This Paper combines interval- valued neutrouphic sets and rough sets. It studies roughness in interval- valued neutrosophic sets and some of its properties. Finally we propose a Hamming distance between lower and upper approximations of interval valued neutrosophic sets.

In this paper, we investigate the expressiveness of the variety of propositional interval neighborhood logics , we establish their decidability on linearly ordered domains and some important subclasses, and we prove the undecidability of a number of extensions of PNL with additional modalities over interval relations. All together, we show that PNL form a quite expressive and nearly maximal decidable fragment of Halpern–Shoham’s interval logic HS.

This paper begins with a response to Josh Gert’s challenge that ‘on a par with’ is not a sui generis fourth value relation beyond ‘better than’, ‘worse than’, and ‘equally good’. It then explores two further questions: can parity be modeled by an interval representation of value? And what should one rationally do when faced with items on a par? I argue that an interval representation of value is incompatible with the possibility that items are on a par (a mathematical (...) proof is given in the appendix). I also suggest that there are three senses of ‘rationally permissible’ which, once distinguished, show that parity does distinctive practical work that cannot be done by the usual trichotomy of relations or by incomparability. In this way, we have an additional argument for parity from the workings of practical reason. (shrink)

Carter (Noûs 55(1):171–198, 2021) argued that while most simple positive numerical sentences are literally false, they can communicate true contents because relevance has a weakening effect on their literal contents. This paper presents a challenge for his account by considering entailments between the imprecise contents of numerical sentences and the imprecise contents of comparatives. I argue that while Carter's weakening mechanism can generate the imprecise contents of plain comparatives such as `A is taller than B', it cannot generate the imprecise (...) contents of comparatives that quantify the difference between their arguments, such as `A is exactly n times as tall as B'. I then propose an alternative theory on which intervals serve as both thick degrees on a scale and denotations of numerical expressions. I argue that the alternative theory can account for the imprecise contents of both forms of comparatives as well as the data that motivate Carter's theory. (shrink)

In this paper, we first defined soft intervalvalued neutrosophic rough sets(SIVN- rough sets for short) which combines interval valued neutrosophic soft set and rough sets and studied some of its basic properties. This concept is an extension of soft interval valued intuitionistic fuzzy rough sets( SIVIF- rough sets). Finally an illustartive example is given to verfy the developped algorithm and to demonstrate its practicality and effectiveness.

A logic of intervals is proposed akin to the one published by Hamblin (Hamblin (1969) and (1971)). Like Hamblin's, the present system is also based on a single primitive. However, the work presented here differs from Hamblin's in a number of respects. Most importantly, the present system is explicitly based on mereological ideas in such a way that not only are the two notions of abutment and temporal order involved in Hamblin's primitive two-place relation "abuts at the earlier end" (...) distinguished ; the temporal ordering itself is built up from a symmetric mereological primitive. The present system is shown to be complete. (shrink)

In this paper we introduce the concept of interval valued neutrosophic soft topological space together with interval valued neutrosophic soft finer and interval valued neutrosophic soft coarser topology. We also define interval valued neutrosophic interior and closer of an interval valued neutrosophic soft set. Some theorems and examples are cites. Interval valued neutrosophic soft subspace topology are studied. Some examples and theorems regarding this concept are presented.

Interval bipolar neutrosophic set is a significant extension of interval neutrosophic set where every element of the set comprises of three independent positive membership functions and three independent negative membership functions. In this study, we first define correlation coefficient, and weighted correlation coefficient measures of interval bipolar neutrosophic sets and prove their basic properties. Then, we develop a new multi-attribute decision making strategy based on the proposed weighted correlation coefficient measure. Finally, we solve an investment problem with interval bipolar neutrosophic (...) information and comparison is given to demonstrate the applicability and effectiveness of the proposed strategy. (shrink)

In this paper, we define a new cosine similarity between two interval valued neutrosophic sets based on Bhattacharya’s distance [19]. The notions of interval valued neutrosophic sets (IVNS, for short) will be used as vector representations in 3D-vector space. Based on the comparative analysis of the existing similarity measures for IVNS, we find that our proposed similarity measure is better and more robust. An illustrative example of the pattern recognition shows that the proposed method is simple and effective.

We survey main developments, results, and open problems on interval temporal logics and duration calculi. We present various formal systems studied in the literature and discuss their distinctive features, emphasizing on expressiveness, axiomatic systems, and (un)decidability results.

