We introduce and study several nonstandard representations of Banach-valued operators defined on the space of Bochner integrable functions. They will be less restrictive than the usual standard representation. In particular, without any hypothesis, we shall find a representation whose kernel belongs to a space of “extended Bochner integrable functions”, introduced by Zimmer by using Loeb measures.

Cumulative Prospect Theory is the modern version of Prospect Theory and it is nowadays considered a valid alternative to the classical Expected Utility Theory. Cumulative Prospect theory implies Gain-Loss Separability, i.e., the separate evaluation of losses and gains within a mixed gamble. Recently, some authors have questioned this assumption of the theory, proposing new paradoxes where the Gain-Loss Separability is violated. We present a generalization of Cumulative Prospect Theory which does not imply Gain-Loss Separability and is able to explain the (...) cited paradoxes. On the other hand, the new model, which we call the bipolar Cumulative Prospect Theory, genuinely generalizes the original Prospect Theory of Kahneman and Tversky, preserving the main features of the theory. We present also a characterization of the bipolar Choquet Integral with respect to a bi-capacity in a discrete setting. (shrink)

The second volume of “Advancing Uncertain Combinatorics through Graphization, Hyperization, and Uncertainization: Fuzzy, Neutrosophic, Soft, Rough, and Beyond” presents a deep exploration of the progress in uncertain combinatorics through innovative methodologies like graphization, hyperization, and uncertainization. This volume integrates foundational concepts from fuzzy, neutrosophic, soft, and rough set theory, among others, to further advance the field. Combinatorics and set theory, two central pillars of mathematics, focus on counting, arrangement, and the study of collections under defined rules. Combinatorics excels in handling (...) uncertainty, while set theory has evolved with concepts such as fuzzy and neutrosophic sets, which enable the modeling of complex real-world uncertainties by addressing truth, indeterminacy, and falsehood. These advancements, when combined with graph theory, give rise to novel forms of uncertain sets in "graphized" structures, including hypergraphs and superhypergraphs. Innovations such as Neutrosophic Oversets, Undersets, and Offsets, as well as the Nonstandard Real Set, build upon traditional graph concepts, pushing both theoretical and practical boundaries. The synthesis of combinatorics, set theory, and graph theory in this volume provides a robust framework for addressing the complexities and uncertainties inherent in both mathematical and real-world systems, paving the way for future research and application. In the first chapter, “A Review of the Hierarchy of Plithogenic, Neutrosophic, and Fuzzy Graphs: Survey and Applications”, the authors investigate the interrelationships among various graph classes, including Plithogenic graphs, and explore other related structures. Graph theory, a fundamental branch of mathematics, focuses on networks of nodes and edges, studying their paths, structures, and properties. A Fuzzy Graph extends this concept by assigning a membership degree between 0 and 1 to each edge and vertex, representing the level of uncertainty. The Turiyam Neutrosophic Graph is introduced as an extension of both Neutrosophic and Fuzzy Graphs, while Plithogenic graphs offer a potent method for managing uncertainty. The second chapter, “Review of Some Superhypergraph Classes: Directed, Bidirected, Soft, and Rough”, examines advanced graph structures such as directed superhypergraphs, bidirected hypergraphs, soft superhypergraphs, and rough superhypergraphs. Classical graph classes include undirected graphs, where edges lack orientation, and directed graphs, where edges have specific directions. Recent innovations, including bidirected graphs, have sparked ongoing research and significant advancements in the field. Soft Sets and their extension to Soft Graphs provide a flexible framework for managing uncertainty, while Rough Sets and Rough Graphs address uncertainty by using lower and upper approximations to handle imprecise data. Hypergraphs generalize traditional graphs by allowing edges, or hyperedges, to connect more than two vertices. Superhypergraphs further extend this by allowing both vertices and edges to represent subsets, facilitating the modeling of hierarchical and