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In A. Kumar, & M. Banerjee [(2012). Definable and rough sets in covering-based approximation spaces. In T. Li. (eds.), Rough sets and knowledge technology(pp. 488–495). Springer-Verlag], A. Kumar, & M. Banerjee [(2015). Algebras of definable and rough sets in quasi order-based approximation spaces. Fundamenta Informaticae, 141(1), 37–55], authors proposed a pair of lower and upper approximation operators based on granules generated by quasiorders. This work is an extension of algebraic results presented therein. A characterisation has been presented for those quasiorder-generated covering-based approximation spaces whose corresponding collections of definable and rough sets form Stone algebras. The notion of rough lattice was proposed in A. Kumar, & M. Banerjee [(2015). Algebras of definable and rough sets in quasi order-based approximation spaces. Fundamenta Informaticae, 141(1), 37–55], A. Kumar [(2020). A Study of Algebras and Logics of Rough Sets Based on Classical and Generalized Approximation Spaces. In Transactions on Rough Sets XXII, LNCS(Vol. 12485, pp. 123–251). Springer]. Some special rough lattices are introduced in this work, viz. rough Stone algebra, $ \sim _{1} $ ∼1-complemented and $ \sim _{2} $ ∼2-complemented rough lattices. Representations of these algebras in terms of rough sets are obtained. Moreover, logics for these algebras are shown to be sound and complete with respect to rough set semantics.

A non-distributive two-sorted hypersequent calculus PDBL and its modal extension MPDBL are proposed for the classes of pure double Boolean algebras and pure double Boolean algebras with operators respectively. A relational semantics for PDBL is next proposed, where any formula is interpreted as a semiconcept of a context. For MPDBL , the relational semantics is based on Kripke contexts, and a formula is interpreted as a semiconcept of the underlying context. The systems are shown to be sound and complete with respect to the relational semantics. Adding appropriate sequents to MPDBL results in logics with semantics based on reflexive, symmetric or transitive Kripke contexts. In particular, one gets the logics MPDBL4 and MPDBL5 with semantics respectively based on reflexive, transitive Kripke contexts and reflexive, symmetric and transitive Kripke contexts. MPDBL4 also happens to be the logic for topological pure double Boolean algebra. It is demonstrated that, using PDBL , the basic notions and relations of conceptual knowledge can be expressed and inferences involving negations can be obtained. Further, drawing a connection with rough set theory, lower and upper approximations of semiconcepts of a context are defined. It is then shown that, using the formulae and sequents involving modal operators in MPDBL5 , these approximation operators and their properties can be captured. [ABSTRACT FROM AUTHOR]

AbstractPossibilistic logic and modal logic are knowledge representation frameworks sharing some common features, such as the duality between possibility and necessity, and the decomposability of necessity for conjunctions, as well as some obvious differences since possibility theory is graded. At the semantic level, possibilistic logic relies on possibility distributions and modal logic on accessibility relations. In the last 30 years, there have been a series of attempts for bridging the two frameworks in one way or another. In this paper, we compare the relational semantics of epistemic logics (such as KD45 and S5) with simpler possibilistic semantics of a fragment of such logics that only uses modal formulas of depth 1. This minimal epistemic logic handles both all-or-nothing beliefs and explicitly ignored facts. We also contrast epistemic logic with the S5-based rough set logic. Finally, this paper presents extensions of generalized possibilistic logic with objective and non-nested multimodal formulas, in the style of modal logics KD45 and S5.