In this book authors for the first time introduce the notion of super interval matrices using special intervals. The advantage of using super interval matrices is that one can build only one vector space using m × n interval matrices, but in case of super interval matrices we can have several such spaces depending on the partition on the interval matrix.

In this article, we apply the notion of interval neutrosophic sets to ideal theory in BCK/BCI-algebras.

The interval neutrosophic uncertain linguistic variables can easily express the indeterminate and inconsistent information in real world, and TOPSIS is a very effective decision making method more and more extensive applications. In this paper, we will extend the TOPSIS method to deal with the interval neutrosophic uncertain linguistic information, and propose an extended TOPSIS method to solve the multiple attribute decision making problems in which the attribute value takes the form of the interval neutrosophic uncertain linguistic variables and attribute weight (...) is unknown. Firstly, the operational rules and properties for the interval neutrosophic variables are introduced. Then the distance between two interval neutrosophic uncertain linguistic variables is proposed and the attribute weight is calculated by the maximizing deviation method, and the closeness coefficients to the ideal solution for each alternatives. Finally, an illustrative example is given to illustrate the decision making steps and the effectiveness of the proposed method. (shrink)

This short commentary discusses the importance of space-time intervals in scientific study. Space-time intervals underlie special relativity, general relativity, and quantum field theory. In doing so, space-time intervals underlie human conscious experience, gravity, and a theory of everything. Space-time intervals also explain many puzzling scientific phenomena: quantum phenomena, dark matter, dark energy, the origin and evolution of the universe, and the life force. The importance of space-time intervals cannot be overestimated. Two articles published in Neuroquantology (...) explain how all this was established from empirical evidence and theory. (shrink)

Objective: Reference values have gained universal acceptance as the most powerful material that helps the decision-making-implementation process of the clinical laboratory. These values ​​may be affected by the geographical location, dietary habits, and other lifestyle changes of individuals applying to the clinical laboratory. Our study aims to determine the reference ranges for the biochemistry test panel, thyroid function tests, and insulin hormone levels, which are frequently needed by clinicians for the province of Gaziantep, with samples obtained from healthy individuals. -/- (...) Materials and Methods: In the study phase, the selection of reference individuals was carried out using the direct method a priori. For the study group, healthy individuals (224 men, 243 women) aged 18-45 were selected. Reference intervals (95% limit) were calculated according to the non-parametric method. -/- Results: When the reference intervals obtained in our study were compared with the reference intervals of the manufacturer, there were differences (> 10% lower or higher) in the upper and lower limits in urea (female and male), creatinine (male), HDL (female), AST (female and male), ALT (female), GGT (female), ALP (common), Lipase (common), CK (male), iron (male), TSH (female and male) markers. Male and female reference intervals for HDL, AST, ALT, and TSH differed significantly. Manufacturer reference ranges for these parameters were common to both sexes. -/- Conclusion: As a result, differences were determined between most of the reference intervals obtained in our study and the reference intervals we routinely use. We think the difference in the reference intervals is due to the differences in dietary habits and environmental factors. (shrink)

Space-time intervals are the fundamental components of conscious experience, gravity, and a Theory of Everything. Space-time intervals are relationships that arise naturally between events. They have a general covariance (independence of coordinate systems, scale invariance), a physical constancy, that encompasses all frames of reference. There are three basic types of space-time intervals (light-like, time-like, space-like) which interact to create space-time and its properties. Human conscious experience is a four-dimensional space-time continuum created through the processing of space-time (...) class='Hi'>intervals by the brain; space-time intervals are the source of conscious experience (observed physical reality). Human conscious experience is modeled by Einstein’s special theory of relativity, a theory designed specifically from the general covariance of space-time intervals (for inertial frames of reference). General relativity is our most accurate description of gravity. In general relativity, the general covariance of space-time intervals is extended to all frames of reference (inertial and non-inertial), including gravitational reference frames; space-time intervals are the source of gravity in general relativity. The general covariance of space-time intervals is further extended to quantum mechanics; space-time intervals are the source of quantum gravity. The general covariance of space-time intervals seamlessly merges general relativity with quantum field theory (the two grand theories of the universe). Space-time intervals consequently are the basis of a Theory of Everything (a single all-encompassing coherent theoretical framework of physics that fully explains and links together all physical aspects of the universe). This theoretical framework encompasses our observed physical reality (conscious experience) as well; space-time intervals link observed physical reality to actual physical reality. This provides an accurate and reliable match between observed physical reality and the physical universe by which we can carry on our activity. The Minkowski metric, which defines generally covariant space-time intervals, may be considered an axiom (premise, postulate) for the Theory of Everything. (shrink)

The nature and structure of time and time-intervals in physical, chemical and biological systems will be elucidated. The relation and dependence among time, energy and taking place of natural processes will be critically analyzed. The bio-processes taking place in nano-time intervals will be identified. Their relevance to nano-bio-science and nano-bio-technology will be developed and nano-time interval-aspect of nano-sciences and nano-technology will be advanced. -/- .

