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Two algebraic structures, the contrapositionally complemented Heyting algebra (ccHa) and the contrapositionally |$\vee $| complemented Heyting algebra (c|$\vee $|cHa), are studied. The salient feature of these algebras is that there are two negations, one intuitionistic and another minimal in nature, along with a condition connecting the two operators. Properties of these algebras are discussed, examples are given and comparisons are made with relevant algebras. Intuitionistic Logic with Minimal Negation (ILM) corresponding to ccHas and its extension |${\textrm {ILM}}$|-|${\vee }$| for c|$\vee (...) $|cHas are then investigated. Besides its relations with intuitionistic and minimal logics, ILM is observed to be related to Peirce’s logic and Vakarelov’s logic MIN. With a focus on properties of the two negations, relational semantics for ILM and |${\textrm {ILM}}$|-|${\vee }$| are obtained with respect to four classes of frames, and inter-translations between the classes preserving truth and validity are provided. ILM and |${\textrm {ILM}}$|-|${\vee }$| are shown to have the finite model property with respect to these classes of frames and proved to be decidable. Extracting features of the two negations in the algebras, a further investigation is made, following logical studies of negations that define the operators independently of the binary operator of implication. Using Dunn’s logical framework for the purpose, two logics |$K_{im}$| and |$K_{im-{\vee }}$| are discussed, where the language does not include implication. The |$K_{im}$|-algebras are reducts of ccHas and are different from relevant algebraic structures having two negations. The negations in the |$K_{im}$|-algebras and |$K_{im-{\vee }}$|-algebras are shown to occupy distinct positions in an enhanced form of Dunn’s kite of negations. Relational semantics for |$K_{im}$| and |$K_{im-{\vee }}$| is provided by a class of frames that are based on Dunn’s compatibility frames. It is observed that this class coincides with one of the four classes giving the relational semantics for ILM and |${\textrm {ILM}}$|-|${\vee }$|⁠. (shrink)

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Young children's early understanding of emotion was investigated by examining their use of emotion terms such as happy, sad, mud, and cry. Five children's emotion language was examined longitudinally from the age of 2 to 5 years, and as a comparison their reference to pains via such terms as burn, sting, and hurt was also examined. In Phase 1 we confirmed and extended prior findings demonstrating that by 2 years of age terms for the basic emotions of happiness, sadness, anger, (...) and fear are commonly used by children as are terms for such related states as crying and hurting. At this early age children produce such terms to refer to self and to others, and to past and future as well as to present states. Over the years from 2 to 5 children's emotion vocabulary expands, their discussion of hypothetical emotions gets underway, and the complexity of their emotion utterances increases. In Phase 2 our analyses go beyond children's production of emotion terms to analyses of their conception of emotion. We focus especially on when children use emotion terms to refer to subjective experiential states of persons. From their earliest uses of these terms in our data children. (shrink)

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One hundred and fifty years ago, a hopeful young researcher reported a recent discovery he had made. Working in the bowels of a medieval castle in the German city of Tübingen, he had isolated a then entirely new type of molecule. This was the birth of a field that would fundamentally change the course of biology, medicine, and beyond. His discovery: DNA. His name: Friedrich Miescher. In this article, the authors try to find answers to the question why—despite the fact (...) that virtually everyone nowadays knows DNA—hardly anyone remembers the man who discovered it. In the history of science, the discovery of DNA was a seminal moment. Why then did it not enter into public memory? Ground‐breaking discoveries can occur in a historical context that is not ready to appreciate them. But that's not all that decides who is remembered and who is forgotten. Scientific pioneers sometimes fail to publicize their findings in a way that ensures that they receive the attention they merit. As discussed here, their personalities and habits may cause discoveries to be “overwritten” by more recent researchers, resulting in distorted cultural memories no longer reflecting the initial event. (shrink)

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A structural theorem for Kleene algebras is proved, showing that an element of a Kleene algebra can be looked upon as an ordered pair of sets, and that negation with the Kleene property is describable by the set-theoretic complement. The propositional logic \ of Kleene algebras is shown to be sound and complete with respect to a 3-valued and a rough set semantics. It is also established that Kleene negation can be considered as a modal operator, due to a perp (...) semantics of \. Moreover, another representation of Kleene algebras is obtained in the class of complex algebras of compatibility frames. One concludes with the observation that \ can be imparted semantics from different perspectives. (shrink)

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Rough Sets were introduced by Z. Pawlak in the year 1982 with the intention to address knowledge representation and data processing from the angle of computation and decision making. The main idea...

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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, ∼1-complemented and ∼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. (shrink)

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Possibilistic 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 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. (shrink)

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Nonlocal reaction–diffusion equations describe various biological and biomedical applications. Their mathematical properties are essentially different in comparison with the local equations, and this difference can lead to important biological implications. This review will present the state of the art in the investigation of nonlocal reaction–diffusion models in biomedical applications. We will consider various models arising in mathematical immunology, neuroscience, cancer modelling, and we will discuss their mathematical properties, nonlinear dynamics, resulting spatiotemporal patterns and biological significance.

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Bioethics, Volume 36, Issue 2, Page 111-112, February 2022.

