In this paper we review some properties of fuzzy observables, mainly as realized by commutative positive operator valued measures. In this context we discuss two representation theorems for commutative positive operator valued measures in terms of projection valued measures and describe, in some detail, the general notion of fuzzification. We also make some related observations on joint measurements.

A pair of spin-j particles, prepared in a singlet state, move away from each other and are examined by two distant observers. If the latter are able to discriminate between the2j+1 values of a component ofJ, there are pairs of observables whose correlation strongly violates Bell's inequality, for arbitrarily large j. However, if neighboring values are lumped together because of limited instrumental resolution, the observable correlations tend to those predicted by classical mechanics.

The notion of fuzzy event is introduced in the theory of measurement in quantum mechanics by indicating in which sense measurements can be considered to yield fuzzy sets. The concept of probability measure on fuzzy events is defined, and its general properties are deduced from the operational meaning assigned to it. It is pointed out that such probabilities can be derived from the formalism of quantum mechanics. Any such probability on a given fuzzy set is related (...) to the frequency of occurrence within that set of points in a random sample, where the sample points are themselves fuzzy sets obtained as outcomes of measurements of, in general, incompatible observables on replicas of the system in the same prepared state. (shrink)

This paper presents a problem of observer-based adaptive fuzzy predefined performance control of a class of nonlinear pure-feedback systems with input delay and unknown control direction. Compared with the existing research, a novel predefined performance controller is proposed, which relaxes the assumption that the initial error is known. In addition, it is difficult to design the controllers due to input delay and nonaffine properties of the pure-feedback systems, which can be simplified by Pade approximation. Moreover, dynamic surface control and (...) Nussbaum functions are applied to overcome the calculation explosion caused by repeated differentiations and unknown control direction, respectively. Based on the above methods, an adaptive fuzzy predefined performance controller is proposed, and it is proved that all the signals of a closed-loop system are semiglobally uniformly ultimately bounded. The tracking errors converge within a predefined range, while the observer estimation errors converge within a small zero region. Finally, the simulation results demonstrate the effectiveness of the proposed control system. (shrink)

Robot manipulators have been extensively used in complex environments to complete diverse tasks. The teleoperation control based on human-like adaptivity in the robot manipulator is a growing and challenging field. This paper developed a disturbance-observer-based fuzzy control framework for a robot manipulator using an electromyography- driven neuromusculoskeletal model. The motion intention was estimated by the EMG-driven NMS model with EMG signals and joint angles from the user. The desired torque was transmitted into the desired velocity for the robot manipulator (...) system through an admittance filter. In the robot manipulator system, a fuzzy logic system, utilizing an integral Lyapunov function, was applied for robot manipulator systems subject to model uncertainties and external disturbances. To compensate for the external disturbances, fuzzy approximation errors, and nonlinear dynamics, a disturbance observer was integrated into the controller. The developed control algorithm was validated with a 2-DOFs robot manipulator in simulation. The results indicate the proposed control framework is effective and crucial for the applications in robot manipulator control. (shrink)

Entropy-based algorithms have been suggested as robust estimators of electroencephalography (EEG) predictability or regularity. This study aimed to examine possible disturbances in EEG complexity as a means to elucidate the pathophysiological mechanisms in chronic stroke, before and after a brain computer interface (BCI)-motor observation intervention. Eleven chronic stroke subjects and nine unimpaired subjects were recruited to examine the differences in their EEG complexity. The BCI-motor observation intervention was designed to promote functional recovery of the hand in stroke subjects. Fuzzy (...) approximate entropy (fApEn), a novel entropy-based algorithm designed to evaluate complexity in physiological systems, was applied to assess the EEG signals acquired from unimpaired subjects and stroke subjects, both before and after training. The results showed that stroke subjects had significantly lower EEG fApEn than unimpaired subjects (p < 0.05) in the motor cortex area of the brain (C3, C4, FC3, FC4, CP3, CP4) in both hemispheres before training. After training, motor function of the paretic upper limb, assessed by the Fugl-Meyer Assessment-Upper Limb (FMA-UL), Action Research Arm Test (ARAT), and Wolf Motor Function Test (WMFT) improved significantly (p < 0.05). Furthermore, the EEG fApEn in stroke subjects increased considerably in the central area of the contralesional hemisphere after training (p < 0.05). A significant correlation was noted between clinical scales (FMA-UL, ARAT, and WMFT) and EEG fApEn in C3/C4 in the contralesional hemisphere (p < 0.05). This finding suggests that the increase in EEG fApEn could be an estimator of the variance in upper limb motor function improvement. In summary, fApEn can be used to identify abnormal EEG complexity in chronic stroke, when used with BCI-motor observation training. Moreover, these findings based on the fApEn of EEG signals also expand the existing interpretation of training-induced functional improvement in stroke subjects. Entropy-based analysis might serve as a novel approach to understanding the abnormal cortical dynamics of stroke and the neurological changes induced by rehabilitation training. (shrink)

Framing effects occur when people respond differently to the same information, just because it is conveyed in different words. For example, in the classic ‘Disease Problem’ introduced by Amos Tversky and Daniel Kahneman, people’s choices between alternative interventions depend on whether these are described positively, in terms of the number of people who will be saved, or negatively in terms of the corresponding number who will die. In this paper, I discuss an account of framing effects based on ‘fuzzy-trace (...) theory’. The central claim of this account is that people represent the numbers in framing problems in a ‘gist-like’ way, as ‘some’; and that this creates a categorical contrast between ‘some’ people being saved (or dying) and ‘no’ people being saved (or dying). I argue that fuzzy-trace theory’s gist-like representation, ‘some’, must have the semantics of ‘some and possibly all’, not ‘some but not all’. I show how this commits fuzzy-trace theory to a modest version of a rival ‘lower bounding hypothesis’, according to which lower-bounded interpretations of quantities contribute to framing effects by rendering the alternative descriptions extensionally inequivalent. As a result, fuzzy-trace theory is incoherent as it stands. Making sense of it requires dropping, or refining, the claim that decision-makers perceive alternatively framed options as extensionally equivalent; and the related claim that framing effects are irrational. I end by suggesting that, whereas the modest lower bounding hypothesis is well supported, there is currently less evidence for the core element of the fuzzy trace account. (shrink)