In this paper we focus our attention on tableau methods for propositional interval temporal logics. These logics provide a natural framework for representing and reasoning about temporal properties in several areas of computer science. However, while various tableau methods have been developed for linear and branching time point-based temporal logics, not much work has been done on tableau methods for interval-based ones. We develop a general tableau method for Venema's \cdt\ logic interpreted over partial orders (\nsbcdt\ for short). It combines (...) features of the classical tableau method for first-order logic with those of explicit tableau methods for modal logics with constraint label management, and it can be easily tailored to most propositional interval temporal logics proposed in the literature. We prove its soundness and completeness, and we show how it has been implemented. (shrink)

In this paper we show that Neutrosophic Statistics is an extension of Interval Statistics, since it deals with all kinds of indeterminacy (with respect to data, inferential procedures, probability distributions, graphical representations, etc.), allows for indeterminacy reduction, and uses neutrosophic probability which is more general than imprecise and classical probabilities, and has more detailed corresponding probability density functions. Whereas Interval Statistics only deals with indeterminacy that can be represented by intervals. And we respond to the arguments of Woodall et (...) al [1]. We show that not all indeterminacies (uncertainties) can be represented by intervals. Moreover, in some applications, we should use hesitant sets (which have less indeterminacy) instead of intervals. We redirect the authors to Plitogenic Probability and Plitogenic Statistics which are the most general forms of Multivariate Probability and Multivariate Statistics respectively (including, of course, Imprecise Probability and Interval Statistics as subclasses). (shrink)

We outline a simple development of special and general relativity based on the physical meaning of the spacetime interval. The Lorentz transformation is not used.

In this paper, we define projection and bidirectional projection measures between interval rough neutrosophic sets and prove their basic properties. Then two new multi attribute decision making strategies are proposed based on interval rough neutrosophic projection and bidirectional projection measures respectively. Then the proposed methods are applied for solving multi attribute decision making problems. Finally, a numerical example is solved to show the feasibility, applicability and effectiveness of the proposed strategies.

In this paper, the sine, cosine and cotangent similarity measures of interval rough neutrosophic sets is proposed. Some properties of the proposed measures are discussed. We have proposed multi attribute decision making approaches based on proposed similarity measures. To demonstrate the applicability, a numerical example is solved.

In this paper, we prove that Neutrosophic Statistics is more general than Interval Statistics, since it may deal with all types of indeterminacies (with respect to the data, inferential procedures, probability distributions, graphical representations, etc.), it allows the reduction of indeterminacy, and it uses the neutrosophic probability that is more general than imprecise and classical probabilities and has more detailed corresponding probability density functions. While Interval Statistics only deals with indeterminacy that can be represented by intervals. And we respond (...) to the arguments by Woodall et al. [1]. We show that not all indeterminacies (uncertainties) may be represented by intervals. Also, in some cases, we should better use hesitant sets (that have less indeterminacy) instead of intervals. We redirect the authors to the Plithogenic Probability and Plithogenic Statistics which are the most general forms of MultiVariate Probability and Multivariate Statistics respectively (including, of course, the Imprecise Probability and Interval Statistics as subclasses). (shrink)

The processing of time intervals in the sub- to supra-second range by the brain is critical for the interaction of primates with their surroundings in activities, such as foraging and hunting. For an accurate processing of time intervals by the brain, representation of physical time within neuronal circuits is necessary. I propose that time dimension of the physical surrounding is represented in the brain by different types of neuronal oscillators, generating spikes or spike bursts at regular intervals. (...) The proposed oscillators include the pacemaker neurons, tonic inputs, and synchronized excitation and inhibition of inter-connected neurons. Oscillators, which are built inside various circuits of brain, help to form modular clocks, processing time intervals or other temporal characteristics specific to functions of a circuit. Relative or absolute duration is represented within neuronal oscillators by “neural temporal unit,” defined as the interval between regularly occurring spikes or spike bursts. Oscillator output is processed to produce changes in activities of neurons, named frequency modulator neuron, wired within a separate module, represented by the rate of change in frequency, and frequency of activities, proposed to encode time intervals. Inbuilt oscillators are calibrated by (a) feedback processes, (b) input of time intervals resulting from rhythmic external sensory stimulation, and (c) synchronous effects of feedback processes and evoked sensory activity. A single active clock is proposed per circuit, which is calibrated by one or more mechanisms. Multiple calibration mechanisms, inbuilt oscillators, and the presence of modular connections prevent a complete loss of interval timing functions of the brain. (shrink)

