Based on the hesitant fuzzy set theory which is introduced by Torra in the paper [12], the notions of Inf-hesitant fuzzy subalgebras, Inf-hesitant fuzzy ideals and Inf-hesitant fuzzy p-ideals in BCK/BCI-algebras are introduced, and their relations and properties are investigated. Characterizations of an Inf-hesitant fuzzy subalgebras, an Inf-hesitant fuzzy ideals and an Inf-hesitant fuzzy p-ideal are considered. Using the notion of BCK-parts, an Inf-hesitant fuzzy ideal is constructed. Conditions for an (...) Inf-hesitant fuzzy ideal to be an Inf-hesitant fuzzy p-ideal are discussed. Using the notion of Inf-hesitant fuzzy ideals, a characterization of a p-semisimple BCI-algebra is provided. Extension properties for an Inf-hesitant fuzzy p-ideal is established. (shrink)

The aim of this manuscript is to introduce the $(\alpha,\beta)$-hesitant fuzzy set and apply it to semigroups. In this paper, as a generalization of the concept of hesitant fuzzy sets to semigroup theory, the concept of $(\alpha,\beta)$-hesitant fuzzy subsemigroups of semigroups is introduced, and related properties are discussed. Furthermore, we define and study $(\alpha,\beta)$-hesitant fuzzy ideals on semigroups. In particular, we investigate the structure of $(\alpha,\beta)$-hesitant fuzzy ideal generated by a hesitant fuzzy (...) class='Hi'>ideal in a semigroup. In addition, we also introduce the concepts of $(\alpha,\beta)$-hesitant fuzzy semiprime sets of semigroups, and characterize regular semigroups in terms of $(\alpha,\beta)$-hesitant fuzzy left ideals and $(\alpha,\beta)$-hesitant fuzzy right ideals. Finally, several characterizations of regular and intra-regular semigroups by the properties of $(\alpha,\beta)$-hesitant ideals are given. (shrink)

In this paper, we defined the concept $\mathcal{SUP}$-hesitant fuzzy interior ideals in $\Gamma$-semigroups, which is generalized of hesitant fuzzy interior ideals in $\Gamma$-semigroups. Additionally, we study fundamental properties of $\mathcal{SUP}$-hesitant fuzzy interior ideals in $\Gamma$-semigroups. Finally, we investigate characterized properties of those.

In this paper, by using the notion of fuzzy points and equality algebras, the notions of fuzzy point equality algebra, equality-subalgebra, and ideal were established. Some characterizations of fuzzy subalgebras were provided by using such concepts. We defined the concepts of $(\in, \in)$ and $(\in, \in\! \vee \, {q})$-fuzzy ideals of equality algebras, discussed some properties, and found some equivalent definitions of them. In addition, we investigated the relation between different kinds of $(\alpha,\beta)$-fuzzy subalgebras (...) and $(\alpha,\beta)$-fuzzy ideals on equality algebras. Also, by using the notion of $(\in, \in)$-fuzzy ideal, we defined two equivalence relations on equality algebras and we introduced an order on classes of $X$, and we proved that the set of all classes of $X$ by these order is a poset. (shrink)

In this study, by the use of Yuan and Lee’s definition of the fuzzy group based on fuzzy binary operation we give a new kind of fuzzy ring. The concept of fuzzy subring, fuzzy ideal and fuzzy ring homomorphism are introduced, and we make a theoretical study their basic properties analogous to those of ordinary rings.

In this study, we investigate the notion of an intuitionistic fuzzy prime ideal and intuitionistic fuzzy weakly 2-absorbing ideal of a lattice as an expansion of a notion of a weakly prime ideal. Then, we characterize the concept of intuitionistic fuzzy weakly 2-absorbing ideals and intuitionistic fuzzy weakly primary ideals and give some results. Finally, we suggest the concept of an intuitionistic fuzzy weakly 2-absorbing ideals in a product of lattices.

Selon le concept de Nancy Fraser du triple mouvement de protection sociale, d’émancipation et de marchandisation, les forces d’émancipation peuvent former une alliance avec la protection sociale ou la marchandisation. Un véritable exemple d’émancipation est la transformation des services résidentiels de soins aux personnes handicapées en assistance personnelle. Toutefois, on ne sait pas encore très bien pourquoi certaines réformes se chevauchent davantage avec la marchandisation et d’autres avec la protection sociale, alors que d’autres pays n’ont pas entrepris de réformes généralisées (...) de leurs services de soins aux personnes handicapées. Cet article tente d’éclairer cette question en examinant l’approche morphogénétique pour expliquer l’évolution des services de soins aux personnes handicapées dans dix pays européens. Une fuzzy set ideal type analysis a été utilisée pour délimiter quatre types de services de soins aux personnes handicapées. L’analyse a classé la Grèce, la Slovénie et l’Espagne dans le type domestique-traditionnel, la Belgique, l’Allemagne et la Suisse dans le type bienveillant-paternaliste, la Suède dans le type universel-progressif, et la Lettonie, la République slovaque et le Royaume-Uni dans le type précaire-progressif. (shrink)

