In topological spaces, the relation of extended contact is a ternary relation that holds between regular closed subsets A, B and D if the intersection of A and B is included in D. The algebraic counterpart of this mereotopological relation is the notion of extended contact algebra which is a Boolean algebra extended with a ternary relation. In this paper, we are interested in the relational representation theory for extended contact algebras. In this respect, we study the correspondences between (...) point-free and point-based models of space in terms of extended contact. More precisely, we prove new representation theorems for extended contact algebras. (shrink)

This paper argues that Amartya Sen’s comparative approach to justice requires a politics that is attentive to the agency of the other. Rethinking representation as a relational, rather than a sovereign, concept captures the relationship between agency and justice that is emerging in global politics today. It is increasingly common that non-governmental actors engage with communities through practices of trust and responsibility without appeal to political authority. Relational representation helps clarify the dynamics of these relationships and provides a (...) way to think about their purpose. That purpose is to effect changes that ameliorate suffering and injustice, working to re-present the represented persons as more capable persons, more free to use their agency. (shrink)

In this work, we study the relational representation of the class of Tarski algebras endowed with a subordination, called subordination Tarski algebras. These structures were introduced in a previous paper as a generalisation of subordination Boolean algebras. We define the subordination Tarski spaces as topological spaces with a fixed basis endowed with a closed relation. We prove that there exist categorical dualities between categories whose objects are subordination Tarski algebras and categories whose objects are subordination Tarski spaces. These results (...) extend the known dualities for modal algebras. Finally, we are going to characterise some algebraic conditions written in the quasi-modal language by means of first-order conditions. (shrink)

This work is part of a wider investigation into lattice-structured algebras and associated dual representations obtained via the methodology of canonical extensions. To this end, here we study lattices, not necessarily distributive, with negation operations. We consider equational classes of lattices equipped with a negation operation ¬ which is dually self-adjoint (the pair (¬,¬) is a Galois connection) and other axioms are added so as to give classes of lattices in which the negation is De Morgan, orthonegation, antilogism, pseudocomplementation (...) or weak pseudocomplementation. These classes are shown to be canonical and dual relational structures are given in a generalized Kripke-style. The fact that the negation is dually self-adjoint plays an important role here, as it implies that it sends arbitrary joins to meets and that will allow us to define the dual structures in a uniform way. (shrink)

The success of models of human behavior based on Bayesian inference over logical formulas or programs is taken as evidence that people employ a “language-of-thought” that has similarly discrete and compositional structure. We argue that this conclusion problematically crosses levels of analysis, identifying representations at the algorithmic level based on inductive biases at the computational level.

According to Bastin et al.’s integrative memory model, familiarity may be attributed to both entity representations and relational representations. However, the model does not specify what triggers familiarity for relational representations. I argue that fluency is a key player in the attribution of familiarity regardless of the type of representation. Two lines of evidence are reviewed in support of my claim.

InReference and Consciousness,1John Campbell attempts to a make a case that what he calls ‘the Relational View’ of visual experience, a view that he champions, is superior to what he calls ‘the Representational View’.2I argue that his attempt fails. In section 1, I spell out the two views. In section 2, I outline Campbell's case that the Relational View is superior to the Representational View and offer a diagnosis of where Campbell goes wrong. In section 3, I examine (...) the case in detail and argue that it fails. Finally, in section 4, I mention two very well-known problems for the Relational View that are unresolved in the book. (shrink)

The concept of innateness is used to make inferences between various better-understood properties, like developmental canalization, evolutionary adaptation, heritability, species-typicality, and so on (‘innateness-related properties’). This article uses a recently-developed account of the representational content carried by inheritance systems like the genome to explain why innateness-related properties cluster together, especially in non-human organisms. Although inferences between innateness-related properties are deductively invalid, and lead to false conclusions in many actual cases, where some aspect of a phenotypic trait develops in reliance on (...) a genetic representation it will tend, better than chance, to have many of the innateness-related properties. The account also shows why inferences between innateness-related properties sometimes fail and argues that such inferences are especially misleading when applied to human psychology and behaviour because human psychological development is especially reliant on non-genetic inherited representations. (shrink)

This paper is about the good side of modal logic, the bad side of modal logic, and how hybrid logic takes the good and fixes the bad.In essence, modal logic is a simple formalism for working with relational structures . But modal logic has no mechanism for referring to or reasoning about the individual nodes in such structures, and this lessens its effectiveness as a representation formalism. In their simplest form, hybrid logics are upgraded modal logics in which reference (...) to individual nodes is possible.But hybrid logic is a rather unusual modal upgrade. It pushes one simple idea as far as it will go: represent all information as formulas. This turns out to be the key needed to draw together a surprisingly diverse range of work . Moreover, it displays a number of knowledge representation issues in a new light, notably the importance of sorting. (shrink)

Any dynamic decision model should be based on conditional objects and must refer to (not necessarily structured) domains containing only the elements and the information of interest. We characterize binary relations, defined on an arbitrary set of conditional events, which are representable by a coherent generalized decomposable conditional measure and we study, in particular, the case of binary relations representable by a coherent conditional probability.