I discuss the attitude of Jewish law sources from the 2nd–:5th centuries to the imprecision of measurement. I review a problem that the Talmud refers to, somewhat obscurely, as impossible reduction. This problem arises when a legal rule specifies an object by referring to a maximized measurement function, e.g., when a rule applies to the largest part of a divided whole, or to the first incidence that occurs, etc. A problem that is often mentioned is whether there might be hypothetical (...) situations involving more than one maximal value of the relevant measurement and, given such situations, what is the pertinent legal rule. Presumption of simultaneous occurrences or equally measured values are also a source of embarrassment to modern legal systems, in situations exemplified in the paper, where law determines a preference based on measured values. I contend that the Talmudic sources discussing the problem of impossible reduction were guided by primitive insights compatible with fuzzy logic presentation of the inevitable uncertainty involved in measurement. I maintain that fuzzy models of data are compatible with a positivistic epistemology, which refuses to assume any precision in the extra-conscious world that may not be captured by observation and measurement. I therefore propose this view as the preferred interpretation of the Talmudic notion of impossible reduction. Attributing a fuzzy world view to the Talmudic authorities is meant not only to increase our understanding of the Talmud but, in so doing, also to demonstrate that fuzzy notions are entrenched in our practical reasoning. If Talmudic sages did indeed conceive the results of measurements in terms of fuzzy numbers, then equality between the results of measurements had to be more complicated than crisp equations. The problem of impossible reduction could lie in fuzzy sets with an empty core or whose membership functions were only partly congruent. Reduction is impossible may thus be reconstructed as there is no core to the intersection of two measures. I describe Dirichlet maps for fuzzy measurements of distance as a rough partition of the universe, where for any region A there may be a non-empty set of - _A, where the problem of impossible reduction applies. This model may easily be combined with probabilistic extention. The possibility of adopting practical decision standards based on -cuts is discussed in this context. I propose to characterize the uncertainty that was presumably capped by the old sages as U- uncertainty, defined, for a non-empty fuzzy set A on the set of real numbers, whose -cuts are intervals of real numbers, as U = 1/h 0 h log [1+]d, where h is the largest membership value obtained by any element of A and is the measure of the -cut of A defined by the Lebesge integral of its characteristic function. (shrink)

The logic of a physical system consists of the elementary observables of the system. We show that for chaotic systems the logic is not any more the classical Boolean lattice but a kind of fuzzy logic which we characterize for a class of chaotic maps. Among other interesting properties the fuzzy logic of chaos does not allow for infinite combinations of propositions. This fact reflects the instability of dynamics and it is shared also by quantum systems with diagonal (...) singularity. We also generalize the fuzzy implication to a probabilistic implication following the hint of von Neumann. In this way we can evaluate the probability of the validity of the logical inference. (shrink)

We show that it is possible to base fuzzy control on fuzzy logic programming. Indeed, we observe that the class of fuzzy Herbrand interpretations gives a semantics for fuzzy programs and we show that the fuzzy function associated with a fuzzy system of IF-THEN rules is the fuzzy Herbrand interpretation associated with a suitable fuzzy program.

A Correction to this paper has been published: https://doi.org/10.1007/s13164-021-00565-2.

The article begins with a discussion of sets and fuzzy sets. It is observed that identifying a set with its indicator function makes it clear that a fuzzy set is a direct and natural generalization of a set. Making this identification also provides simplified proofs of various relationships between sets. Connectives for fuzzy sets that generalize those for sets are defined. The fundamentals of ordinary probability theory are reviewed and these ideas are used to motivate fuzzy (...) probability theory. Observables (fuzzy random variables) and their distributions are defined. Some applications of fuzzy probability theory to quantum mechanics and computer science are briefly considered. (shrink)

Recently, scholars have begun to shift their focus toward the idea of the marketization of startups and the relationship with entrepreneurial psychology or other factors; however, the establishment of a unified and clear standard of entrepreneurship educational methods remains unfulfilled. Our study investigates 46 representative startups in four industries, including financial technology, biotechnology, education, and cultural tourism areas in Guangdong-Hong Kong-Macao Greater Bay Area and Southeast Asia to observe factors from different backgrounds but matter in common for building entrepreneurship education (...) systems and methods in different countries. We used the fuzzy qualitative comparison method to survey startup entrepreneurs and executives through questionnaires, selecting startup key factors including entrepreneurial psychology, product advantage, market and cultural environment, entrepreneurial policy, and geographical advantage. The survey was conducted on six key variables, namely, geographical advantage, to observe the conditional grouping and paths of factors influencing the establishment of Startups from an overall perspective. This study explores the path combination that plays a key role in the establishment of new enterprises, and further uses specific industry cases to verify the rationality and credibility of the path combination. The main conclusions are as follows: There are five combination paths affecting the establishment of new enterprises, which are “psychology and market,” “psychology, product, and region,” “psychology, culture and policy,” “psychology, market, and culture,” and “market, policy, and region” combination paths; Entrepreneur psychology, market environment, and entrepreneurship policy are the core conditions to improve the effectiveness of the establishment of new enterprises, while the other three variables are non-core variables in different paths; There are different paths of entrepreneurial paths and factor combinations in different regions or industries. (shrink)