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The notion of a context in formal concept analysis and that of an approximation space in rough set theory are unified in this study to define a Kripke context. For any context (G,M,I), a relation on the set G of objects and a relation on the set M of properties are included, giving a structure of the form ((G,R), (M,S), I). A Kripke context gives rise to complex algebras based on the collections of protoconcepts and semiconcepts of the underlying context. (...) On abstraction, double Boolean algebras (dBas) with operators and topological dBas are defined. Representation results for these algebras are established in terms of the complex algebras of an appropriate Kripke context. As a natural next step, logics corresponding to classes of these algebras are formulated. A sequent calculus is proposed for contextual dBas, modal extensions of which give logics for contextual dBas with operators and topological contextual dBas. The representation theorems for the algebras result in a protoconcept-based semantics for these logics. (shrink)

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The Mahabharata in Global Political and Social Thought studies the role of the epic Mahabharata in shaping modern social, political, and religious thought. It positions the Mahabharata as an influential political text and explores its role in the global history of ideas. In this edited volume, the gaze extends beyond India to also focus on Japan, China, Thailand, Iran, the Arab world, Germany, and Britain. It aims to showcase how the Mahabharata helped connect India to much wider, pan-Eurasian, intellectual and (...) political networks and demonstrates how the epic became central in globally entangled debates about religion in general and Indian religion in particular. (shrink)

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Darwin described biological species as groups of morphologically similar individuals. These groups of individuals can split into several subgroups due to natural selection, resulting in the emergence of new species. Some species can stay stable without the appearance of a new species, some others can disappear or evolve. Some of these evolutionary patterns were described in our previous works independently of each other. In this work we have developed a single model which allows us to reproduce the principal patterns in (...) Darwin’s diagram. Some more complex evolutionary patterns are also observed. The relation between Darwin’s definition of species, stated above, and Mayr’s definition of species is also discussed. (shrink)

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Contributed research papers chiefly on various aspects of Indic philosophy, Vedic literature, etc.

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It is simple enough to claim that academic research institutions ought to be trustworthy. Building the culture and taking the steps necessary to earn and preserve institutional trust are, however, complex processes. The experience motivating this special report—a request for the Center for Talented Youth at Johns Hopkins University to collaborate on research regarding the genetics of intelligence—illustrates how ensuring institutional trustworthiness can be in tension with a commitment to fostering research. In this essay, we explore the historical context for (...) biomedical research institutions like Johns Hopkins that have worked to build local community trust. In so doing, we consider how the example under focus in this special report can lead to greater consideration of how research institutions balance fostering trust with their other commitments. (shrink)

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The theory of rough sets starts with the notion of an approximation space , which is a pair ( U , R ), U being the domain of discourse, and R an equivalence relation on U . R is taken to represent the knowledge base of an agent, and the induced partition reflects a granularity of U that is the result of a lack of complete information about the objects in U . The focus then is on approximations of concepts (...) on the domain, in the context of the granularity. The present article studies the theory in the situation where information is obtained from different sources. The notion of approximation space is extended to define a multiple-source approximation system with distributed knowledge base , which is a tuple , where N is a set of sources and P ranges over all finite subsets of N . Each R P is an equivalence relation on U satisfying some additional conditions, representing the knowledge base of the group P of sources. Thus each finite group of sources and hence individual source perceives the same domain differently (depending on what information the group/individual source has about the domain), and the same concept may then have approximations that differ with the groups. In order to express the notions and properties related with rough set theory in this multiple-source situation, a quantified modal logic LMSAS D is proposed. In LMSAS D , quantification ranges over modalities, making it different from modal predicate logic and modal logic with propositional quantifiers. Some fragments of LMSAS D are discussed and it is shown that the modal system KTB is embedded in LMSAS D . The epistemic logic is also embedded in LMSAS D , and cannot replace the latter to serve our purpose. The relationship of LMSAS D with first and second-order logics is presented. Issues of expressibility, axiomatization and decidability are addressed. (shrink)

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India is the world’s largest democracy. It is also a peculiarly violent one, frustrating liberals who expect democracies to be well-behaved – a horse still unbridled to rule of law. Its riders have...

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Taking post-traumatic stress disorder (PTSD) as an example, we present a concept for transdisciplinary cooperation between life sciences and humanities. PTSD is defined as a long-term persisting anxiety disorder after severe psychological traumata. Initially recognized in war veterans, PTSD also appears in victims of crime and violence or survivors of natural catastrophes, e.g., earthquakes. We consider PTSD as a prototype topic to realize transdisciplinary projects, because this disease is multifacetted from different points of view. Based on physiological and molecular biological (...) research to understand the causes of this disease, conventional academic medicine (to Western medicine) and pharmacology can offer a panel of drugs for treatment, albeit only with limited success. Hence, other treatment options are indispensable. Chinese medicine is frequently regarded as alternative to complement Western medicine. In fact, Chinese medicine offers a large array of both pharmacological and non-pharmacological treatments for PTSD patients. Narrative therapy represents a non-pharmacological approach combating PTSD both in Western medicine as well as in Chinese medicine to improve quality of life of affected patients. Narratives on traumatic experiences form a new genre of life writing in Asian American literature, whose excitement is considerably fueled by the tension between fictitious and very personal narratives taken from reality. Systematic academic reflections on narratives from PTSD patients in the field of Asian American studies may support the improvement of narrative therapy in medical practice. Chinese medicine has a strong philosophical background and may, therefore, serve as junction between life sciences with their strong rational and reductionistic way to generate new knowledge and more holistic approaches in traditional medicines and humanities. In this regard, Chinese medicine may represent a missing link between life science and life writing. (shrink)

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