As a generation of fuzzy set, the notion of complex fuzzy set which is an innovative concept is introduced by Ramot, Milo, Friedman and Kandel. The purpose of this article is to apply complex fuzzy set to BCK/BCI-algebras. The notions of a complex subalgebra and a complex left reduced ideal in a BCK/BCI- algebra are introduced, and related properties are investigated. Characterizations of a complex subalgebra are provided, and the homomorphic image of a complex subalgebra and (...) a complex left reduced ideal. (shrink)

In this paper, an adaptive fuzzy containment condtrol is considered for nonlinear multiagent systems, in which it contains the unknown control coefficient and actuator fault. The uncertain nonlinear function has been approximated by fuzzy logic system. The unknown control coefficient and the remaining control rate of actuator fault can be solved by introducing a Nussbaum function. In order to avoid the repeated differentiations of the virtual controllers, first-order filters are added to the traditional backstepping control method. By designing (...) the maximum norm of ideal adaptive parameters, only one adaptive parameter needs to be adjusted online for each agent itself. An adaptive fuzzy containment controller is constructed through the backstepping control technique and compensating signals. It is demonstrated that all the signals in nonlinear multiagent systems are bounded by designing adaptive fuzzy containment controller, and all followers can converge to the convex hull built by the leaders. The simulation studies can further confirm the effectiveness of the proposed control method in this paper. (shrink)

A logic is a doctrine of the logos, that is, of meaningful discourse; hence the first thing we expect from it is an account of what makes the logos meaningful — of what a meaning is. There is no single such doctrine or account: it is part of the immense richness of meaningful discourse that we can shift back and forth between several logics — several organized ways of reasoning, of providing reasons or grounds for our claims. Building on previous (...) work on Hegel's dialectical logic, the author here identifies three distinct logics simultaneously in play in our conversations. Analytic logic structures its organization of discourse around negation, contraries, and hence arguments forcing a conclusion to follow (under threat of inconsistency) from some premises. Dialectical logic's main tool is the construction of narratives, hence the attempted incorporation of interlocutors within one's own story. The third option, here labeled gradual logic, sees sorites (which are recalcitrant anomalies for the analytic approach) as ideal cases, since the bleeding of a predicate into an alleged contrary points the way to reaching an agreement among initially conflicting parties: to them eventually coming to regard themselves as stressing different aspects of one and the same thing. (shrink)

The paper introduces the concept of B-Almost distributive fuzzy lattice in terms of its principal ideal fuzzy lattice. Necessary and sufficient conditions for an ADFL to become a B-ADFL are investigated. We also prove the equivalency of B-algebra and B-fuzzy algebra. In addition, we extend PSADL to PSADFL and prove that B-ADFL implies PSADFL.

For each continuous t-norm &, a class of fuzzy topological spaces, called &-topological spaces, is introduced. The motivation stems from the idea that to each many-valued logic there may correspond a theory of many-valued topology, in particular, each continuous t-norm may lead to a theory of fuzzy topology. It is shown that for each continuous t-norm &, the subcategory consisting of &-topological spaces is simultaneously reflective and coreflective in the category of fuzzy topological spaces, hence gives rise (...) to an autonomous theory of fuzzy topology. Topologizing a fuzzy pre-ordered set with the fuzzy Scott topology yields a functor from the category of fuzzy pre-ordered sets and maps that preserve suprema of flat ideals to the category of &-topological spaces. It is proved that this functor is a full one if and only if the t-norm & is Archimedean. (shrink)

Continuous environmental concerns regarding construction industry have been driving general constructors of mega infrastructure projects to incorporate green contractors. Although conventional multiple attributes decision-making methodologies have provided feasible ways to select contractor, high complexity in scenarios of megaprojects still challenges existing MADM methods in concurrently accommodating three key issues of decision hesitancy, attributes interdependency, and group attitudinal character. To elicit decision-makers’ hesitant fuzzy assessments more objectively and comprehensively, we define an expression tool called interval-valued dual hesitant fuzzy uncertain (...) unbalanced linguistic set and develop aggregation operators through its operations. To exploit attributes interdependency, we establish a synthesized attributes’ weighting model to fuse an attributes interdependency-based weighting vector and an argument-dependent weighting vector, which are, respectively, derived through Decision-Making and Trial Evaluation Laboratory technique and maximizing deviation method. To effectively utilize decision-makers’ group attitudinal characters, we also develop a TOPSIS-based method to rationally transform group ideal attitudes into order-inducing vectors. On the strength of the above methods, an integrated MADM approach is then constructed. Finally, illustrative case study and experiments are conducted to validate our approach. (shrink)