Why is it so plausible that business organisations in contemporary society use values in their communication? In order to answer this question, a sociological, system theoretical approach is applied which approaches values not pre-empirically as invisible drivers for action but as observable semantics that form organisational behaviour. In terms of empirical material, it will be shown that business organisations resort to a communication of values whenever uncertainty or complexity is very high. Inevitably, value semantics are applied in organisations first (...) when the speakers are uncertain about which stakeholders to whom they have to address (uncertainty) or when different stakeholder groups have to be addressed simultaneously (complexity); second, when the identity of the organisation has to be described; and third, when future strategic options that cannot be expressed by quantitative terms have to be communicated. Values accordingly play a role in organisational practice when certain aspects are indeterminate. Therefore, they are a means for organisations to communicate under fuzzy circumstances. On the basis of these findings, new approaches to value management can now be formulated. (shrink)

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)

This article begins with a review of the framework of fuzzy probability theory. The basic structure is given by the σ-effect algebra of effects (fuzzy events) $\mathcal{E}{\text{ }}\left( {\Omega ,\mathcal{A}} \right)$ and the set of probability measures $M_1^ + {\text{ }}\left( {\Omega ,\mathcal{A}} \right)$ on a measurable space $\left( {\Omega ,\mathcal{A}} \right)$ . An observable $X:\mathcal{B} \to {\text{ }}\mathcal{E}{\text{ }}\left( {\Omega ,\mathcal{A}} \right)$ is defined, where $\begin{gathered} X:\mathcal{B} \to {\text{ }}\mathcal{E}{\text{ }}\left( {\Omega ,\mathcal{A}} \right) \\ \left( {\Lambda (...) ,{\text{ }}\mathcal{B}} \right) \\ \end{gathered} $ is the value space of X. It is noted that there exists a one-to-one correspondence between states on $\mathcal{E} \left( {\Omega ,\mathcal{A} } \right)$ and elements of $M_1^ + {\text{ }}\left( {\Omega ,\mathcal{A} } \right)$ and between observables $X:\mathcal{B} \to \mathcal{E} \left( {\Omega ,\mathcal{A} } \right)$ and σ-morphisms from $\mathcal{E} \left( {\Lambda , \mathcal{B}} \right)$ to $\mathcal{E} \left( {\Omega , \mathcal{A}} \right)$ . Various combinations of observables are discussed. These include compositions, products, direct products, and mixtures. Fuzzy stochastic processes are introduced and an application to quantum dynamics is considered. Quantum effects are characterized from among a more general class of effects. An alternative definition of a statistical map $M_1^ + {\text{ }}\left( {\Lambda ,\mathcal{B} } \right)$ is given and it is shown that any statistical map has a unique extension to a statistical operator. Finally, various combinations of statistical maps are discussed and their relationships to the corresponding combinations of observables are derived. (shrink)

Why is it so plausible that business organisations in contemporary society use values in their communication? In order to answer this question, a sociological, system theoretical approach is applied which approaches values not pre-empirically as invisible drivers for action but as observable semantics that form organisational behaviour. In terms of empirical material, it will be shown that business organisations resort to a communication of values whenever uncertainty or complexity is very high. Inevitably, value semantics are applied in organisations first (...) when the speakers are uncertain about which stakeholders to whom they have to address or when different stakeholder groups have to be addressed simultaneously ; second, when the identity of the organisation has to be described; and third, when future strategic options that cannot be expressed by quantitative terms have to be communicated. Values accordingly play a role in organisational practice when certain aspects are indeterminate. Therefore, they are a means for organisations to communicate under fuzzy circumstances. On the basis of these findings, new approaches to value management can now be formulated. (shrink)

Spatiotemporal regulation of the biochemical information is often linked to supramolecular organizations proteins and nucleic acids, the driving forces of which have yet to be elucidated. Although the critical role of multivalency in phase transition has been recognized, the organization principles of higher-order structures need to be understood. Here, we present a fuzzy mathematical framework to handle the heterogeneity of interactions patterns and the resultant multiplicity of conformational states in protein assemblies. In this model, redundant binding motifs can establish (...) simultaneous and partial interactions with multiple targets. We demonstrate that these multivalent, weak contacts facilitate polymer formation, while recapitulating the observed valency-dependence. In addition, the impact of linker dynamics and motif binding affinity, as well as the interplay between the two effects was studied. Our results support that fuzziness is a critical factor in driving higher-order protein organizations, and this could be used as a general framework to simulate different kinds of supramolecular assemblies. (shrink)

Air temperature prediction can play a significant role in studies related to climate change, radiation and heat flux estimation, and weather forecasting. This study applied and compared the outcomes of three advanced fuzzy inference models, i.e., dynamic evolving neural-fuzzy inference system, hybrid neural-fuzzy inference system, and adaptive neurofuzzy inference system for AT prediction. Modelling was done for three stations in North Dakota, USA, i.e., Robinson, Ada, and Hillsboro. The results reveal that FIS type models are well suited (...) when handling highly variable data, such as AT, which shows a high positive correlation with average daily dew point, total solar radiation, and negative correlation with average wind speed. At the Robinson station, DENFIS performed the best with a coefficient of determination of 0.96 and a modified index of agreement of 0.92, followed by ANFIS with R2 of 0.94 and md of 0.89, and HyFIS with R2 of 0.90 and md of 0.84. A similar result was observed for the other two stations, i.e., Ada and Hillsboro stations where DENFIS performed the best with R2: 0.953/0.960, md: 0.903/0.912, then ANFIS with R2: 0.943/0.942, md: 0.888/0.890, and HyFIS with R2: 0.908/0.905, md: 0.845/0.821, respectively. It can be concluded that all three models are capable of predicting AT with high efficiency by only using DP, TSR, and WS as input variables. This makes the application of these models more reliable for a meteorological variable with the need for the least number of input variables. The study can be valuable for the areas where the climatological and seasonal variations are studied and will allow providing excellent prediction results with the least error margin and without a huge expenditure. (shrink)