Cross entropy measure is one of the best way to calculate the divergence of any variable from the priori one variable. We define a new cross entropy measure under interval neutrosophic set environment.

The goal of this paper is to see how mental and language representations are unique from a video-game perspective, using two main criteria. First, I will posit that the level of being both an interactive work of fiction and a self-involving interactive fiction belongs to a fuzzy interval and that some works – and, therefore, some video games – are more immersive than others. Second, I will observe how propositions tie the player’s representations of the real world and the game (...) world. Starting from psychological theories of pretense in children’s make-believe games, I will then expand Nichols and Stich’s cognitive theory of pretense to include an extra layer related to the game world, i.e., player-specific representations that govern player-specific propositions. The representations dealing with the work world are the socially shared ones, while the possible-world representations, dealing with most of the game world, are player-specific and tied to unique language use. (shrink)

Darwiche and Pearl’s seminal 1997 article outlined a number of baseline principles for a logic of iterated belief revision. These principles, the DP postulates, have been supplemented in a number of alternative ways. Most suggestions have resulted in a form of ‘reductionism’ that identifies belief states with orderings of worlds. However, this position has recently been criticised as being unacceptably strong. Other proposals, such as the popular principle (P), aka ‘Independence’, characteristic of ‘admissible’ operators, remain commendably more modest. In this (...) paper, we supplement the DP postulates and (P) with a number of novel conditions. While the DP postulates constrain the relation between a prior and a posterior conditional belief set, our new principles notably govern the relation between two posterior conditional belief sets obtained from a common prior by different revisions. We show that operators from the resulting family, which subsumes both lexicographic and restrained revision, can be represented as relating belief states associated with a ‘proper ordinal interval’ (POI) assignment, a structure more fine-grained than a simple ordering of worlds. We close the paper by noting that these operators satisfy iterated versions of many AGM era postulates, including Superexpansion, that are not sound for admissible operators in general. (shrink)

Sometimes different partitions of the same space each seem to divide that space into propositions that call for equal epistemic treatment. Famously, equal treatment in the form of equal point-valued credence leads to incoherence. Some have argued that equal treatment in the form of equal interval-valued credence solves the puzzle. This paper shows that, once we rule out intervals with extreme endpoints, this proposal also leads to incoherence.

The paper proposes a new technique for dealing with multi-attribute decision making problems through an extended TOPSIS method under neutrosophic cubic environment. Neutrosophic cubic set is the generalized form of cubic set and is the hybridization of a neutrosophic set with an interval neutrosophic set. In this study, we have defined some operation rules for neutrosophic cubic sets and proposed the Euclidean distance between neutrosophic cubic sets. In the decision making situation, the rating of alternatives with respect to some predefined (...) attributes are presented in terms of neutrosophic cubic information where weights of the attributes are completely unknown. In the selection process, neutrosophic cubic positive and negative ideal solutions have been defined. An extended TOPSIS method is then proposed for ranking the alternatives and finally choosing the best one. Lastly, an illustrative example is solved to demonstrate the decision making procedure and effectiveness of the developed approach. (shrink)

There is a trade-off between specificity and accuracy in existing models of belief. Descriptions of agents in the tripartite model, which recognizes only three doxastic attitudes—belief, disbelief, and suspension of judgment—are typically accurate, but not sufficiently specific. The orthodox Bayesian model, which requires real-valued credences, is perfectly specific, but often inaccurate: we often lack precise credences. I argue, first, that a popular attempt to fix the Bayesian model by using sets of functions is also inaccurate, since it requires us to (...) have interval-valued credences with perfectly precise endpoints. We can see this problem as analogous to the problem of higher order vagueness. Ultimately, I argue, the only way to avoid these problems is to endorse Insurmountable Unclassifiability. This principle has some surprising and radical consequences. For example, it entails that the trade-off between accuracy and specificity is in-principle unavoidable: sometimes it is simply impossible to characterize an agent’s doxastic state in a way that is both fully accurate and maximally specific. What we can do, however, is improve on both the tripartite and existing Bayesian models. I construct a new model of belief—the minimal model—that allows us to characterize agents with much greater specificity than the tripartite model, and yet which remains, unlike existing Bayesian models, perfectly accurate. (shrink)