Abstract: The semantics of modal logics for reasoning about belief or knowledge is often described in terms of accessibility relations, which is too expressive to account for mere epistemic states of an agent. This paper proposes a simple logic whose atoms express epistemic attitudes about formulae expressed in another basic propositional language, and that allows for conjunctions, disjunctions and negations of belief or knowledge statements. It allows an agent to reason about what is known about the beliefs held by another agent. This simple epistemic logic borrows its syntax and axioms from the modal logic KD. It uses only a fragment of the S5 language, which makes it a two-tiered propositional logic rather than as an extension thereof. Its semantics is given in terms of epistemic states understood as subsets of mutually exclusive propositional interpretations. Our approach offers a logical grounding to uncertainty theories like possibility theory and belief functions. In fact, we define the most basic logic for possibility theory as shown by a completeness proof that does not rely on accessibility relations. [Copyright &y& Elsevier]

Updates in a knowledge base, given as an information system in rough set theory, may need to be made due to changes in (i) the set of attributes, (ii) attribute-values, or (iii) the set of objects (instances). In this article, we propose a logic for information systems which incorporates all these three aspects of updates. The logic can capture the flow of information as well as its effects on the approximations of concepts. A sound and complete deductive system for the logic is presented. The decidability issue is also discussed. [ABSTRACT FROM AUTHOR]

ABSTRACTBiofilm formation is associated with the ability of Candida albicans, the major human fungal pathogen, to resist antifungal therapies and grow on tissues, catheters, and medical devices. In order to better understand the relationship between C. albicansmorphology and biofilm formation, we examined biofilms generated in response to expression of UME6, a key filament-specific transcriptional regulator. As UME6levels rise, C. albicanscells are known to transition from yeast to hyphae, and we also observed a corresponding increase in the level of biofilm formation in vitro. In addition to forming a biofilm, we observed that a C. albicansstrain expressing constitutive high levels of UME6promoted tissue invasion in a reconstituted human three-dimensional model of oropharyngeal candidiasis. Confocal microscopy indicated that both the top and bottom layers of the biofilm generated upon high-level constitutive UME6expression consist primarily of hyphal cells. UME6-driven biofilm formation was reduced upon deletion of Hgc1, a cyclin-related protein important for hyphal development, as well as Sun41, a putative cell wall glycosidase. Constitutive high-level UME6expression was also able to completely bypass both the filamentation and biofilm defects of a strain deleted for Efg1, a key transcriptional regulator of these processes. Finally, we show that both Sun41 and Efg1 affect the ability of UME6to induce certain filament-specific transcripts. Overall, these findings indicate a strong correlation between increased C. albicanshyphal growth and enhanced biofilm formation and also suggest functional relationships between UME6and other regulators of biofilm development.

Abstract: We focus on families of Pawlak approximation spaces, called multiple-source approximation systems (MSASs). These reflect the situation where information arrives from multiple sources. The behaviour of rough sets in MSASs is investigated – different notions of lower and upper approximations, and definability of a set in a MSAS are introduced. In this context, a generalized version of an information system, viz. multiple-source knowledge representation (KR)-system, is discussed. Apart from the indiscernibility relation which can be defined on a multiple-source KR-system, two other relations, viz. similarity and inclusion are considered. To facilitate formal reasoning with rough sets in MSASs, a quantified propositional modal logic LMSAS is proposed. Interpretations for sets of well-formed formulae (wffs) of LMSAS are defined on MSASs, and the various properties of rough sets in MSASs translate into logically valid wffs of the system. LMSAS is shown to be sound and complete with respect to this semantics. Some decidable problems are addressed. In particular, it is shown that for any LMSAS-wff , it is possible to check whether is satisfiable in a certain class of interpretations with MSASs of a given finite cardinality. Moreover, it is also decidable whether any wff is satisfiable in the class of all interpretations with MSASs having domain of a given finite cardinality. [Copyright &y& Elsevier]

The specific ability of the major human fungal pathogen Candida albicans, as well as many other pathogenic fungi, to extend initial short filaments (germ tubes) into elongated hyphal filaments is important for a variety of virulence-related processes. However, the molecular mechanisms that control hyphal extension have remained poorly understood for many years. We report the identification of a novel C. albicans transcriptional regulator, UME6, which is induced in response to multiple host environmental cues and is specifically important for hyphal extension. Although capable of forming germ tubes, the ume6Δ/ume6Δ mutant exhibits a clear defect in hyphal extension both in vitro and during infection in vivo and is attenuated for virulence in a mouse model of systemic candidiasis. We also show that UME6 is an important downstream component of both the RFG1-TUP1 and NRG1-TUP1 filamentous growth regulatory pathways, and we provide evidence to suggest that Nrg1 and Ume6 function together by a negative feedback loop to control the level and duration of filament-specific gene expression in response to inducing conditions. Our results suggest that hyphal extension is controlled by a specific transcriptional regulatory mechanism and is correlated with the maintenance of high-level expression of genes in the C. albicans filamentous growth program.