The work on prototypes in ontologies pioneered by Rosch [10] and elaborated by Lakoff [8] and Freund [3] is related to vagueness in the sense that the more remote an instance is from a prototype the fewer people agree that it is an example of that prototype. An intuitive example is the prototypical “mother”, and it is observed that more specific instances like ”single mother”, “adoptive mother”, “surrogate mother”, etc., are less and less likely to be classified as “mothers” by (...) experimental subjects. From a different direction Gärdenfors [4] provided a persuasive account of natural predicates to resolve paradoxes of induction like Goodman’s “Grue” predicate [5]. Gärdenfors proposed that “quality dimensions” arising from human cognition and perception impose topologies on concepts such that the ones that appear “natural” to us are convex in these topologies. We show that these two cognitive principles — prototypes and predicate convexity — are equivalent to unimodal (convex) fuzzy characteristic functions for sets. Then we examine the case when the fuzzy set characteristic function is not convex, in particular when it is multi-modal. We argue that this is an indication that the fuzzy concept should really be regarded as a super concept in which the decomposed components are subconcepts in an ontological taxonomy. (shrink)

This article, a contribution to the Common Knowledge symposium “Fuzzy Studies: On the Consequence of Blur,” documents how some modern artists and critics have argued against any sort of verbal thinking about art. Beyond describing works of visual art and pronouncing on their relative quality, critics often assume responsibility for explaining what a given work means. Because paintings and sculptures are less precisely codified, less articulate, than verbalized communications, they may seem to require verbal translation. Yet some artists and (...) critics have warned that the advantageous emotional force of a visual presentation is diminished or even destroyed by the generalizing classifications that verbal thinking entails. Sensation suffers from any reconstitution in words. “Watch Out for Thinking” focuses on the views of two critics (Clement Greenberg, Charles Harrison) and two artists (Willem de Kooning, Donald Judd), each of whom was sympathetic to the principle that visual observation and expression should remain independent of verbal explanation. Their common principle required that each develop some method of dealing with the gap between the experience of sensation and the thoughts generated by or directed at such feeling. On this issue, each disagreed with the others, whether expressing his difference directly or indirectly; and the differences often hinged on matters of aesthetic judgment. Ironically, the practice of such judgment demanded verbal concepts for its articulation. In turn, the verbal discourse tended to render the initial aesthetic judgment more extreme, more polarizing, than it may have felt as a lived response to a specific work of art. To remedy the situation, a viewer might allow feeling to divert the logical course of thinking. (shrink)

The measurement of one or more observables can be considered to yield sample points which are in general fuzzy sets. Operationally these fuzzy sample points are the outcomes of calibration procedures undertaken to ensure the internal consistency of a scheme of measurement. By introducing generalized probability measures on σ-semifields of fuzzy events, one can view a quantum mechanical state as an ensemble of probability measures which specify the likelihood of occurrence of any specific fuzzy sample point (...) at some instant. These sample points are the possible outcomes of any infinitely rapid succession of measurements at that instant of any sequence of observables of the system. (shrink)

Facial expressions of pain may be best conceptualized as an example of an evolved propensity to communicate distress, rather than as a distinct category of facial expression. The operant model goes beyond the evolutionary account, as it can explain how the (facial) expression of pain can become maladaptive as a result of its capability to elicit attention and caring behavior in the observer.

A reproducibility principle is formulated and adopted as the guiding criterion for the acceptance of an experimental procedure as a simultaneous measurement of several observables. It is pointed out that this criterion can be applied to classical as well as quantum physics, and that it incorporates compatible as well as incompatible observables. The concept of fuzzy probability measure is presented as a possible mathematical tool for the description of statistical processes involving measurements of incompatible observables.

This paper proposes an integral sliding mode control method of a class of uncertain chaotic systems with saturation inputs. Firstly, fuzzy logic system is used to estimate the unknown nonlinear function. Then, a disturbance observer is constructed to estimate a compound disturbance, which contains the external disturbance, the error of saturation input and control output, and the fuzzy estimation error. Subsequently, a proposed integral sliding mode controller can ensure that all signals of the closed-loop system are ultimately bounded, (...) and based on the dynamic system of the integral sliding mode variable itself, the ultimate bound of the tracking error can be estimated. Simulation results show that the proposed ISMC method is more effective than the traditional ISMC method. (shrink)

The positive operator (valued) measures (POMs) allow one to generalize the notion of observable beyond the traditional one based on projection valued measures (PVMs). Here, we argue that this generalized conception of observable enables a consistent notion of unsharp reality and with it an adequate concept of joint properties. A sharp or unsharp property manifests itself as an element of sharp or unsharp reality by its tendency to become actual or to actualize a specific measurement outcome. This actualization (...) tendency—or potentiality—of a property is quantified by the associated quantum probability. The resulting single-case interpretation of probability as a degree of reality will be explained in detail and its role in addressing the tensions between quantum and classical accounts of the physical world will be elucidated. It will be shown that potentiality can be viewed as a causal agency that evolves in a well-defined way. (shrink)

“Deep Thoughts” and “Fuzzy Memories” were fan favorites as transitional pieces between larger set pieces on Saturday Night Live in the 1990s. Delivered over soothing music and serene images, Jack Handey's bits never showed his face on screen, calling to mind his observation that “the face of a child can say it all, especially the mouth part of the face.” Some dark and offbeat takes on the human condition often have an existentialist feel. Existentialism is a philosophy concerned with (...) “the individual, the experience of choice, and the absence of rational understanding of the universe with a consequent dread or sense of absurdity in human life.” In other words, human beings find themselves trying to live meaningful lives without truly comprehending the nature of what that meaning may be, or whether or not true meaning could even exist. (shrink)

De Cock and Kerre, in considering Poincaré paradox, observed that the intuitive notion of "approximate similarity" cannot be adequately represented by the fuzzy equivalence relations. In this note we argue that the deduction apparatus of fuzzy logic gives adequate tools with which to face the question. Indeed, a first-order theory is proposed whose fuzzy models are plausible candidates for the notion of approximate similarity. A connection between these structures and the point-free metric spaces is also established.