In this paper we provide an analysis of dynamic dispositionalism. It is usually claimed that dispositions are dynamic properties. However, there is no exhaustive analysis of dynamism in the dispositional literature. We will argue that the dynamic character of dispositions can be analyzed in terms of three features: (i) temporal extension, (ii) necessary change and (iii) future orientedness. Roughly, we will defend the idea that dynamism entails a continuous view of time, to be analyzed in mathematical terms, where intervals (...) are its constitutive elements, whose duration lasts as much as a certain change takes to occur (in support of i). Such changes are the necessary components for the flowing of time because we think there cannot be time without change, (thus supporting ii) and that the forward-looking feature of properties is what determines the direction of time (as per iii). The paper is structured in 5 sections. In the first section, we set the problem: we outline and criticize some dispositional theories that defend an unsatisfying notion of dynamism. In the second, third and fourth sections we defend each desideratum for a disposition to be dynamic. Finally, we draw some conclusions and consider potential future research. (shrink)

Conscious experience is the direct observation of conscious events. Human conscious experience is four-dimensional. Conscious events are linked (associated) by spacetime intervals to produce a coherent conscious experience. This explains why conscious experience appears to us the way it does. Conscious experience is an orientation in space and time, an understanding of the position of the observer in space and time. Causality, past-future relations, learning, memory, cognitive processing, and goal-directed actions all evolve from four-dimensional conscious experience. A neural correlate (...) for four-dimensional conscious experience can be found in the human brain and is modelled by Einstein's special theory of relativity. The relativistic concept of spacetime interval is central for understanding conscious experience and cognition. (shrink)

The physical basis of conscious experience is revealed by direct observation and analysis of any conscious experience. Human conscious experience has an invariant structural mode of organization based on the three types of space-time intervals (light-like, time-like, space-like). Sensory input activates the autonomic nervous system, endocrine system, and ascending reticular activating system to produce the awake conscious state. The dorsal and ventral frontoparietal attention networks are activated. Dorsal and ventral cortical functional streams carry “what”, “where”, and “when” information to (...) the medial temporal lobe for the encoding, storage, and recall of conscious experience (episodic memory). Hippocampal place cells and time cells encode events in space and time within spatiotemporal contexts conveyed by entorhinal cortex grid cells and ramping cells. Theta phase precession unifies the encoding of space and time in the hippocampus so that segments of space and time are encoded in the hippocampus. Theta travelling waves ensure that the instantaneous output of the hippocampus consists of topographically-organized segments of space and time, space-time intervals. By parsing spatiotemporal contexts into quantal units of where and when events occur (spacetime intervals), hippocampal neurons bridge, and thereby organize events, in a conceptual organization of events (conscious experience). Space-time intervals are extracted from the hippocampus by a prefrontal cortex-basal ganglia-thalamic-prefrontal cortex loop for the cognitive, affective, and motivational aspects of conscious experience. (shrink)

In humans, knowing the world occurs through spatial-temporal experiences and interpretations. Conscious experience is the direct observation of conscious events. It makes up the content of consciousness. Conscious experience is organized in four dimensions. It is an orientation in space and time, an understanding of the position of the observer in space and time. A neural correlate for four-dimensional conscious experience has been found in the human brain which is modeled by Einstein’s Special Theory of Relativity. Spacetime intervals are (...) fundamentally involved in the organization of coherent conscious experiences. They account for why conscious experience appears to us the way it does. They also account for assessment of causality and past-future relationships, the integration of higher cognitive functions, and the implementation of goal-directed behaviors. Spacetime intervals in effect compose and direct our conscious life. The relativistic concept closes the explanatory gap and solves the hard problem of consciousness (how something subjective like conscious experience can arise in something physical like the brain). There is a place in physics for consciousness. We describe all physical phenomena through conscious experience, whether they be described at the quantum level or classical level. Since spacetime intervals direct the formation of all conscious experiences and all physical phenomena are described through conscious experience, the equation formulating spacetime intervals contains the information from which all observable phenomena may be deduced. It might therefore be considered expression of a theory of everything. (shrink)