Continuous environmental concerns regarding construction industry have been driving general constructors of mega infrastructure projects to incorporate green contractors. Although conventional multiple attributes decision-making methodologies have provided feasible ways to select contractor, high complexity in scenarios of megaprojects still challenges existing MADM methods in concurrently accommodating three key issues of decision hesitancy, attributes interdependency, and group attitudinal character. To elicit decision-makers’ hesitant fuzzy assessments more objectively and comprehensively, we define an expression tool called interval-valued dual hesitant fuzzy uncertain (...) unbalanced linguistic set and develop aggregation operators through its operations. To exploit attributes interdependency, we establish a synthesized attributes’ weighting model to fuse an attributes interdependency-based weighting vector and an argument-dependent weighting vector, which are, respectively, derived through Decision-Making and Trial Evaluation Laboratory technique and maximizing deviation method. To effectively utilize decision-makers’ group attitudinal characters, we also develop a TOPSIS-based method to rationally transform group ideal attitudes into order-inducing vectors. On the strength of the above methods, an integrated MADM approach is then constructed. Finally, illustrative case study and experiments are conducted to validate our approach. (shrink)

Appeals to intersectionality serve to remind us that social categories like race and gender cannot be adequately understood independently from each other. But what, exactly, is the intersectional thesis a thesis about? Answers to this question are remarkably diverse. Intersectionality is variously understood as a claim about the nature of social kinds, oppression, or experience ; about the limits of antidiscrimination law or identity politics ; or about the importance of fuzzy sets, multifactor analysis, or causal modeling in social (...) science. (shrink)

Over the years, the urban heat vulnerability has evolved as a pressing global concern for researchers and policymakers alike. Numerous studies have aimed at mitigating the adverse effects of urban heat vulnerability on public health and safety. However, the critical task of selecting the most fitting indicator for urban heat islands in public spaces is not emphasized in the existing studies, considering the diverse indices available. Beyond identification, studies that delve into the prioritization of these indices and the determination of (...) optimal variables along with their respective weights are scanty. The present study attempts to address these gaps in urban heat vulnerability research through the lens of natural solutions. The study employs a fuzzy analytical hierarchy approach to ascertain the weights of selected criteria, providing a nuanced understanding of the multifaceted factors influencing their applicability. Real-time impact estimation using the fuzzy technique for order of preference by similarity to ideal solutions enhances the practicality of the findings. The results reveal a set of pivotal characteristics crucial for constructing a robust heat vulnerability index, facilitating the prioritization of selected criteria. The implementation of this hybrid methodology culminates in a streamlined, precise, and practical tool for evaluating heat vulnerability in hot urban public spaces. These findings contribute valuable insights to the academic discourse and offer a tangible resource for policymakers and practitioners. The proactive approach provides a roadmap for addressing impending challenges related to urban heat vulnerability, marking a positive step toward creating resilient and sustainable urban environments. (shrink)

The correlation coefficient between two variables plays an important role in statistics. Also, the accuracy of relevance assessment depends on information from a set of discourses. The data collected from numerous statistical studies are full of exceptions. The Pythagorean fuzzy hypersoft set is a parameterized family that deals with the subattributes of the parameters and an appropriate extension of the Pythagorean fuzzy soft set. It is also the generalization of the intuitionistic fuzzy hypersoft set, which is used (...) to accurately assess insufficiency, anxiety, and uncertainties in decision-making. The PFHSS can accommodate more uncertainties compared to the IFHSS, and it is the most substantial methodology to describe fuzzy information in the decision-making process. The core objective of the this study is to develop the notion and features of the correlation coefficient and the weighted correlation coefficient for PFHSS and to introduce the aggregation operators such as Pythagorean fuzzy hypersoft weighted average and Pythagorean fuzzy hypersoft weighted geometric operators under the PFHSS scenario. A prioritization technique for order preference by similarity to the ideal solution under PFHSS based on correlation coefficients and weighted correlation coefficients is presented. Through the developed methodology, a technique for solving multiattribute group decision-making problem is planned. Also, the importance of the developed methodology and its application in indicating multipurpose antivirus mask throughout the COVID-19 pandemic period is presented. A brief comparative analysis is described with the advantages, effectiveness, and flexibility of numerous existing studies that demonstrate the effectiveness of the proposed method. (shrink)