Research into expertise is relatively common in cognitive science concerning expertise existing across many domains. However, much less research has examined how experts within the same domain assess the performance of their peer experts. We report the results of a modified think-aloud study conducted with 18 pilots . Pairs of same-ranked pilots were asked to rate the performance of a captain flying in a critical pre-recorded simulator scenario. Findings reveal considerable variance within performance categories, differences in the process used as (...) evidence in support of a performance rating, different numbers and types of facts identified, and differences in how specific performance events affect choice of performance category and gravity of performance assessment. Such variance is consistent with low inter-rater reliability. Because raters exhibited good, albeit imprecise, reasons and facts, a fuzzy mathematical model of performance rating was developed. The model provides good agreement with observed variations. (shrink)

The paper is a critique of the widespread conception of logic as a neutral arbiter between metaphysical theories, one that makes no `substantive’ claims of its own (David Kaplan and John Etchemendy are two recent examples). A familiar observation is that virtually every putatively fundamental principle of logic has been challenged over the last century on broadly metaphysical grounds (however mistaken), with a consequent proliferation of alternative logics. However, this apparent contentiousness of logic is often treated as though it were (...) neutralized by the possibility of studying all these alternative logics within an agreed metalogical framework, typically that of first-order logic with set theory. In effect, metalogic is given the role of neutral arbiter. The paper will consider a variety of examples in which deep logical disputes re-emerge at the meta-level. One case is quantified modal logic, where some varieties of actualism require a modal meta-language (as opposed to the usual non-modal language of possible worlds model theory) in order not to make their denial of the Barcan formula self-defeating. Similarly, on some views the intended model theory for second-order logic can only be given in a second-order metalanguage—this may be needed to avoid versions of Russell’s paradox when the first-order quantifiers are read as absolutely unrestricted. It can be shown that the phenomenon of higher-order vagueness eventually forces fuzzy logical treatments of vagueness to use a fuzzy metalanguage, with consequent repercussions for what first-order principles are validated. The difficulty of proving the completeness of first-order intuitionistic logic on its intended interpretation by intuitionistically rather than just classically valid means is a more familiar example. These case studies will be discussed in some detail to reveal a variety of ways in which even metalogic is metaphysically contested, substantial and non-neutral. (shrink)

This article explores some of the roles of computer simulation in measurement. A model-based view of measurement is adopted and three types of measurement—direct, derived, and complex—are distinguished. It is argued that while computer simulations on their own are not measurement processes, in principle they can be embedded in direct, derived, and complex measurement practices in such a way that simulation results constitute measurement outcomes. Atmospheric data assimilation is then considered as a case study. This practice, which involves combining information (...) from conventional observations and simulation-based forecasts, is characterized as a complex measuring practice that is still under development. The case study reveals challenges that are likely to resurface in other measuring practices that embed computer simulation. It is also noted that some practices that embed simulation are difficult to classify; they suggest a fuzzy boundary between measurement and non-measurement. 1 Introduction2 A Contemporary View of Measurement3 Three Types of Measurement4 Can Computer Simulations Measure Real-World Target Systems?5 Case Study: Atmospheric Data Assimilation5.1 Why data assimilation?5.2 A complex measuring practice under development5.3 Epistemic iteration6 The Boundaries of Measurement7 Epistemology, Not Terminology. (shrink)

Using photographs and testimonials, we will analyze details of the “miracle of the spinning sun” on October 13, 1917, at solar noon near Fatima. The phenomenon predicted ahead of time, occurred as the clouds cleared on what began as a rainy day. Various explanations have been presented but do not stand up to a comparative analysis of eyewitnesses, weather data, and photographs. This article aims to bring clarity to this event through the analysis of certified photographs and testimonies comparing them (...) to official meteorological and astronomical data. Our study confirms key points of the testimonials while focusing on objective data. The shadows and reflections reveal two soft light sources emerging from a rather dark background: one seen as a “pale sun”, and another overhead, fuzzy and as softly bright. The latter, likely being caused by a clear cloud, blurred the shadows of the weak “sun”. Strangely, the portions of clothing exposed to this “sun” dried quickly. This warm source, uncannily moonlike, was also able to cast distinct shadows on sloping surfaces and under objects. Eventually, these shadows will help us to estimate the height of the “sun” at ~30°, lower than the expected 42°. Therefore, the directly observed source could not have been the sun, and most probably not any physiological, psychological, or meteorological effect. (shrink)

Empathy is a construct that is notoriously difficult to define. Murphy and colleagues argue for leaning into the construct's inherent fuzziness and reverting to what they term a classical definition informed by the observations of philosophers and clinicians: as a dynamic, “unfolding process of imaginatively experiencing the subjective consciousness of another person, sensing, understanding, and structuring the world as if one were that person.” Although consistent with some historical conceptualizations, this definition risks incorporating so many processes it would make empathy (...) difficult to operationalize or distinguish from any generally socially sensitive interaction. Defining empathy instead as the attempted representation, or simulation, of another's subjective internal experiences would increase its clarity and empirical utility. (shrink)

Empathy is a construct that is notoriously difficult to define. Murphy and colleagues argue for leaning into the construct's inherent fuzziness and reverting to what they term a classical definition informed by the observations of philosophers and clinicians: as a dynamic, “unfolding process of imaginatively experiencing the subjective consciousness of another person, sensing, understanding, and structuring the world as if one were that person.” Although consistent with some historical conceptualizations, this definition risks incorporating so many processes it would make empathy (...) difficult to operationalize or distinguish from any generally socially sensitive interaction. Defining empathy instead as the attempted representation, or simulation, of another's subjective internal experiences would increase its clarity and empirical utility. (shrink)