group-based relationships. The third chapter, “Survey of Intersection Graphs, Fuzzy Graphs, and Neutrosophic Graphs”, explores the intersection graph models within the realms of Fuzzy Graphs, Intuitionistic Fuzzy Graphs, Neutrosophic Graphs, Turiyam Neutrosophic Graphs, and Plithogenic Graphs. The chapter highlights their mathematical properties and interrelationships, reflecting the growing number of graph classes being developed in these areas. Intersection graphs, such as Unit Square Graphs, Circle Graphs, and Ray Intersection Graphs, are crucial for understanding complex graph structures in uncertain environments. The fourth chapter, “Fundamental Computational Problems and Algorithms for SuperHyperGraphs”, addresses optimization problems within the SuperHypergraph framework, such as the SuperHypergraph Partition Problem, Reachability, and Minimum Spanning SuperHypertree. The chapter also adapts classical problems like the Traveling Salesman Problem and the Chinese Postman Problem to the SuperHypergraph context, exploring how hypergraphs, which allow hyperedges to connect more than two vertices, can be used to solve complex hierarchical and relational problems. The fifth chapter, “A Short Note on the Basic Graph Construction Algorithm for Plithogenic Graphs”, delves into algorithms designed for Plithogenic Graphs and Intuitionistic Plithogenic Graphs, analyzing their complexity and validity. Plithogenic Graphs model multi-valued attributes by incorporating membership and contradiction functions, offering a nuanced representation of complex relationships. The sixth chapter, “Short Note of Bunch Graph in Fuzzy, Neutrosophic, and Plithogenic Graphs”, generalizes traditional graph theory by representing nodes as groups (bunches) rather than individual entities. This approach enables the modeling of both competition and collaboration within a network. The chapter explores various uncertain models of bunch graphs, including Fuzzy Graphs, Neutrosophic Graphs, Turiyam Neutrosophic Graphs, and Plithogenic Graphs. In the seventh chapter, “A Reconsideration of Advanced Concepts in Neutrosophic Graphs: Smart, Zero Divisor, Layered, Weak, Semi, and Chemical Graphs”, the authors extend several fuzzy graph classes to Neutrosophic graphs and analyze their properties. Neutrosophic Graphs, a generalization of fuzzy graphs, incorporate degrees of truth, indeterminacy, and falsity to model uncertainty more effectively. The eighth chapter, “Short Note of Even-Hole-Graph for Uncertain Graph”, focuses on Even-Hole-Free and Meyniel Graphs analyzed within the frameworks of Fuzzy, Neutrosophic, Turiyam Neutrosophic, and Plithogenic Graphs. The study investigates the structure of these graphs, with an emphasis on their implications for uncertainty modeling. The ninth chapter, “Survey of Planar and Outerplanar Graphs in Fuzzy and Neutrosophic Graphs”, explores planar and outerplanar graphs, as well as apex graphs, within the contexts of fuzzy, neutrosophic, Turiyam Neutrosophic, and plithogenic graphs. The chapter examines how these types of graphs are used to model uncertain parameters and relationships in mathematical and real-world systems. The tenth chapter, “General Plithogenic Soft Rough Graphs and Some Related Graph Classes”, introduces and explores new concepts such as Turiyam Neutrosophic Soft Graphs and General Plithogenic Soft Graphs. The chapter also examines models of uncertain graphs, including Fuzzy, Intuitionistic Fuzzy, Neutrosophic, and Plithogenic Graphs, all designed to handle uncertainty in diverse contexts. The eleventh chapter, “Survey of Trees, Forests, and Paths in Fuzzy and Neutrosophic Graphs”, provides a comprehensive study of Trees, Forests, and Paths within the framework of Fuzzy and Neutrosophic Graphs. This chapter focuses on classifying and analyzing graph structures like trees and paths in uncertain environments, contributing to the ongoing development of graph theory in the context of uncertainty. (shrink)

In the context of Multiple criteria decision analysis, we present the necessary and sufficient conditions allowing to represent an ordinal preferential information provided by the decision maker by a Choquet integral w.r.t a 2-additive capacity. We provide also a characterization of this type of preferential information by a belief function which can be viewed as a capacity. These characterizations are based on three axioms, namely strict cycle-free preferences and some monotonicity conditions called MOPI and 2-MOPI.

