arXiv subjects

A. Mani

Publications and source records attributed to A. Mani.

26 records · Page 2Linked to original sources

arXiv2013

Dialectics of Knowledge Representation in a Granular Rough Set Theory

The concepts of rough and definite objects are relatively more determinate than those of granules and granulation in general rough set theory (RST) [1]. Representation of rough objects can however depend on the dialectical relation between granulation and definiteness. In this research, we make this exact in the context of RST over proto-transitive approximation spaces. This approach can be directly extended to many other types of RST. These are used for formulating an extended concept of knowledge interpretation (KI)(relative the situation for classical RST) and the problem of knowledge representation (KR) is solved. These will be of direct interest in granular KR in RST as developed by the present author [2] and of rough objects in general. In [3], these have already been used for five different semantics by the present author. This is an extended version of [4] with key examples and more results.

cs.AI↗

arXiv2013

Algebraic Semantics of Similarity-Based Bitten Rough Set Theory

We develop two algebraic semantics for bitten rough set theory (\cite{SW}) over similarity spaces and their abstract granular versions. Connections with choice based generalized rough semantics developed in \cite{AM69} by the present author and general cover based rough set theories are also considered.

math.LO↗

arXiv2012

Quantum discord and non-Markovianity of quantum dynamics

The problem of recognizing (non-)Markovianity of a quantum dynamics is revisited through analyzing quantum correlations. We argue that instantaneously-vanishing quantum discord provides a necessary and sufficient condition for Markovianity of a quantum map. This is used to introduce a measure of non-Markovianity. This measure, however, requires demanding knowledge about the system and the environment. By using a quantum correlation monogamy property and an ancillary system, we propose a simplified measure with less requirements. Non-Markovianity is thereby decided by quantum state tomography of the system and the ancilla.

quant-ph↗

arXiv2012

Current-induced membrane discharge

Possible mechanisms for over-limiting current (OLC) through aqueous ion-exchange membranes (exceeding diffusion limitation) have been debated for half a century. Flows consistent with electro-osmotic instability (EOI) have recently been observed in microfluidic experiments, but the existing theory neglects chemical effects and remains to be quantitatively tested. Here, we show that charge regulation and water self-ionization can lead to OLC by "current-induced membrane discharge" (CIMD), even in the absence of fluid flow. Salt depletion leads to a large electric field which expels water co-ions, causing the membrane to discharge and lose its selectivity. Since salt co-ions and water ions contribute to OLC, CIMD interferes with electrodialysis (salt counter-ion removal) but could be exploited for current-assisted ion exchange and pH control. CIMD also suppresses the extended space charge that leads to EOI, so it should be reconsidered in both models and experiments on OLC.

physics.chem-ph↗

arXiv2011

Dialectics of Counting and Measures of Rough Theories

New concepts of rough natural number systems, recently introduced by the present author, are used to improve most rough set-theoretical measures in general Rough Set theory (\textsf{RST}) and measures of mutual consistency of multiple models of knowledge. In this research paper, the explicit dependence on the axiomatic theory of granules of \cite{AM99} is reduced and more results on the measures and representation of the numbers are proved.

math.LO↗

arXiv2009

A Program in Dialectical Rough Set Theory

A dialectical rough set theory focussed on the relation between roughly equivalent objects and classical objects was introduced in \cite{AM699} by the present author. The focus of our investigation is on elucidating the minimal conditions on the nature of granularity, underlying semantic domain and nature of the general rough set theories (RST) involved for possible extension of the semantics to more general RST on a paradigm. On this basis we also formulate a program in dialectical rough set theory. The dialectical approach provides better semantics in many difficult cases and helps in formalising a wide variety of concepts and notions that remain untamed at meta levels in the usual approaches. This is a brief version of a more detailed forthcoming paper by the present author.

math.LO↗

arXiv2009

Meaning, Choice and Algebraic Semantics of Similarity Based Rough Set Theory

Both algebraic and computational approaches for dealing with similarity spaces are well known in generalized rough set theory. However, these studies may be said to have been confined to particular perspectives of distinguishability in the context. In this research, the essence of an algebraic semantics that can deal with all possible concepts of distinguishability over similarity spaces is progressed. Key to this is the addition of choice-related operations to the semantics that have connections with modal logics as well. Among these we focus on a semantics that is based on local clear distinguishability over similarity spaces.

math.LO↗

arXiv2006

Super Rough Semantics

In this research a new algebraic semantics of rough set theory including additional meta aspects is proposed. The semantics is based on enhancing the standard rough set theory with notions of 'relative ability of subsets of approximation spaces to approximate'. The eventual algebraic semantics is developed via many deep results in convexity in ordered structures. A new variation of rough set theory, namely 'ill-posed rough set theory' in which it may suffice to know some of the approximations of sets, is eventually introduced.

math.LO↗