A simple logic for reasoning about incomplete knowledge

International audienceThe 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

A non-distributive logic for semiconcepts of a context and its modal extension with semantics based on Kripke contexts

A non-distributive two-sorted hypersequent calculus \textbf{PDBL} and its modal extension \textbf{MPDBL} are proposed for the classes of pure double Boolean algebras and pure double Boolean algebras with operators respectively. A relational semantics for \textbf{PDBL} is next proposed, where any formula is interpreted as a semiconcept of a context. For \textbf{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 \textbf{MPDBL} results in logics with semantics based on reflexive, symmetric or transitive Kripke contexts. One of these systems is a logic for topological pure double Boolean algebras. It is demonstrated that, using \textbf{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 \textbf{MPDBL}, these approximation operators and their properties can be captured

Formal reasoning with rough sets in multiple-source approximation systems

AbstractWe 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 α, it is possible to check whether α is satisfiable in a certain class of interpretations with MSASs of a given finite cardinality. Moreover, it is also decidable whether any wff α is satisfiable in the class of all interpretations with MSASs having domain of a given finite cardinality

Informatics and Computer Science Roughness of a Fuzzy Set

An integration between the theories of fuzzy sets and rough sets has been attempted by providing a measure of roughness of a fuzzy set. Several properties of this new measure are established. Some of the possible applications for handling uncertainties in the field of pattern recognition are mentioned. 1

Capturing the uncertainties of retail development: The case of emerging markets

This paper aims to better understand how retail development in emerging markets might occur by carrying out a detailed analysis of Indian retailing and then applying the results to a wider range of emerging markets. The goal is to identify potential patterns of future retail development in emerging economies. The scenarios approach was considered an appropriate methodology for investigating developing economies as it accepts structural uncertainty with multiple interpretations and multiple futures. In fact for retailing, there are countless ‘right’ answers, endless combinations of business models and infinite permutations of key themes and approaches. Conceptualising the evolution of different retail formats taking the scenarios approach is therefore a prudent choice of methodology, especially in wanting to avoid the dangers of over formalising the format development process within the retail context in emerging markets. Four possible visions for retail development in India, each with their own benefits and costs: a Kirana Kingdom, Sanskriti Planets, Sasta World or Mishrit Universe were developed from the primary research conducted and then tested in the context of other emerging markets. A combination of regulatory intervention and the changing cultural disposition of consumers on account of changing socio-economic conditions play a significant role in the development of retailing in emerging markets. The significant role of the politics of retailing in emerging markets has also been highlighted in this paper. Retail development in emerging markets can therefore be aligned more closely to combination theory where the consumer-regulation configuration plays a significant role in how retail evolves and develops in these markets

Comparison of tremor induced by valproate and lithium in bipolar disorder using a hand steadiness tester

Background: Quantitative measurement of valproate and lithium induced tremor using hand steadiness tester and their comparison in bipolar disorder.Methods: 200 newly diagnosed patients of bipolar disorder were randomly allocated into two equal groups receiving lithium (300mg twice daily) and sodium valproate (500 mg twice daily) after they fulfilled the inclusion / exclusion criteria of the study. 87 patients from Lithium group and 93 from Valproate completed the study.  Hand Tremor was assessed quantitatively at 0, 6, 12, 18 and 24 weeks using hand steadiness tester. Anxiety level of the study subjects was assessed to be insignificant using a standardized anxiety scale.  Final data was assessed after 24 weeks by using Stat Calc and Z test. P value <0.05 was considered to be significant.Results: No significant difference was found in terms of the development and transition of tremor induced by valproate and lithium (p=0.22).  However more men developed tremor with lithium when compared with females (p<0.05) and the mean age of patients who developed tremor appeared to be significantly higher in lithium group (54.7±3.9) than valproate (39.6±5.1).Conclusions: Tremor of hands is a common side effect of lithium and valproate treatment. Timely, objective assessment of onset and extent of tremor has always remained a challenge to the clinicians. Hand Steadiness tester is a simple, portable, inexpensive, non-invasive instrument that can be used to ascertain the development and transition of tremor in a quantitative manner. This would guide the clinicians as when to intervene for better management of such tremors

Protection against acute adriamycin-induced cardiotoxicity by garlic: Role of endogenous antioxidants and inhibition of TNF-α expression

BACKGROUND: Oxidative stress is the major etiopathological factor in adriamycin-induced cardiotoxicity. Relatively low amounts of endogenous antioxidant makes the heart vulnerable to oxidative stress-induced damage. Chronic oral administration of garlic has been reported to enhance the endogenous antioxidants of heart. We hypothesized that garlic-induced enhanced cardiac antioxidants may offer protection against acute adriamycin-induced cardiotoxicity. RESULTS: Rats were either administered freshly prepared garlic homogenate (250 and 500 mg/kg daily, orally, for 30 days) or probucol (cumulative dose, 120 mg/kg body weight divided in 12, i.p. over a period of 30 days) or double distilled water (vehicle), followed by a single dose of adriamycin (30 mg/kg i.p.). In the adriamycin group, increased oxidative stress was evidenced by a significant increase in myocardial TBARS (thiobarbituric acid reactive substances) and decrease in myocardial SOD (superoxide dismutase), catalase and GPx (glutathione peroxidase) activity. Histopathological studies showed focal as well as subendocardial myocytolysis with infiltration of macrophages, lymphocytes and edema. Immunocytochemistry showed marked expression of TNF-α (tumor necrosis factor-alpha) in the myocardium. Increase in myocardial TBARS and decrease in endogenous antioxidants by adriamycin was prevented significantly in the garlic treated rat hearts, which was comparable to the probucol-treated group. Histopathological evidence of protection was also evident in both garlic-treated and probucol-treated groups. Probucol, 250 mg/kg and 500 mg/kg of garlic reduced adriamycin induced TNF-α expression in the myocardium and was associated with reduced myocyte injury. CONCLUSIONS: It is concluded that chronic garlic administration prevents acute adriamycin-induced cardiotoxicity and decreases myocardial TNF-α expression

INSULIN RESISTANCE IN END STAGE RENAL DISEASE (ESRD) PATIENTS IN EASTERN INDIA: A POPULATION BASED OBSERVATIONAL STUDY

Background &amp; Objective: Despite considerable advances made in the field of medicine in general, and nephrology in particular, Chronic Kidney Disease (CKD) and End Stage Renal Disease (ESRD) remain public health challenges of enormous proportion. Aim: Considering that the association between Insulin resistance and CKD and ESRD has been established in studies conducted abroad, we propose to verify the association in Indian setting i.e. among ESRD patients in eastern India. Materials and Methods: 95 patients were included in control group and 97 patients were included in ESRD group. Only consenting individuals chosen through the filters of appropriate inclusion and exclusion criteria were made part of the study. Results: The statistical software Minitab 16 was used to analyze the data. Serum fasting Insulin level, HOMA-IR, serum hsCRP, serum urea, serum creatinine levels were significantly higher in ESRD patients compared to age and sex matched control individuals. Conclusion: Our study confirms the association between ESRD and IR found in other studies. Although the association between ESRD and IR has been established, the causality relation between them is not very clear. Further exploration of the issue is warranted. Keywords: End Stage Renal Disease, Chronic Kidney Disease, Insulin Resistanc