Substructural logics are obtained from the sequent calculi for classical or intuitionistic logic by suitably restricting or deleting some or all of the structural rules (Restall, 2000; Ono, 1998). Recently, this field of research has come to encompass a number of logics - e.g. many fuzzy or paraconsistent logics - which had been originally introduced out of different, possibly semantical, motivations. A finer proof-theoretical analysis of such logics, in fact, revealed that it was possible to subsume them under the (...) previous definition (see e.g. Aguzzoli and Ciabattoni, 2000).Although proof systems for substructural logics are currently being investigated with remarkable success, their algebraic models do not seem equally satisfactory. In fact:(i) such structures are often very weak, i.e. they do not possess many interesting algebraic properties;(ii) as a consequence, their theories of ideals, congruences, and representation are as a rule scarcely developed, or even lacking.In this paper, we address these difficulties. (shrink)

The expressions ‘high quality care’ and ‘low quality care’ are cognitive and linguistic artefacts that help to structure people’s lives and thinking; for example, moves are now afoot internationally to pay bonuses to health professionals for delivering high quality care. United States programmes, most conspicuously, are assuming that high quality care can be validly distinguished from low quality care, and incentivised through bonuses. This distinction is always at least implicit, for high quality care has no meaning without low quality care. (...) Through a ‘deconstructionist reading,’ this article discusses limitations of categorising the quality of care as either high or low. The limitations of this ‘binary opposition’ can include a lack of defining attributes; vagueness and fuzziness at the ‘boundaries’ between high quality care and low quality care; concealment of quality as a continuum; and use of the binary opposition to effect social order and control. Health policy implications of our analysis are discussed. Drawing upon the general medical services contract in the United Kingdom, we suggest an approach to overcoming the oversimplification and imprecision that categorisation tends to produce. (shrink)

In a recent paper as an alternative to models based on the notion of ideal mathematical point, characterized by a property of separatedness, we considered a viewpoint based on the notion of continuous change, making use of elements of a non-classical logic, in particular the fuzzy sets theory, with events represented as spatiotemporally blurred blobs. Here we point out and discuss a number of aspects of this imperfect symbolic description that might potentially be misleading. Besides that, we analyze (...) its relation to various concepts used commonly to model physical systems, denoted by terms like: point, set, continuous, discrete, infinite, or local, clarifying further how our viewpoint is different and asking whether, in light of our main postulate, any of these notions, or their opposites, if exist, are in their usual meanings suitable to accurately describe the natural phenomena. (shrink)

Roger Shepard's creativity and scientific contributions have left an indelible mark on Psychology and Cognitive Science. In this tribute, I acknowledge and show how his approach to universal laws helped Oden and me shape and develop our universal law of pattern recognition, as formulated in the Fuzzy Logical Model of Perception (FLMP). [Shepard; Tenenbaum & Griffiths].

‘Reasoning’ can be considered a general concept that, upon speaking, is the ‘enraonar’, a Catalan word that should not be mistaken with ‘explain’ nor with ‘discuss’ which imply more detail, and cover different situations. This article is presented as an essay on the ancient ideal of ‘enraonar’. To that end, it is explained in what sense ‘enraonar’ and reason are one of the most complex phenomena thought has to deal with. Here it is argued that these natural phenomena require (...) a systematic and ‘scientific’ study, and that withoutthis knowledge computer science cannot simulate people’s every-day ‘enraonar’. (shrink)

In this paper we introduce the notion of ideals on neutrosophic set which is considered as a generalization of fuzzy and fuzzy intuitionistic ideals studies in [9,11] , the important topological neutrosophic ideals has been given in [4]. The concept of neutrosophic local function is also introduced for a neutrosophic topological space. These concepts are discussed with a view to fiind new neutrosophic topology from the original one in [8]. The basic structure, especially a basis for such generated (...) neutrosophic topologies and several relations between different topological neutrosophic ideals and neutrosophic topologies are also studied here. Possible application to GIS topology rules are touched upon. -/- . (shrink)

“Neutrosophics Knowledge” has been created for publications on advanced studies in neutrosophy, neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics that started in 1995 and their applications in any field, such as the neutrosophic structures developed in algebra, geometry, topology, etc. The submitted papers should be professional, in good English and Arabic, containing a brief review of a problem and obtained results. Neutrosophy is a new branch of philosophy that studies the origin, nature, and scope of neutralities, as well as (...) their interactions with different ideational spectra. (shrink)

This chapter contains sections titled: The Bayesian Orthodoxy Idealization Two Approaches to a Theory of Probability Adjustment for Nonclassical Logics Carnap's Confirmation Theory Proportional Syllogisms Kyburg's Fuzzy Probabilities Levi's Indeterminate Systems Qualitative Theories of Probability The Dynamics of Subjective Probability Probability Theory and Quantum Theory.