The starting point of this work is the gap between two distinct traditions in information engineering: knowledge representation and data - driven modelling. The first tradition emphasizes logic as a tool for representing beliefs held by an agent. The second tradition claims that the main source of knowledge is made of observed data, and generally does not use logic as a modelling tool. However, the emergence of fuzzy logic has blurred the boundaries between these two traditions by putting forward (...) fuzzy rules as a Janus-faced tool that may represent knowledge, as well as approximate non-linear functions representing data. This paper lays bare logical foundations of data - driven reasoning whereby a set of formulas is understood as a set of observed facts rather than a set of beliefs. Several representation frameworks are considered from this point of view: classical logic, possibility theory, belief functions, epistemic logic, fuzzy rule-based systems. Mamdani's fuzzy rules are recovered as belonging to the data - driven view. In possibility theory a third set-function, different from possibility and necessity plays a key role in the data - driven view, and corresponds to a particular modality in epistemic logic. A bi-modal logic system is presented which handles both beliefs and observations, and for which a completeness theorem is given. Lastly, our results may shed new light in deontic logic and allow for a distinction between explicit and implicit permission that standard deontic modal logics do not often emphasize. (shrink)

On the basis of Mackey's axiomatic approach to quantum physics or, equivalently, of a “state-event-probability” (SEVP) structure, using a quite standard “fuzzification” procedure, a set of unsharp events (or “effects”) is constructed and the corresponding “state-effect-probability” (SEFP) structure is introduced. The introduction of some suitable axioms gives rise to a partially ordered structure of quantum Brouwer-Zadeh (BZ) poset; i.e., a poset endowed with two nonusual orthocomplementation mappings, a fuzzy-like orthocomplementation, and an intuitionistic-like orthocomplementation, whose set of sharp elements is (...) an orthomodular complete lattice. As customary, by these orthocomplementations the two modal-like necessity and possibility operators are introduced, and it is shown that Ludwig's and Jauch-Piron's approaches to quantum physics are “interpreted” in complete SEFP. As a marginal result, a standard procedure to construct a lot of unsharp realizations starting from any sharp realization of a fixed observable is given, and the relationship among sharp and corresponding unsharp realizations is studied. (shrink)

A highly abstracted theory of measurement is synthesized from classical measurement theory, fuzzy set theory, generalized information theory, and predicate calculus. The theory does not require specific truth value concepts, nor does it specify what subsets of the reals can be observed, thus avoiding the usual fundamental difficulties. Problems such as the definition of systems, the significance of observations, numerical scales and observables, etc. are examined. The general logico-algebraic approach to quantum/classical physics is justified as a special case of (...) measurement theory. (shrink)

Designing a data-responsive system requires accurate input to ensure efficient results. The growth of technology in sensing methods and the needs of various kinds of data greatly impact data fusion (DF)-related study. A coordinative DF framework entails the participation of many subsystems or modules to produce coordinative features. These features are utilized to facilitate and improve solving certain domain problems. Consequently, this paper proposes a general Multiple Coordinative Data Fusion Modules (MCDFM) framework for real-time and heterogeneous data sources. We develop (...) the MCDFM framework to adapt various DF application domains requiring macro and micro perspectives of the observed problems. This framework consists of preprocessing, filtering, and decision as key DF processing phases. These three phases integrate specific purpose algorithms or methods such as data cleaning and windowing methods for preprocessing, extended Kalman filter (EKF) for filtering, fuzzy logic for local decision, and software agents for coordinative decision. These methods perform tasks that assist in achieving local and coordinative decisions for each node in the network of the framework application domain. We illustrate and discuss the proposed framework in detail by taking a stretch of road intersections controlled by a traffic light controller (TLC) as a case study. The case study provides a clearer view of the way the proposed framework solves traffic congestion as a domain problem. We identify the traffic features that include the average vehicle count, average vehicle speed (km/h), average density (%), interval (s), and timestamp. The framework uses these features to identify three congestion periods, which are the nonpeak period with a congestion degree of 0.178 and a variance of 0.061, a medium peak period with a congestion degree of 0.588 and a variance of 0.0593, and a peak period with a congestion degree of 0.796 and a variance of 0.0296. The results of the TLC case study show that the framework provides various capabilities and flexibility features of both micro and macro views of the scenarios being observed and clearly presents viable solutions. (shrink)

This article has two main goals: to examine and classify the ways data can be used to advance normative theorizing in political theory, and to demonstrate such usages in the contested disciplinary field of religion–state relations and specifically regarding the hotly debated model of the separation of religion and state. Regarding the former, it is suggested here that the general observation that evaluation of political institutions must rely on proper understanding of such institutions and hence be data-sensitive, can be further (...) detailed or classified, via the following categories: conversion, institutional clarity, theoretical clarity and finally, theory improvement. With regard to the latter we examine how data regarding religion–state relations enables a better understanding (via the noted novel classifications or categories) of two important debates: ‘delineation’ (i.e. the argument that pure separation of religion and state does not exist) and ‘separation-establishment’ (i.e. arguing that models other than separation are permissible in religion–state relations). (shrink)

This article has two main goals: to examine and classify the ways data can be used to advance normative theorizing in political theory, and to demonstrate such usages in the contested disciplinary field of religion–state relations and specifically regarding the hotly debated model of the separation of religion and state. Regarding the former, it is suggested here that the general observation that evaluation of political institutions must rely on proper understanding of such institutions and hence be data-sensitive, can be further (...) detailed or classified, via the following categories: conversion, institutional clarity, theoretical clarity and finally, theory improvement. With regard to the latter we examine how data regarding religion–state relations enables a better understanding (via the noted novel classifications or categories) of two important debates: ‘delineation’ (i.e. the argument that pure separation of religion and state does not exist) and ‘separation-establishment’ (i.e. arguing that models other than separation are permissible in religion–state relations). (shrink)

