Approximations from Anywhere and General Rough Sets

Not all approximations arise from information systems. The problem of fitting approximations, subjected to some rules (and related data), to information systems in a rough scheme of things is known as the \emph{inverse problem}. The inverse problem is more general than the duality (or abstract representation) problems and was introduced by the present author in her earlier papers. From the practical perspective, a few (as opposed to one) theoretical frameworks may be suitable for formulating the problem itself. \emph{Granular operator spaces} have been recently introduced and investigated by the present author in her recent work in the context of antichain based and dialectical semantics for general rough sets. The nature of the inverse problem is examined from number-theoretic and combinatorial perspectives in a higher order variant of granular operator spaces and some necessary conditions are proved. The results and the novel approach would be useful in a number of unsupervised and semi supervised learning contexts and algorithms.Comment: 20 Pages. Scheduled to appear in IJCRS'2017 LNCS Proceedings, Springe

"Possible Definitions of an ’A Priori’ Granule\ud in General Rough Set Theory" by A. Mani

We introduce an abstract framework for general rough set theory from a mereological perspective and consider possible concepts of ’a priori’ granules and granulation in the same. The framework is ideal for relaxing many of the\ud relatively superfluous set-theoretic axioms and for improving the semantics of many relation based, cover-based and dialectical rough set theories. This is a\ud relatively simplified presentation of a section in three different recent research papers by the present author.\u

Dealing with uncertain entities in ontology alignment using rough sets

This is the author's accepted manuscript. The final published article is available from the link below. Copyright @ 2012 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.Ontology alignment facilitates exchange of knowledge among heterogeneous data sources. Many approaches to ontology alignment use multiple similarity measures to map entities between ontologies. However, it remains a key challenge in dealing with uncertain entities for which the employed ontology alignment measures produce conflicting results on similarity of the mapped entities. This paper presents OARS, a rough-set based approach to ontology alignment which achieves a high degree of accuracy in situations where uncertainty arises because of the conflicting results generated by different similarity measures. OARS employs a combinational approach and considers both lexical and structural similarity measures. OARS is extensively evaluated with the benchmark ontologies of the ontology alignment evaluation initiative (OAEI) 2010, and performs best in the aspect of recall in comparison with a number of alignment systems while generating a comparable performance in precision

Simplifying Inductive Schemes in Temporal Logic

In propositional temporal logic, the combination of the connectives "tomorrow" and "always in the future" require the use of induction tools. In this paper, we present a classification of inductive schemes for propositional linear temporal logic that allows the detection of loops in decision procedures. In the design of automatic theorem provers, these schemes are responsible for the searching of efficient solutions for the detection and management of loops. We study which of these schemes have a good behavior in order to give a set of reduction rules that allow us to compute these schemes efficiently and, therefore, be able to eliminate these loops. These reduction laws can be applied previously and during the execution of any automatic theorem prover. All the reductions introduced in this paper can be considered a part of the process for obtaining a normal form of a given formula