One oft the most fascinating abilities of humans is the ability to become conscious of the own physical and mental states. In this systematic investigation of self-consciousness, a representational theory is developed that is able to distinguish between different levels of self-consciousness. The most basic levels are already present in such simple animals as ants. From these basic forms, which are also relevant for adult human self-consciousness, high-level self-consciousness including self-knowledge can arise. Thereby, the theory is not only able to (...) integrate developmental considerations but also to sharply distinguish different aspects of the complex phenomenon self-consciousness. Pathological breakdowns of these different aspects, as they can be found in schizophrenia, are explained by specific impairments on different levels of self-representation. In this way, the work shows that a naturalistic theory of self-consciousness is possible, if the analysis starts with very simple and basic mechanisms instead of starting on the »top of the iceberg«. (shrink)

We analyze the representation of binary relations in general, and in particular of functions and of total antisymmetric relations, in monadic third order logic, that is, the simple typed theory of sets with three types. We show that there is no general representation of functions or of total antisymmetric relations in this theory. We present partial representations of functions and of total antisymmetric relations which work for large classes of these relations, and show that there is an adequate representation (...) of cardinality in this theory. The relation of our work to similar work by Henrard and Allen Hazen is discussed. This work can be understood as part of a program of assessing the capabilities of weak logical frameworks: our results are applicable for example, to the framework in David Lewis’s Parts of Classes. (shrink)

One of the main tools in the study of nonmonotonic consequence relations is the representation of such relations in terms of preferential models. In this paper we give an unified and simpler framework to obtain such representation theorems.

Recent research in numerical cognition has begun to systematically detail the ability of humans and nonhuman animals to perceive the magnitudes of nonsymbolic ratios. These relationally defined analogs to rational numbers offer new potential insights into the nature of human numerical processing. However, research into their similarities with and connections to symbolic numbers remains in its infancy. The current research aims to further explore these similarities by investigating whether the magnitudes of nonsymbolic ratios are associated with space just as symbolic (...) numbers are. In two experiments, we found that responses were faster on the left for smaller nonsymbolic ratio magnitudes and faster on the right for larger nonsymbolic ratio magnitudes. These results further elucidate the nature of nonsymbolic ratio processing, extending the literature of spatial–numerical associations to nonsymbolic relative magnitudes. We discuss potential implications of these findings for theories of human magnitude processing in general and how this general processing relates to numerical processing. (shrink)

Cet article se base sur des résultats d’enquête récents montrant que, chez des adolescents marocains âgés de dix à dix-huit ans, les manifestations de pensée critique dialogique se si-tuent majoritairement dans une « perspective épistémologique » appelée « relativisme » par un modèle développemental élaboré dans les quinze dernières années avec la méthode de la théorie ancrée. Pour comprendre ces résultats de recherche, qui contrastent avec ceux obte-nus auprès d’adolescents québécois et français appartenant aux mêmes groupes d’âge, nous décrivons, dans (...) un premier temps, le modèle développemental dans lequel ils prennent sens. Nous illustrons ensuite les manifestations de « perspective épistémologique relativiste » chez les adolescents marocains à l’aide d’extraits de verbatim. Les élèves ont tendance à se décen-trer de leur vécu personnel, à se représenter le point de vue d’autrui en général et à co-construire des points de vue convergents avec les pairs. Dans un deuxième temps, prenant appui sur une approche de la représentation sociale en tant que « scène », et sur la littérature touchant aux rôles des aînés dans les sociétés africaines, nous éclairons ces résultats de re-cherche par l’analyse d’une représentation sociale fréquemment mobilisée par les jeunes Ma-rocains interviewés : celle de la hiérarchie des âges et du devoir d’écoute envers les plus âgés. L’analyse de cette « scène » met en lumière des attitudes sociales inculquées aux adolescents en contexte culturel marocain, susceptibles de favoriser le développement d’une « perspective épistémologique relativiste » en matière de pensée critique dialogique. (shrink)

There are eighteen isomorphism types of finite relation algebras with eight or fewer elements, and all of them are representable. We determine all the cardinalities of sets on which these algebras have representations.