A robust adaptive fuzzy nonlinear controller based on dynamic surface and integral sliding mode control strategy is proposed to realize trajectory tracking for a class of quadrotor UAVs. In this study, the composite factors including parametric uncertainties and external disturbances are added to controller design, which make it more realistic. The quadrotor model is divided into two subsystems of attitude and position that make the control design become feasible. The main contributions of the proposed ADSISMC strategy are as follows: (...) The combination of dynamic surface and integral sliding mode makes the system always in sliding stage by finding the appropriate initial position compared with the common sliding mode, and the complexity of explosion in backstepping method is eliminated. By introducing the fuzzy system, the unknown functions and uncertainties can be approximated which significantly improves the robustness and the tracking performance. The switching control strategy is utilized to compensate for the errors between estimated and ideal inputs; the tracking performance of the whole system has been significantly improved. The simulation results show the effectiveness of the proposed control method. (shrink)

In this paper we propose a multi-criteria model based on the fuzzy preferences approach which can be implemented in the prenegotiation phase to evaluate the negotiations packages. The applicability of some multi-criteria ranking methods were discussed for building a scoring function for negotiation packages. The first one is Simple Additive Weighting technique which determines the sum of the partial satisfactions from each negotiation issue and aggregate them using the issue weights. The other one is Distance Based Methods, with its (...) extension based on the distances to ideal or anti-ideal package, i.e. the TOPSIS procedure. In our approach the negotiator's preferences over the issues are represented by fuzzy membership functions and next a selected multi-criteria decision making method is adopted to determine the global rating of each package. The membership functions are used here as the equivalents of utility functions spread over the negotiation issues, which let us compare different type of data. One of the key advantages of the approach proposed is its usefulness for building a general scoring function in the ill-structured negotiation problem, namely the situation in which the problem itself as well as the negotiators preferences cannot be precisely defined, the available information is uncertain, subjective and vague. Secondly, all proposed variants of scoring functions produce consistent rankings, even though the new packages are added and do not result in rank reversal. (shrink)

The move from respecting science to scientism, i.e., the idealization of science and scientific method, is simple: We go from acknowledging the sciences as fruitful human activities to oversimplifying the ways they work, and accepting a fuzzy belief that Science and Scientific Method, will give us a direct pathway to the true making of the world, all included. The idealization of science is partly the reason why we feel we need to impose the so-called scientific terminologies and methodologies to (...) all aspects of our lives, education too. Under this rationale, educational policies today prioritize science, not only in curriculum design, but also as a method for educational practice. One might expect that, under the scientistic rationale, science education would thrive. Contrariwise, I will argue that scientism disallows science education to give an accurate image of the sciences. More importantly, I suggest that scientism prevents one of science education’s most crucial goals: help students think. Many of my arguments will borrow the findings and insights of science education research. In the last part of this paper, I will turn to some of the most influential science education research proposals and comment on their limits. If I am right, and science education today does not satisfy our most important reasons for teaching science, perhaps we should change not just our teaching strategies, but also our scientistic rationale. But that may be a difficult task. (shrink)

Since the world is full of indeterminacy, the Neutrosophics found their place into contemporary research. We now introduce for the first time the notions of Neutrosophic Crisp Sets and Neutrosophic Topology on Crisp Sets. We develop the 2012 notion of Neutrosophic Topological Spaces and give many practical examples. Neutrosophic Science means development and applications of Neutrosophic Logic, Set, Measure, Integral, Probability etc., and their applications in any field. It is possible to define the neutrosophic measure and consequently the neutrosophic integral (...) and neutrosophic probability in many ways, because there are various types of indeterminacies, depending on the problem we need to solve. Indeterminacy is different from randomness. Indeterminacy can be caused by physical space, materials and type of construction, by items involved in the space, or by other factors. In 1965 [51], Zadeh generalized the concept of crisp set by introducing the concept of fuzzy set, corresponding to the situation in which there is no precisely defined set;there are increasing applications in various fields, including probability, artificial intelligence, control systems, biology and economics. Thus, developments in abstract mathematics using the idea of fuzzy sets possess sound footing. In accordance, fuzzy topological spaces were introduced by Chang [12] and Lowen [33]. After the development of fuzzy sets, much attention has been paid to the generalization of basic concepts of classical topology to fuzzy sets and accordingly developing a theory of fuzzy topology [1-58]. In 1983, the intuitionistic fuzzy set was introduced by K. Atanassov [55, 56, 57] as a generalization of the fuzzy set, beyond the degree of membership and the degree of non-membership of each element. In 1999 and 2002, Smarandache [71, 72, 73, 74] defined the notion of Neutrosophic Sets, which is a generalization of Zadeh’s fuzzy set and Atanassov's intuitionistic fuzzy set. Some neutrosophic concepts have been investigated by Salama et al. [61-70]. Forwarding the study of neutrosophic sets, this book consists of seven chapters, targeting to:  generalize the previous studies in [1-59], and[91-94] so to define the neutrosopic crisp set and neutrosophic set concepts;  discuss their main properties; A. A. Salama & Florentin Smarandache  introduce and study some concepts of neutrosophic crisp and neutrosophic topological spaces and deduce their properties;  deduce many types of functions and give the relationships between different neutrosophic topological spaces, which helps to build new properties of neutrosophic topological spaces;  stress once more the importance of Neutrosophic Ideal as a nontrivial extension of neutrosophic set and neutrosophic logic [71, 72, 73, 74];  propose applications on computer sciences by using neutrosophic sets. (shrink)