Dilation occurs when an interval probability estimate of some event E is properly included in the interval probability estimate of E conditional on every event F of some partition, which means that one’s initial estimate of E becomes less precise no matter how an experiment turns out. Critics maintain that dilation is a pathological feature of imprecise probability models, while others have thought the problem is with Bayesian updating. However, two points are often overlooked: (1) knowing that E is stochastically (...) independent of F (for all F in a partition of the underlying state space) is sufficient to avoid dilation, but (2) stochastic independence is not the only independence concept at play within imprecise probability models. In this paper we give a simple characterization of dilation formulated in terms of deviation from stochastic independence, propose a measure of dilation, and distinguish between proper and improper dilation. Through this we revisit the most sensational examples of dilation, which play up independence between dilator and dilatee, and find the sensationalism undermined by either fallacious reasoning with imprecise probabilities or improperly constructed imprecise probability models. (shrink)

Building on my previous exploration of the role of dance in the contemporary French political philosopher Jacques Rancière’s Aisthesis: Scenes from the Aesthetic Regime of Art, first published in French in 2011, the present essay turns to another book originally published in the same year, The Intervals of Cinema. Having previously established that the core of Rancière’s philosophical method is an analysis of philosophical homonyms into figurative dancing conceptual partners, I begin by applying that method to the first chapter (...) of Intervals, “Cinematic Vertigo: Hitchcock to Vertov and Back.” There I identify two series of such dancing partners, as follows: Hitchcock’s image-controlling, capitalist vertiginous fall, and Vertov’s movement-equalizing, communist balanced dance. I then critique the implicit marginalizing of women and female bodies in the films and chapter, including Hitchcock’s protagonist’s best friend and ex-fiancé, and Vertov’s cosmetologists and switchboard operators. Finally, I offer a corrective from the proto-feminist life of my grandmother, a onetime cosmetologist, switchboard operator, and Glamour Shots amateur model, my grandmother, Louise Nunnelley, or “Mamaw.” Such are the unacknowledged material basis of Rancière’s radical democratic philosophy, the specifically-embodied and positioned female dancers who continue to get lost in his figurative dance. (shrink)

One of the disadvantages of the point estimate in survey sampling is that it fluctuates from sample to sample due to sampling error, as the estimator only provides a point value for the parameter under discussion. The neutrosophic approach, pioneered by Florentin Smarandache, is an excellent tool for estimating the parameters under consideration in sampling theory since it yields interval estimates in which the parameter lies with a very high probability. As a result, the neutrosophic technique, which is a generalization (...) of classical approach, is used to deal with ambiguous, indeterminate, and uncertain data. In this investigation, we suggest a new general family of ratio and exponential ratio type estimators for the elevated estimation of neutrosophic population mean of the primary variable utilizing known neutrosophic auxiliary parameters. For the first degree approximation, the bias and Mean Squared Error (MSE) of the suggested estimators are computed. The neutrosophic optimum values of the characterizing constants are determined, as well as the minimum value of the neutrosophic MSE of the suggested estimator is obtained for these optimum values of the characterizing scalars. Because the minimum MSE of the classical estimators of population mean lies inside the estimated interval of the neutrosophic estimators, the neutrosophic estimators are better than the equivalent classical estimators. The empirical investigation, which used both real and simulated data sets, backs up the theoretical findings. For practical utility in various areas of applications, the estimator with the lowest MSE or highest Percentage Relative Efficiency (PRE) is recommended. (shrink)

In this paper, we make a short history about: the neutrosophic set, neutrosophic numerical components and neutrosophic literal components, neutrosophic numbers, neutrosophic intervals, neutrosophic hypercomplex numbers of dimension n, and elementary neutrosophic algebraic structures. Afterwards, their generalizations to refined neutrosophic set, respectively refined neutrosophic numerical and literal components, then refined neutrosophic numbers and refined neutrosophic algebraic structures.

Semantic dispositionalism is roughly the view that meaning a certain thing by a word, or possessing a certain concept, consists in being disposed to do something, e.g., infer a certain way. Its main problem is that it seems to have so many and disparate exceptions. People can fail to infer as required due to lack of logical acumen, intoxication, confusion, deviant theories, neural malfunctioning, and so on. I present a theory stating possession conditions of concepts that are counterfactuals, rather than (...) disposition attributions, but which is otherwise similar to inferentialist versions of dispositionalism. I argue that it can handle all the exceptions discussed in the literature without recourse to ceteris paribus clauses. Psychological exceptions are handled by suitably undemanding requirements (unlike that of giving the sum of any two numbers) and by setting the following two preconditions upon someone’s making the inference: that she considers the inference and has no motivating reason against it. The non-psychological exceptions, i.e., cases of neural malfunctioning, are handled by requiring that the counterfactuals be true sufficiently often during the relevant interval. I argue that this accommodates some important intuitions about concept possession, in particular, the intuition that concept possession is vague along a certain dimension. (shrink)