The representational nature of human cognition and thought in general has been a source of controversies. This is particularly so in the context of studies of unconscious cognition, in which representations tend to be ontologically and structurally segregated with regard to their conscious status. However, it appears evolutionarily and developmentally unwarranted to posit such segregations, as,otherwise, artifact structures and ontologies must be concocted to explain them from the viewpoint of the human cognitive architecture. Here, from a by-and-large Classical cognitivist viewpoint, (...) I show why this segregation is wrong, and elaborate on the need to postulate an ontological and structural continuity between unconscious and conscious representations. Specifically, I hypothesize that this continuity is to be found in the symbolic-based interplay between the syntax and the semantics of thought, and I propose a model of human information processing characterized by the integration of syntactic and semantic representations. (shrink)

This book provides an original perspective on the debate about anti-representationalism and the nature of philosophy. This debate has come to prominence in recent years through the work of people like Richard Rorty, Paul Horwich, Huw Price and Amie Thomasson. It is the first book to explicitly consider this well-known pragmatist kind of anti-representationalism in relation to anti-representationalist views in other areas of philosophy, in particular the philosophy of perception and cognitive science. Taking as its point of departure the neo-pragmatism (...) of Rorty and Price, it critiques the way these (and other) thinkers develop, on this basis, a positive view of philosophy and its remit. By examining the debate about representationalism versus anti-representationalism in perception and cognitive science it provides a different way of understanding the significance of neo-pragmatism, as well as providing an independently interesting perspective on these other debates. A central idea in this perspective involves distinguishing between a world-for-us and a world-in-itself, though in a different way from Kant and many other philosophers. The book extends these reflections to examine questions about realism and the limits of metaphysics for anti-representationalist pragmatism, arguing the view can uphold a common sense kind of realism, as well as the value of distinctively philosophical enquiry in metaphysics. (shrink)

The aim of this paper is to explore the connections between semiotics and biology by examining the behaviors of both humans and non-cognizant agents, using Bayesian and heuristic inference. The argument is that higher-level organisms use complex predictive reasoning to deal with uncertainty, while non-cognizant species, such as SARS-CoV-2, rely on an economy-driven heuristic to enter host cells. From this viewpoint, the current pandemic is characterized as a clash of representations resulting from the anthropocentric construction of the self, which neglects (...) the complexities of the natural world. (shrink)

In Cognitive Integration: Attacking The Bounds of Cognition Richard Menary argues that the real pay-off from extended-mind-style arguments is not a new form of externalism in the philosophy of mind, but a view in which the 'internal' and 'external' aspects of cognition are integrated into a whole. Menary argues that the manipulation of external vehicles constitutes cognitive processes and that cognition is hybrid: internal and external processes and vehicles complement one another in the completion of cognitive tasks. However, we cannot (...) make good on these claims without understanding the cognitive norms by which we manipulate bodily external vehicles of cognition. -/- Shaun Gallagher: “Menary sets out some extremely welcome clarifications that help to integrate the models of embodied and extended cognition. He not only provides convincing responses to all of the main objections that have been made against these approaches, he also puts flesh on the integrated model by incorporating concepts such as epistemic action, by expanding the discussion to include a Peircean view of representation, by demonstrating its evolutionary roots, and by exploring its implications for language and cognition. This is one of those books that takes us forward a number of giant steps. Menary makes it comprehensive and comprehensible.” . (shrink)

In Chapter 10, Sandra D. Mitchell addresses the relations between many models that arise from the partiality of representation. She defends the idea that multiple compatible models can be integrated in a way that increases scientific knowledge. To illustrate how her “integrative pluralism” works, she shows how three perspectives on protein folding—the physical, the chemical, and the biological perspective—can “fill out” and correct one another.