Function-first approaches illuminate phenomena by investigating their functional roles. I first describe virtues of this approach. By foregrounding normal instances of knowledge, for example, function-first theorising offers a much-needed corrective to epistemology's counterexample-driven momentum towards increasingly byzantine, marginal cases. And epistemic practices are shaped by human limitations, needs, vices, and power relations. These non-ideal, naturalistic forces of embodied sociality form the roots of function-first theorising, which creates a fecund foundation for social epistemology. Secondly, I consider an objection to function-first (...) theorising. The objection holds that function-first approaches lack adjudicatory power. That is, function-first proposals are overly compatible with diverse claims about knowledge, which encourages “just so” speculation. In response to this concern, I advocate methodological pluralism in epistemological theorising. All methods have limitations; researchers must be mindful of those limits and fruitfully combine multiple methods. I illustrate with Hannon's function-first based arguments for “epistemic pragmatism”, which denies that the meaning of “knows” is determined by truth conditions. Finally, I argue that function-first theorising motivates staunch anti-skepticism about knowledge. Practical forces cannot chisel a sharp threshold for how much evidence is required for knowledge. But thinking this supports radical skepticism about knowledge conflates fuzzy thresholds and high ones. (shrink)

In this paper we consider a claim that in the natural world there is no fact of the matter about the spatio-temporal separation of events. In order to make sense of such a notion and construct useful models of the world, it is proposed to use elements of a non-classical logic. Specifically, we focus here on causality, as a concept tightly related with the assumption of there being distinct, separate events, proposing a model according to which it can be considered (...) to be spatio-temporally graded. It is outlined how this can be described using the formalism of fuzzy sets theory, with the degree of causality varying between 1, that is no separation between causes and effects, and 0, that is perfect separation between causes and their effects as in classical ’billiard balls’ models of physical systems, namely such based on the notion of ideal mathematical point. Our model posits that subjective moments of time are like fuzzy sets, with their extension determined by local degrees of causality, resulting from information integration processes extended gradually in space and time. This, we argue, is how a notion of causality could be, to a certain degree, spared and reconciled with a variant of Bergsonian duration theory as formulated in the theory of continuous change. Relation of the proposed viewpoint to other theories, as well as possible solutions it suggests to various problems, in particular the measurement problem, are also discussed. (shrink)

The papers in this special issue are based on presentations delivered at the conference Epistemic Aspects of Many-valued Logics, held at the Institute of Philosophy of the Academy of Sciences of the Czech Republic, in Prague, 2010. All papers consequently revolve around the application of non-classical logical tools—mathematical fuzzy logic and/or probability theory—to epistemological issues.Timothy Williamson employs a modal epistemic logic enriched with probabilities to generalize an argument against the KK-principle. He argues that we can know a proposition even (...) if our evidential probability for that proposition is low. In fact he argues that the evidential probability of a known proposition can be (arbitrarily) close to 0. The argument is first presented with a basic idealized model, which is then extended to much more complicated and realistic models. This then raises a problem for decision theory, since you can know that p, while your evidence tells you (strongly) that not p. Wil .. (shrink)

Commonplace syntactic constructions in natural language seem to generate ontological commitments to a dazzling array of metaphysical categories - aggregations, sets, ordered n-tuples, possible worlds, intensional entities, ideal objects, species, intensive and extensive quantities, stuffs, situations, states, courses of events, nonexistent objects, intentional and discourse objects, general objects, plural objects, variable objects, arbitrary objects, vague kinds and concepts, fuzzy sets, and so forth. But just because a syntactic construction in some natural language appears to invoke a new category (...) of entity, are we theoreticians epistemically justified in holding that there are such entities? This would hardly seem sufficient. To be epistemically justified, the ontology to which we theoreticians are committed must pass strict standards: the entities must be of the sort required by our best comprehensive theory of the world. The thesis of this paper is that fine-grained type-free intensional entities are like this. If the thesis is right, these entities have a special objective status perhaps not possessed by some of the other ontological categories associated with special syntactic constructions in natural language. In fact, it is plausible to hold that fine-grained type-free intensional entities provide the proper minimal framework for constructing logical and linguistic theories. In this paper my strategy will be to survey the competing conceptions of fine-grained type-free intensionality and to present arguments in support of one of them. Following this narrowing down process, I will go on to the indicated epistemological considerations. (shrink)