Most philosophers believe that we have experiences as of temporally extended phenomena like change, motion, and succession. Almost all theories of time consciousness explain these temporal experiences by subscribing to the doctrine of the specious present, the idea that the contents of our experiences embrace temporally extended intervals of time and are presented as temporally structured. Against these theories, I argue that the doctrine is false and present a theory that does not require the notion of a specious present. (...) Furthermore, I argue that the different aspects of temporal experiences arise from different mechanisms operating separately. If the theory is true, then temporal experiences do not tell us anything special about the nature of consciousness and its temporal properties per se. (shrink)

Ontologies of living things are increasingly grounded on the concepts and practices of current life science. Biological development is a process, undergone by living things, which begins with a single cell and (in an important class of cases) ends with formation of a multicellular organism. The process of development is thus prima facie central for ideas about biological individuality and organismality. However, recent accounts of these concepts do not engage developmental biology. This paper aims to fill the gap, proposing the (...) lineage view of stem cells as an ontological framework for conceptualizing organismal development. This account is grounded on experimental practices of stem cell research, with emphasis on new techniques for generating biological organization in vitro. On the lineage view, a stem cell is the starting point of a cell lineage with a specific organismal source, time-interval of existence, and ‘tree topology’ of branch-points linking the stem to developmental termini. The concept of ‘enkapsis’ accommodates the cell-organism relation within the lineage view; this hierarchical notion is further explicated by considering the methods and results of stem cell experiments. Results of this examination include a (partial) characterization of stem cells’ developmental versatility, and the context-dependence of developmental processes involving stem cells. (shrink)

At the heart of the Bayesianism is a rule, Conditionalization, which tells us how to update our beliefs. Typical formulations of this rule are underspecified. This paper considers how, exactly, this rule should be formulated. It focuses on three issues: when a subject’s evidence is received, whether the rule prescribes sequential or interval updates, and whether the rule is narrow or wide scope. After examining these issues, it argues that there are two distinct and equally viable versions of Conditionalization to (...) choose from. And which version we choose has interesting ramifications, bearing on issues such as whether Conditionalization can handle continuous evidence, and whether Jeffrey Conditionalization is really a generalization of Conditionalization. (shrink)

This paper describes a cubic water tank equipped with a movable partition receiving various amounts of liquid used to represent joint probability distributions. This device is applied to the investigation of deductive inferences under uncertainty. The analogy is exploited to determine by qualitative reasoning the limits in probability of the conclusion of twenty basic deductive arguments (such as Modus Ponens, And-introduction, Contraposition, etc.) often used as benchmark problems by the various theoretical approaches to reasoning under uncertainty. The probability bounds imposed (...) by the premises on the conclusion are derived on the basis of a few trivial principles such as "a part of the tank cannot contain more liquid than its capacity allows", or "if a part is empty, the other part contains all the liquid". This stems from the equivalence between the physical constraints imposed by the capacity of the tank and its subdivisions on the volumes of liquid, and the axioms and rules of probability. The device materializes de Finetti's coherence approach to probability. It also suggests a physical counterpart of Dutch book arguments to assess individuals' rationality in probability judgments in the sense that individuals whose degrees of belief in a conclusion are out of the bounds of coherence intervals would commit themselves to executing physically impossible tasks. (shrink)

A number of Bayesians claim that, if one has no evidence relevant to a proposition P, then one's credence in P should be spread over the interval [0, 1]. Against this, I argue: first, that it is inconsistent with plausible claims about comparative levels of confidence; second, that it precludes inductive learning in certain cases. Two motivations for the view are considered and rejected. A discussion of alternatives leads to the conjecture that there is an in-principle limitation on formal representations (...) of belief: they cannot be both fully accurate and maximally specific. (shrink)