Distributed Cognition and Integrational Linguistics have much in common. Both approaches see communicative activity and intelligent behaviour in general as strongly con- text-dependent and action-oriented, and brains as permeated by history. But there is some ten- sion between the two frameworks on three important issues. The majority of theorists of distributed cognition want to maintain some notions of mental representation and computa- tion, and to seek generalizations and patterns in the various ways in which creatures like us couple with (...) technologies, media, and other agents; many also want to offer explanations at subpersonal levels which may undercut the autonomy of personal-level accounts. In contrast, dominant views in integrational linguistics reject all invocation of representation, resist the explanatory search for similarity across contexts and moments, and see linguistics as a lay dis- cipline which should not offer explanations in terms alien to ordinary agents. On each of these issues, I argue that integrationists could move closer to the distributed cognition frame- work without losing the most important aspects of their view: integrationist criticisms of mainstream or classical theories can be respected while alliances with revised cognitivist views about representation, context, and explanation are developed. Ó 2004 Elsevier Ltd. All rights reserved. (shrink)

In this paper we argue for an integrated inferential conception about theories and representations and its role in accounting for the theoretical value of philosophically disregarded representational practices, such as the systematic use of phase space diagrams within the theoretical context of statistical mechanics. This proposal would rely on both inferentialism about scientific representations (Suárez 2004) and inferentialism about particular physical theories (Wallace 2017). We defend that both perspectives somehow converge into an integrated inferentialism by means of the thesis theories (...) as being composed of representations, as defended from the representational semantic conception defended by Suárez and Pero (2019). (shrink)

I will sketch, but not argue for here, a hypothesis about its origins and structure. What philosophers think of as folk psychology has dual origins. One is a genuine "intuitive psychology." This is an evolved predictive tool seen also in some nonhuman animals and very young children. It is "peripheral" in what it recognizes and describes. Primarily, it recognizes seeing and acting (including trying) as activities of others. This is common element in how human and non-human animals deal with each (...) other. The full folk psychology that we are familiar with in philosophical discussion also includes a model of psychological interactions within the periphery. This model is based perhaps on discourse, the exchange of sentences in public – roughly as Wilfrid Sellars suggested many years ago. This part of folk psychology, unlike the first, might be expected to show some cultural variation. The resulting framework might be fine for describing certain kinds of human thought, but it is problematic when applied more generally. (shrink)

The paper introduces an extension of the proposal according to which conceptual representations in cognitive agents should be intended as heterogeneous proxytypes. The main contribution of this paper is in that it details how to reconcile, under a heterogeneous representational perspective, different theories of typicality about conceptual representation and reasoning. In particular, it provides a novel theoretical hypothesis - as well as a novel categorization algorithm called DELTA - showing how to integrate the representational and reasoning assumptions of the (...) theory-theory of concepts with the those ascribed to the prototype and exemplars-based theories. (shrink)

This paper discusses cross-border projects and their respective social representations to local groups. We present as a case study the boatmen who pilot their boats between Brazil and France on the construction of the Binational Bridge. Catraieiros are currently responsible for much of the logistics between Amapá and French Guiana. Our theoretical framework is based on the literature on Regional Integration and Social Representation. We applied interviews to one third of the catraieiros. We concluded that in the Subject-Representation-Object (...) relationship, the group that understood itself as responsible for the dialogue between two cities built a negative and threatening representation on the Bridge. (shrink)

I assess the conditions that philosophers of mind usually use to identify mental representations. I argue in favor of a minimal definition of mental representation, which is similar to definitions endorsed by some philosophers of embodied cognition. I claim that, even if we endorse this minimal definition of mental representation, important aspects of perception cannot be explained in representational terms. Therefore I suggest endorsing a non-representational approach to perception made of a combination of the enactive approach and ecological (...) psychology and claim that perception is a direct relation to opportunities for action offered by perceptual niches. (shrink)