In this paper we study intermediate logics between the logic G≤∼, the degree preserving companion of Gödel fuzzy logic with involution G∼ and classical propositional logic CPL, as well as the intermediate logics of their finite-valued counterparts G≤n∼. Although G≤∼ and G≤ are explosive w.r.t. Gödel negation ¬, they are paraconsistent w.r.t. the involutive negation ∼. We introduce the notion of saturated paraconsistency, a weaker notion than ideal paraconsistency, and we fully characterize the ideal and the saturated (...) paraconsistent logics between G≤n∼ and CPL. We also identify a large family of saturated paraconsistent logics in the family of intermediate logics for degree-preserving finite-valued Łukasiewicz logics. (shrink)

This article explores the domain of legal analysis and its methodologies, emphasising the significance of generalisation in legal systems. It discusses the process of generalisation in relation to legal concepts and the development of ideal concepts that form the foundation of law. The article examines the role of logical induction and its similarities with semantic generalisation, highlighting their importance in legal decision-making. It also critiques the formal-deductive approach in legal practice and advocates for more adaptable models, incorporating fuzzy (...) logic, non-monotonic defeasible reasoning, and artificial intelligence. The potential application of neural networks, specifically deep learning algorithms, in legal theory is also discussed. The article discusses how neural networks encode legal knowledge in their synaptic connections, while the syllogistic model condenses legal information into axioms. The article also highlights how neural networks assimilate novel experiences and exhibit evolutionary progression, unlike the deductive model of law. Additionally, the article examines the historical and theoretical foundations of jurisprudence that align with the basic principles of neural networks. It delves into the statistical analysis of legal phenomena and theories that view legal development as an evolutionary process. The article then explores Friedrich Hayek’s theory of law as an autonomous self-organising system and its compatibility with neural network models. It concludes by discussing the implications of Hayek’s theory on the role of a lawyer and the precision of neural networks. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Four Philosophical Models of the Relation Between Theory and PracticeEstelle R. JorgensenSince music education straddles theory and practice, my purpose is to sketch the strengths and weaknesses of four philosophical models of the relationship between theory and practice. I demonstrate that none of them suffices when taken alone; each has something to offer and its own detractions. And I conclude with four suggested ways in which the analysis can (...) be helpful to music teachers and those interested in their work.Clarifying what is meant by theory and practice raises a nest of conceptual problems. Concerning theory, it may be tempting to equate the terms "theory" and "philosophy." Among their shared properties, these terms deal with conceptual and abstract entities that, from the Enlightenment at least, have been held to be distinct from the phenomenal world. They also clarify ideas and distinguish one concept from another. Among their different purposes, the object of philosophy is the asking of questions in a search for wisdom or truth whereas theory is formulated for explanatory purposes, especially within the frame of scientific propositions that can be refuted through empirical observations. The tests of philosophy are, therefore, those of symbolic logic evidenced in principles such as [End Page 21] internal consistency, correspondence with evidence (deductive, inductive, or analogical), and coherence within a unity or whole. Although logical criteria may also be important in formulating and testing theory,1 it is tested and refuted primarily through means of qualitative descriptions and quantitative assessments of observable phenomena.Regarding practice, one is also confronted with an ambiguous construct that may be interpreted descriptively (what is done in the phenomenal world or taken to be the general state of affairs) or normatively (what is desirable or ideal). There is also the distinction between the practice of a seasoned performer and practice in the sense of striving towards the mastery of a competent and expert practice. In this regard, Vernon Howard distinguishes between "practice" (or the skills exemplified by proficient or expert performers) and "practise (or acquiring the level of mastery of proficient or expert performance)."2 For him, the ambiguous and paradoxical nature of artistic practice highlights the complexity of degrees of attaining mastery of skills or exemplary practice and the diverse array of skills ranging from habit to critical thinking involved in the practice of any art. Although each practice is distinguished by its own belief systems, rituals, expectations, and commonsense, boundaries between differing practices are sometimes "soft" or fuzzy, as one seeps into another.3 Consequently, it is often difficult to distinguish one from another at the margins where one practice becomes another.DichotomyThe notion of theory and practice as independent or a dichotomous relationship between the phenomenal world on the one hand and the mind and spirit on the other has its roots in the ancient world. For Plato, the world of "appearances," referring to the phenomenal world understood by imagination (eikasia) and belief (pistis), should be distinguished from the higher, abstract "intelligible world" grasped through thinking (dianoia), knowledge (episteme), and intelligence (noesis).4 René Descartes' later bifurcation of the inner and outer worlds and inversion of Platonic values and understandings resulted in the ascendancy of careful and deliberate observation of the phenomenal world over philosophical reflection.5 His ideas helped to set the stage for the Enlightenment and the Industrial, Scientific, and Information Revolutions. Empiricism, science, and technology gradually displaced philosophy as primary ways of knowing the phenomenal world and understanding the nature of mind, human cognition, feeling, and being. Making hard-boundaried distinctions between within and without one's self, the phenomenal world and the world of spiritual things, and theory and practice were important insights. These distinctions provided for limits on the sorts of ways in which truth could be known. Reasoned deliberation [End Page 22] and imaginative thought have particular usefulness in the world of theory while sensory perception and careful observation are especially useful in the phenomenal world of practice. So while the scholar might speculate about phenomena, observational tools are also useful in coming to know and understand them. Reason and observation each have particular strengths, and it ought not be assumed that philosophy or scientific observation... (shrink)