The paper explicates the stages of the author’s philosophical evolution in the light of Kopnin’s ideas and heritage. Starting from Kopnin’s understanding of dialectical materialism, the author has stated that category transformations of physics has opened from conceptualization of immutability to mutability and then to interaction, evolvement and emergence. He has connected the problem of physical cognition universals with an elaboration of the specific system of tools and methods of identifying, individuating and distinguishing objects from a scientific theory domain. The (...) role of vacuum conception and the idea of existence (actual and potential, observable and nonobservable, virtual and hidden) types were analyzed. In collaboration with S.Crymski heuristic and regulative functions of categories of substance, world as a whole as well as postulates of relativity and absoluteness, and anthropic and self-development principles were singled out. Elaborating Kopnin’s view of scientific theories as a practically effective and relatively true mapping of their domains, the author in collaboration with M. Burgin have originated the unified structure-nominative reconstruction (model) of scientific theory as a knowledge system. According to it, every scientific knowledge system includes hierarchically organized and complex subsystems that partially and separately have been studied by standard, structuralist, operationalist, problem-solving, axiological and other directions of the current philosophy of science. 1) The logico-linguistic subsystem represents and normalizes by means of different, including mathematical, languages and normalizes and logical calculi the knowledge available on objects under study. 2) The model-representing subsystem comprises peculiar to the knowledge system ways of their modeling and understanding. 3) The pragmatic-procedural subsystem contains general and unique to the knowledge system operations, methods, procedures, algorithms and programs. 4) From the viewpoint of the problem-heuristic subsystem, the knowledge system is a unique way of setting and resolving questions, problems, puzzles and tasks of cognition of objects into question. It also includes various heuristics and estimations (truth, consistency, beauty, efficacy, adequacy, heuristicity etc) of components and structures of the knowledge system. 5) The subsystem of links fixes interrelations between above-mentioned components, structures and subsystems of the knowledge system. The structure-nominative reconstruction has been used in the philosophical and comparative case-studies of mathematical, physical, economic, legal, political, pedagogical, social, and sociological theories. It has enlarged the collection of knowledge structures, connected, for instance, with a multitude of theoreticity levels and with an application of numerous mathematical languages. It has deepened the comprehension of relations between the main directions of current philosophy of science. They are interpreted as dealing mainly with isolated subsystems of scientific theory. This reconstruction has disclosed a variety of undetected knowledge structures, associated also, for instance, with principles of symmetry and supersymmetry and with laws of various levels and degrees. In cooperation with the physicist Olexander Gabovich the modified structure-nominative reconstruction is in the processes of development and justification. Ideas and concepts were also in the center of Kopnin’s cognitive activity. The author has suggested and elaborated the triplet model of concepts. According to it, any scientific concept is a dependent on cognitive situation, dynamical, multifunctional state of scientist’s thinking, and available knowledge system. A concept is modeled as being consisted from three interrelated structures. 1) The concept base characterizes objects falling under a concept as well as their properties and relations. In terms of volume and content the logical modeling reveals partially only the concept base. 2) The concept representing part includes structures and means (names, statements, abstract properties, quantitative values of object properties and relations, mathematical equations and their systems, theoretical models etc.) of object representation in the appropriate knowledge system. 3) The linkage unites a structures and procedures that connect components from the abovementioned structures. The partial cases of the triplet model are logical, information, two-tired, standard, exemplar, prototype, knowledge-dependent and other concept models. It has introduced the triplet classification that comprises several hundreds of concept types. Different kinds of fuzziness are distinguished. Even the most precise and exact concepts are fuzzy in some triplet aspect. The notions of relations between real scientific concepts are essentially extended. For example, the definition and strict analysis of such relations between concepts as formalization, quantification, mathematization, generalization, fuzzification, and various kinds of identity are proposed. The concepts «PLANET» and «ELEMENTARY PARTICLE» and some of their metamorphoses were analyzed in triplet terms. The Kopnin’s methodology and epistemology of cognition was being used for creating conception of the philosophy of law as elaborating of understanding, justification, estimating and criticizing legal system. The basic information on the major directions in current Western philosophy of law (legal realism, feminism, criticism, postmodernism, economical analysis of law etc.) is firstly introduced to the Ukrainian audience. The classification of more than fifty directions in modern legal philosophy is suggested. Some results of historical, linguistic, scientometric and philosophic-legal studies of the present state of Ukrainian academic science are given. (shrink)