The specific ability of the major human fungal pathogen Candida albicans, as well as many other pathogenic fungi, to extend initial short filaments (germ tubes) into elongated hyphal filaments is important for a variety of virulence-related processes. However, the molecular mechanisms that control hyphal extension have remained poorly understood for many years. We report the identification of a novel C. albicanstranscriptional regulator, UME6, which is induced in response to multiple host environmental cues and is specifically important for hyphal extension. Although capable of forming germ tubes, the ume6Δ/ume6Δ mutant exhibits a clear defect in hyphal extension both in vitro and during infection in vivo and is attenuated for virulence in a mouse model of systemic candidiasis. We also show that UME6is an important downstream component of both the RFG1-TUP1and NRG1-TUP1filamentous growth regulatory pathways, and we provide evidence to suggest that Nrg1 and Ume6 function together by a negative feedback loop to control the level and duration of filament-specific gene expression in response to inducing conditions. Our results suggest that hyphal extension is controlled by a specific transcriptional regulatory mechanism and is correlated with the maintenance of high-level expression of genes in the C. albicansfilamentous growth program.

Discusses the integration on the theories of fuzzy sets and rough sets that attempts to provide a measure of roughness of a fuzzy set. Definition of basic concepts on the rough set theories; Studies on the properties relative to a domain of discourse.

While studying rough equality within the framework of the modal system S5, an algebraic structure called rough algebra [1], came up. Its features were abstracted to yield a topological quasi-Boolean algebra (tqBa). In this paper, it is observed that rough algebra is more structured than a tqBa. Thus, enriching the tqBa with additional axioms, two more structures, viz. pre-rough algebra and rough algebra, are denned. Representation theorems of these algebras are also obtained. Further, the corresponding logical systems 12are proposed and eventually, 2is proved to be sound and complete with respect to a rough set semantics.

A propositional logic for rough sets was proposed in [2]. The present work establishes a relationship between the finitary fragment of this logic and 3-valued Lukasiewicz logic 3. It is also observed that there is an embedding from 3 into the modal system S5.

Curacin A is a thiazoline‐containing lipid from the marine cyanobacterium Lyngbya majuscula.Despite being a potent inhibitor of microtubule assembly and of colchicine binding to tubulin, curacin A bears little or no structural resemblance to colchicine or to any other tubulin ligand. We investigated the interaction of curacin A with bovine brain tubulin using three different approaches. We first examined its effect on the intra‐chain formation of a cross‐link in β‐tubulin by N,N′‐ ethylenebis(iodoacetamide). Formation of this cross‐link, between cys239and cys354, is blocked by colchicine and its A‐ring analogues as well as by various other inhibitors of colchicine binding; C‐ring analogues do not inhibit its formation. Curacin A strongly inhibited formation of this cross‐link. Second, we examined the effect of curacin A on the time‐dependent exposure of sulfhydryl groups on tubulin as measured by alkylation with iodo[14C]acetamide. Curacin A inhibited this very strongly, more so than either colchicine or podophyllotoxin. Last, we investigated the effect of curacin A on the time‐dependent exposure of hydrophobic areas on the tubulin molecule. We found that curacin A had only a small effect on this process, comparable in magnitude to that of podophyllotoxin. Curacin A thus appears to have an unusual interaction with tubulin. Its binding site on tubulin is likely to overlap with that of the A‐ring of colchicine. Drug Dev. Res. 40:223–229, 1997. © 1997 Wiley‐Liss, Inc.