Hierarchical models are commonly used for modelling uncertainty. They arise whenever there is a `correct' or `ideal' uncertainty model but the modeller is uncertain about what it is. Hierarchical models which involve probability distributions are widely used in Bayesian inference. Alternative models which involve possibility distributions have been proposed by several authors, but these models do not have a clear operational meaning. This paper describes a new hierarchical model which is mathematically equivalent to some of the earlier, possibilistic models (...) and also has a simple behavioural interpretation, in terms of betting rates concerning whether or not a decision maker will agree to buy or sell a risky investment for a specified price. We give a representation theorem which shows that any consistent model of this kind can be interpreted as a model for uncertainty about the behaviour of a Bayesian decision maker. We describe how the model can be used to generate buying and selling prices and to make decisions. (shrink)

This article provides a conceptual map of the debate on ideal and non‐ideal theory. It argues that this debate encompasses a number of different questions, which have not been kept sufficiently separate in the literature. In particular, the article distinguishes between the following three interpretations of the ‘ideal vs. non‐ideal theory’ contrast: (i) full compliance vs. partial compliance theory; (ii) utopian vs. realistic theory; (iii) end‐state vs. transitional theory. The article advances critical reflections on each of (...) these sub‐debates, and highlights areas for future research in the field. (shrink)

What are appropriate criteria for assessing a theory of morality? In Ideal Code, Real World, Brad Hooker begins by answering this question, and then argues for a rule-consequentialist theory. According to rule-consequentialism, acts should be assessed morally in terms of impartially justified rules, and rules are impartially justified if and only if the expected overall value of their general internalization is at least as great as for any alternative rules. In the course of developing his rule-consequentialism, Hooker discusses impartiality, (...) well-being, fairness, equality, the question of how the 'general internalization' of rules is to be interpreted by rule-consequentialism, and the main objections to rule-consequentialism. He also discusses the social contract theory of morality, act-consequentialism, and the question of which moral prohibitions and which duties to help others rule-consequentialism endorses. The last part of the book considers the implications of rule-consequentialism for some current controversies in practical ethics. (shrink)

Does rationality require logical omniscience? Our best formal theories of rationality imply that it does, but our ordinary evaluations of rationality seem to suggest otherwise. This paper aims to resolve the tension by arguing that our ordinary evaluations of rationality are not only consistent with the thesis that rationality requires logical omniscience, but also provide a compelling rationale for accepting this thesis in the first place. This paper also defends an account of apriori justification for logical beliefs that is designed (...) to explain the rational requirement of logical omniscience. On this account, apriori justification for beliefs about logic has its source in logical facts, rather than psychological facts about experience, reasoning, or understanding. This account has important consequences for the epistemic role of experience in the logical domain. In a slogan, the epistemic role of experience in the apriori domain is not a justifying role, but rather an enabling and disabling role. (shrink)

It is conventional wisdom among political philosophers that ideal principles of justice must guide our attempts to design institutions to avert actual injustice. Call this the ideal guidance approach. I argue that this view is misguided— ideal principles of justice are not appropriate "guiding principles" that actual institutions must aim to realize, even if only approximately. Fortunately, the conventional wisdom is also avoidable. In this paper, I develop an alternative approach to institutional design, which I call institutional (...) failure analysis. The basic intuition of this approach is that our moral assessment of institutional proposals is most effective when we proceed from a detailed understanding of the causal processes generating problematic social outcomes. Failure analysis takes the institutional primary design task to be obviating or averting institutional failures. Consequently, failure analysis enables theorists to prescribe more effective solutions to actual injustice because its focuses on understanding the injustice, rather than specifying an ideal of justice. (shrink)