Contemporary logicians have expanded upon the old notions of psychologism in logic and proposed new, weakened versions of it. Those weakened versions postulate that psychologistic logic does not have to inform about the ontology or metaphysics of reasoning. Instead, logic applied in cognitive science could serve as one of many paradigms for making empirical predictions about the observable process of human reasoning. The purpose of this article is to entertain this notion and answer the question: what properties should a (...) logical system formally representing actual human reasoning have? Based on the existing evidence from cognitive science and neuroscience we identified three potential candidates: context-sensitivity (satisfied for example by adaptive logics), content-sensitivity (satisfied by non-Fregean logics) and probabilism (satisfied for example by fuzzy logics). (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Philosophy and Literature 27.1 (2003) 151-163 [Access article in PDF] Defining "Poetry" Robert B. Pierce SINCE TERMS ARE THE TOOLS of literary study, it is important to keep these tools in good condition, above all by having clear and functional meanings for them. Notoriously, many critical arguments about texts are in fact differences about terminology, and many confused arguments are built on vague or arbitrarily used terms. Few have (...) been the subject of more critical worrying and infighting than "poetry," 1 and few are more disparately defined. Definitions that are fuzzy or tendentious confuse many a discussion of poetry, and in particular they often narrow our response to the rich variety of the texts in front of us by silently imposing a view of what poetry ought to be. I would like to suggest that a Wittgensteinian approach to meaning can cut through a lot of the difficulty that surrounds the term. The refined understanding of the term "poetry" will result in a certain demystification, but it will dissipate only a false mystery based on confusion, not the real mystery of depth and richness that poetry can offer.What does it mean to approach this issue as a Wittgensteinian? The main principle is that the meaning of a term is its use, the way people deploy it in their speaking and writing, the work that it does. 2 A word does not have an essential core of meaning of which the various social uses are approximations; rather those social uses are the meaning. Thus meaning is a social phenomenon, and the way to determine it is to [End Page 151] look outward at how people use a term, not inward for some presumed mental essence that the term designates. Meaning is conventionally divided into reference and sense. What the term "poetry" refers to is a group of publicly visible things in the social world that we call poems, but there is no distillation in the mind that is the essence of poetry, the sense of the term. Of course we have a sense of the term that controls its range of reference. That sense is made up of our bases for calling one thing poetry and not another: the qualities that incline us to see a text as a poem. Wittgenstein would call these defining qualities criteria. The crucial fact is that they are determined by social processes and so are available to public inspection, not hidden away to be discovered only by introspection.Another observation about what it is to assign meaning to a term is important here. If someone asserts that "poetry" means X, he or she can appropriately be asserting that in fact the offered definition describes how people use the term, or else he or she can be suggesting how the term should or will be used in a specific discourse, that is, offering a definition proposal or stipulative definition. In the latter case the proposer needs to show the utility of the change from ordinary speech for his or her purposes. That is of course what literary critics do when they specify meanings for a term like "tragedy" or "irony" that are different from common usage. It is not that Wayne Booth's way of talking about irony uses the real meaning (both his and the ordinary senses are perfectly real since both are socially used), but that his is more useful for literary criticism than the general usage because it is more precise and nuanced. 3Thus it would make sense to begin defining "poetry" by looking at how people use the term and in particular how it is used in literary discourse. However, though I will pay some attention to what critics actually say and write, I would like primarily to offer certain proposals for refining our use of the term so as to avoid confusion and vagueness. It is not that this investigation will be approaching the real meaning of "poetry," which I have suggested is an imaginary goal, but that it will propose a use of the term constituting a vehicle for talking and writing about poetry that... (shrink)

Play is a frequent and relevant activity during childhood, and developmental psychologists agree that it offers a unique window on development. Play, however, remains a fuzzy concept, and difficulties persist in its definition, often leading to obstacles in building and comparing experimental studies. This may be due to widespread tendencies to define play by referring to non-observable inner states, to consider playing something that occurs in the head rather than in-the-world and to overreliance on developmental stages. Enactive approaches (...) to child play have instead recently stressed the importance of play contexts, considering child play an activity in-the-world rather than a mental state, thereby de-intellectualizing play and pretense. Along these lines, in this paper the authors propose a novel approach to the definition of play types by considering the roles of organism, environment, and task constraints, within the framework of Material Engagement Theory. Focusing on the material world surrounding the child and the interactions which characterize play, we critically review the strategy of resorting to non-observable categories in the study of play, and we propose a new model (the Kaleidoscope Model) for play analysis. (shrink)

This paper contains a logic enabling us to reason in the presence of vague- ness phenomena. We consider an epistemological vagueness of concepts caused by the unavailability of total information about a continuous world which we describe in observational terms. Lack of information is manifested by the existence of borderline cases for concepts. Since we are unable to perceive concepts exactly, we cannot establish a sharp boundary between an extension of a concept and its complement. Some results for reasoning about (...) vague concepts are already known in the literature [1], [2], [3], [4], [10]. Usually, a semantics of vague concepts is developed within the theory of fuzzy sets or the theory of supertruth [9]. Following the idea that reasoning about vague concepts requires a special logic, we introduce a propositional language with sentential operators en- abling us to dene positive, negative, and borderline regions of any vague concept. A semantics of the language is rened within a framework of the theory of rough sets . The admitted semantics provides means for dening extensions of concepts in a formal way. We show that these extensions re ect properly our intuition connected with vagueness. For ex- ample, the law of excluded middle is not valid on the level of extensions. Moreover, for any concept, the extensions of formulas representing its pos- itive, negative, and borderline regions provide a partition of a universe of discourse. (shrink)

When a boat disappears over the horizon, does a distant observer detect the last moment in which the boat is visible, or the first moment in which the boat is not visible? This apparently ludicrous way of reasoning, heritage of long-lasting medieval debates on decision limit problems, paves the way to sophisticated contemporary debates concerning the methodological core of mathematics, physics and biology. These ancient, logically-framed conundrums throw us into the realm of bounded objects with fuzzy edges, where our (...) mind fails to provide responses to plain questions such as: given a closed curve with a boundary how do you recognize what is internal and what is external? We show how the choice of an alternative instead of another is not arbitrary, rather points towards entirely different ontological, philosophical and physical commitments. This paves the way to novel interpretations and operational approaches to challenging issues such as black hole singularities, continuous time in quantum dynamics, chaotic nonlinear paths, logarithmic plots, demarcation of living beings. In the sceptical reign where judgements seem to be suspended forever, the contemporary scientist stands for a sort of God equipped with infinite power who is utterly free to dictate the rules of the experimental settings. (shrink)

The early discovery of cis‐regulatory elements able to promote transcription of genes over large distances led to the postulate that elements, termed insulators, should also exist that would limit the action of enhancers, LCRs and silencers to defined domains. Such insulators were indeed found during the past fifteen years in a wide range of organisms, from yeast to humans. Recent advances point to an important role of transcription factors in insulator activity and demonstrate that the operational observation of an insulator (...) effect relies on a delicate balance between the “efficiency” of the insulator and that of the element to be counteracted. In addition, genuine insulator elements now appear less common than initially envisaged, and they are only found at loci displaying a high density of coding or regulatory information. Where this is not the case, chromatin domains of opposing properties are thought to confront each other at “fuzzy” boundaries. In this article, we propose models for both fixed and fuzzy boundaries that incorporate probabilistic and dynamic parameters. BioEssays 26:523–532, 2004. © 2004 Wiley Periodicals, Inc. (shrink)