There is a widely held view on measurement inferences, that goes back to Stevens’s ([1946]) theory of measurement scales and ‘permissible statistics’. This view defends the following prohibition: you should not make inferences from averages taken with ordinal scales (versus quantitative scales: interval or ratio). This prohibition is general—it applies to all ordinal scales—and it is sometimes endorsed without qualification. Adhering to it dramatically limits the research that the social and biomedical sciences can conduct. I provide a Bayesian analysis of (...) this inferential problem, determining when measurements from ordinal scales can be used to confirm hypotheses about relative group averages. The prohibition, I conclude, cannot be upheld, even in a qualified sense. The beliefs needed to make average comparisons are less demanding than those appropriate for quantitative scales. I illustrate with the alleged paradigm ordinal scale, Mohs’ scale of mineral hardness, arguing that the literature has mischaracterized it. (shrink)

We have defined the Neutrosophic Over- /Under-/Off-Set and -Logic for the first time in 1995 and published in 2007. During 1995-2016 we presented them to various national and international conferences and seminars ([16]-[37]) and did more publishing during 2007-2016 ([1]-[15]). These new notions are totally different from other sets/logics/probabilities. We extended the neutrosophic set respectively to Neutrosophic Overset {when some neutrosophic component is > 1}, to Neutrosophic Underset {when some neutrosophic component is < 0}, and to Neutrosophic Offset {when some (...) neutrosophic components are off the interval [0, 1], i.e. some neutrosophic component > 1 and other neutrosophic component < 0}. This is no surprise since our real-world has numerous examples and applications of over-/under-/off-neutrosophic components. (shrink)

In temporal binding, the temporal interval between one event and another, occurring some time later, is subjectively compressed. We discuss two ways in which temporal binding has been conceptualized. In studies showing temporal binding between a voluntary action and its causal consequences, such binding is typically interpreted as providing a measure of an implicit or pre-reflective “sense of agency”. However, temporal binding has also been observed in contexts not involving voluntary action, but only the passive observation of a cause-effect sequence. (...) In those contexts, it has been interpreted as a top-down effect on perception reflecting a belief in causality. These two views need not be in conflict with one another, if one thinks of them as concerning two separate mechanisms through which temporal binding can occur. In this paper, we explore an alternative possibility: that there is a unitary way of explaining temporal binding both within and outside the context of voluntary action as a top-down effect on perception reflecting a belief in causality. Any such explanation needs to account for ways in which agency, and factors connected with agency, have been shown to affect the strength of temporal binding. We show that principles of causal inference and causal selection already familiar from the literature on causal learning have the potential to explain why the strength of people’s causal beliefs can be affected by the extent to which they are themselves actively involved in bringing about events, thus in turn affecting binding. (shrink)

According to comparativism, degrees of belief are reducible to a system of purely ordinal comparisons of relative confidence. (For example, being more confident that P than that Q, or being equally confident that P and that Q.) In this paper, I raise several general challenges for comparativism, relating to (i) its capacity to illuminate apparently meaningful claims regarding intervals and ratios of strengths of belief, (ii) its capacity to draw enough intuitively meaningful and theoretically relevant distinctions between doxastic states, (...) and (iii) its capacity to handle common instances of irrationality. (shrink)

In their seeking of simplicity, scientists fall into the error of Whitehead's "fallacy of misplaced concreteness." They mistake their abstract concepts describing reality for reality itself--the map for the territory. This leads to dogmatic overstatements, paradoxes, and mysteries such as the deep incompatibility of our two most fundamental physical theories--quantum mechanics and general relativity. To avoid such errors, we should evoke Whitehead's conception of the universe as a universe-in-process, where physical relations perpetually beget new physical relations. Today, the most promising (...) interpretations of quantum mechanics exemplify this Whiteheadian idea, formalizing physical systems, and the universe itself, as ongoing histories of actualizations of potential states, where actual states and potential states exist in mutually implicative relation as two separate categories of reality—an idea first proposed by Aristotle and rehabilitated by Heisenberg. In these interpretations, the classical conception of a history as a derivative story about fundamental physical objects is reversed: the classical physical object becomes the derivative story about fundamental histories of quantum states. The consistent histories interpretation of Robert Griffiths and the decoherent histories interpretation of Roland Omnès are cardinal examples of this approach to quantum mechanics. Another example, the relational realist interpretation, begins with the decoherent histories approach and formalizes it explicitly as a Whiteheadian interpretation, taking his “algebraic method” and applying it to quantum mechanics via algebraic topology. This branch of mathematics can be thought of as a “de-concretized” geometry in that it focuses only on the logical relations among objects and regions (and relations of these relations) rather than the fixed magnitudes of lines, planes, and other such rigid intervals. It has all the robust logical structure of geometry yet allows for an elasticity of relations that makes topological mathematical structures inherently immune misplaced concretization. (shrink)