We prove a nonstandard density result. It asserts that if a particular formula is true for functions in a set K of linear continuous functions between Banach spaces E and D, then it remains valid for functions that are limits, in the uniform convergence topology on a given class ℳ of subsets of E, of nets of vectors in K. We then apply this result to various class ℳ and setsK in the context of E-valued Bochner integrable functions defined (...) on a finite measure space. (shrink)

Barresi & Moore contrast two theories of autism: (1) in autism there is a general inability to integrate first and third person information (of any kind), and (2) in autism there is a specific inability to represent an agent's perceptual or volitional mental state being about another agents mental state. Two lines of experimental evidence suggest that the first of these is too broad, favoring instead the more specific “theory of mind” account.

Redner (politics, Monash U., Melbourne, Australia) builds on the thesis that crucial changes in human cultural history correlate with fundamental transformations in modes of representation. He traces human development from primitive culture to that of the present age to construct a comprehensive theory of culture. His theory challenges some established approaches in disciplines such as philosophy, semiotics, sociology, political theory, aesthetics, and history itself. Annotation copyright by Book News, Inc., Portland, OR.

MV-algebras stand for the many-valued Łukasiewicz logic the same as Boolean algebras for the classical logic. States on MV-algebras were first mentioned [20] in probability theory and later also introduced in effort to capture a notion of `an average truth-value of proposition' [15] in Łukasiewicz many-valued logic. In the presented paper, an integral representation theorem for finitely-additive states on semisimple MV-algebra will be proven. Further, we shall prove extension theorems concerning states defined on sub-MV-algebras and normal partitions of (...) unity generalizing in this way the well-known Horn-Tarski theorem for Boolean algebras. (shrink)

The search for understanding is a major aim of science. Traditionally, understanding has been undervalued in the philosophy of science because of its psychological underpinnings; nowadays, however, it is widely recognized that epistemology cannot be divorced from psychology as sharp as traditional epistemology required. This eliminates the main obstacle to give scientific understanding due attention in philosophy of science. My aim in this paper is to describe an account of scientific understanding as an emergent feature of our mastering of different (...) (causal) explanatory frameworks that takes place through the mastering of scientific practices. Different practices lead to different kinds of representations. Such representations are often heterogeneous. The integration of such representations constitute understanding. (shrink)

Any theory of information needs to comply with what we call the implementation, formalization, and representation constraints. These constraints are justified by basic considerations concerning scientific modelling and methodology. In the first part of this paper, we argue that the implementation and formalization constraints cannot be satisfied because the relation between Shannon information and IIT must be clarified. In the second part of the paper, we focus on the representation constraint. We argue that IIT cannot succeed in satisfying (...) this constraint for semantic contents without offering models for concepts, conceptual roles, and context sensitivity. In the final part of the paper, further complications are raised with respect to the distinction between consciousness and attention, which apply more specifically to the representation constraint. We conclude with some recommendations as to how IIT may succeed in solving these problems, highlighting the advantages and enormous potential of IIT as a scientific theory. (shrink)

Representation is integral to the functioning and legitimacy of modern government. Yet political theorists have often been reluctant to engage directly with questions of representation, and empirical political scientists have closed down such questions by making representation synonymous with congruence. Conceptually unproblematic and normatively inert for some, representation has been deemed impossible to pin down analytically and to defend normatively by others. But this is changing. Political theorists are now turning to political representation as (...) a subject worthy of theoretical investigation in its own right. In their effort to rework the theory of political representation, they are also hoping to impact how representation is assessed and studied empirically. This volume gathers together chapters by key contributors to what amounts to a "representative turn" in political theory. Their approaches and emphases are diverse, but taken together they represent a compelling and original attempt at re-conceptualizing political representation and critically assessing the main theoretical and political implications following from this, namely for how we conceive and assess representative democracy. Each contributor is invited to look back and ahead on the transformations to democratic self-government introduced by the theory and practice of political representation. Representation and democracy: outright conflict, uneasy cohabitation, or reciprocal constitutiveness? For those who think democracy would be better without representation, this volume is a must-read: it will question their assumptions, while also exploring some of the reasons for their discomfort. Reclaiming Representation is essential reading for scholars and graduate researchers committed to staying on top of new developments in the field. (shrink)

