operates on symbolic structures that have logical content and variables and because its computations have the properties that are normally assigned to rules. The systems serve complementary functions
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