Let Uq be the quantum group associated to sl2 with char≠2 and qk not a root of unity. The article is devoted to the model-theoretic study of the quantum plane kq[x,y], considered as an -structure, where is the language of representations of Uq. It is proved that the lattice of definable k-subspaces of kq[x,y] is complemented. This is deduced from the same result for the Uq-module M, which is defined to be the direct sum of all finite dimensional representations of (...) Uq. It follows that the ring of definable scalars for the quantum plane is a von Neumann regular epimorphic ring extension of the quantum group Uq. (shrink)

Choquet integrals and capacities play a crucial role in modern decision theory. Comonotony is a central concept for these theories because the main property of a Choquet integral is its additivity for comonotone functions. We consider a Choquet integral representation of preferences showing uncertainty aversion (pessimism) and propose axioms on time consistency which yield a candidate for conditional Choquet integrals. An other axiom characterizes the role of comonotony in the use of information. We obtain two conditioning rules (...) for capacities which amount to the well-known Bayes' and Dempster–Schafer's updating rules. We are allowed to interpret both of them as a lack of confidence in information in a dynamic extension of pessimism. (shrink)

The present study evaluates the cognitive representation of a kicking movement performed by a human and a humanoid robot, and how they are represented in experts and novices of soccer and robotics, respectively. To learn about the expertise-dependent development of memory structures, we compared the representation structures of soccer experts and robot experts concerning a human and humanoid robot kicking movement. We found different cognitive representation structures for both expertise groups under two different motor performance conditions . (...) In general, the expertise relies on the perceptual-motor knowledge of the human motor system. Thus, the soccer experts’ cognitive representation of the humanoid robot movement is dominated by their representation of the corresponding human movement. Additionally, our results suggest that robot experts, in contrast to soccer experts, access functional features of the technical system of the humanoid robot in addition to their perceptual-motor knowledge about the human motor system. Thus, their perceptual-motor and neuro-functional machine representation are integrated into a cognitive representation of the humanoid robot movement. (shrink)

In this paper, we defend a novel, multidimensional account of representational unification, which we distinguish from integration. The dimensions of unity are simplicity, generality and scope, non-monstrosity, and systematization. In our account, unification is a graded property. The account is used to investigate the issue of how research traditions contribute to representational unification, focusing on embodied cognition in cognitive science. Embodied cognition contributes to unification even if it fails to offer a grand unification of cognitive science. The study of this (...) failure shows that unification, contrary to what defenders of mechanistic explanation claim, is an important mechanistic virtue of research traditions. (shrink)

Recent advances in the field of statistical learning have established that learners are able to track regularities of multimodal stimuli, yet it is unknown whether the statistical computations are performed on integrated representations or on separate, unimodal representations. In the present study, we investigated the ability of adults to integrate audio and visual input during statistical learning. We presented learners with a speech stream synchronized with a video of a speaker’s face. In the critical condition, the visual (e.g. /gi/) and (...) auditory (e.g. /mi/) signals were occasionally incongruent, which we predicted would produce the McGurk illusion, resulting in the perception of an audiovisual syllable (e.g. /ni/). In this way, we used the McGurk illusion to manipulate the underlying statistical structure of the speech streams, such that perception of these illusory syllables facilitated participants’ ability to segment the speech stream. Our results therefore demonstrate that participants can integrate audio and visual input to perceive the McGurk illusion during statistical learning. We interpret our findings as support for modality-interactive accounts of statistical learning. (shrink)