I develop an account of how mathematized theories in physics represent physical systems, in response to the frequent claim that any such account must presuppose a non-mathematized, and usually linguistic, description of the system represented. The account I develop contains a circularity, in that representation is a mathematical relation between the models of a theory and the system as represented by some other model --- but I argue that this circularity is not vicious, in any case refers in linguistic accounts (...) of meaning and representation, and is simply a consequence of the fact that we have no unmediated, representation-independent access to the world. (shrink)

We show, for any ordinal γ ≥ 3, that the class RaCAγ is pseudo-elementary and has a recursively enumerable elementary theory. ScK denotes the class of strong subalgebras of members of the class K. We devise games, Fⁿ (3 ≤ n ≤ ω), G, H, and show, for an atomic relation algebra A with countably many atoms, that Ǝ has a winning strategy in Fω(At(A)) ⇔ A ∈ ScRaCAω, Ǝ has a winning strategy in Fⁿ(At(A)) ⇐ A ∈ ScRaCAn, Ǝ (...) has a winning strategy in G(At(A)) ⇐ A ∈ RaCAω, Ǝ has a winning strategy in H(At(A)) ⇒ A ∈ RaRCAω for 3 ≤ n < ω. We use these games to show, for γ ≥ 5 and any class K of relation algebras satisfying RaRCAγ ⊆ K ⊆ ScRaCA₅, that K is not closed under subalgebras and is not elementary. For infinite γ, the inclusion RaCAγ ⊂ ScRaCAγ is strict. For infinite γ and for a countable relation algebra A we show that A has a complete representation if and only if A is atomic and Ǝ has a winning strategy in F(At(A)) if and only if A is atomic and A ∈ ScRaCAγ. (shrink)

This study aims to resolve contradictory conclusions on the relative importance of lexical and syntactic knowledge in second language (L2) listening with evidence from academic English. It was hypothesized that when lexical and syntactic knowledge is measured in auditory receptive tasks contextualized in natural discourse, the measures will be more relevant to L2 listening, so that both lexical and syntactic knowledge will have unique contributions to L2 listening. To test this hypothesis, a quantitative study was designed, in which lexical and (...) syntactic knowledge was measured via partial dictation, an auditory receptive task contextualized in a discourse context. Academic English listening was measured via a retired IELTS listening test. A group of 258 college-level native Chinese learners of English completed these tasks. Pearson correlations showed that both lexical and syntactic measures correlated strongly with English listening (r =.77 and r =.67 respectively). Hierarchical regression analyses showed that both measures jointly explained 62% of the variance in the listening score and that each measure had its unique contribution. These results demonstrated the importance of considering construct representation substantially and using measures that well reflect constructs in practical research. (shrink)

This introduction to the philosophy of social psychological science repudiates traditional empiricist and hermeneutical accounts, advancing instead a realist philosophy that stresses the social dimensions of mind and action.

It is known that for all finite n ≥ 5, there are relation algebras with n-dimensional relational bases but no weak representations. We prove that conversely, there are finite weakly representable relation algebras with no n-dimensional relational bases. In symbols: neither of the classes RA n and wRRA contains the other.

Extending a construction of Andreka, Givant, and Nemeti (2019), we construct some finite vector spaces and use them to build finite non-representable relation algebras. They are simple, measurable, and persistently finite, and they validate arbitrary finite sets of equations that are valid in the variety RRA of representable relation algebras. It follows that there is no finitely axiomatisable class of relation algebras that contains RRA and validates every equation that is both valid in RRA and preserved by completions of relation (...) algebras. Consequently, the variety generated by the completions of representable relation algebras is not finitely axiomatisable. This answers a question of Maddux (2018). (shrink)

It is shown that the automorphism group of a relation algebra ${\cal B}_P$ constructed from a projective geometry P is isomorphic to the collineation group of P. Also, the base automorphism group of a representation of ${\cal B}_P$ over an affine geometry D is isomorphic to the quotient of the collineation group of D by the dilatation subgroup. Consequently, the total number of inequivalent representations of ${\cal B}_P$ , for finite geometries P, is the sum of the numbers ${\mid (...) Col(P)\mid\over {\mid Col(D)\mid/\mid Dil(D)\mid}}$ where D ranges over a list of the non-isomorphic affine geometries having P as their geometry at infinity. This formula is used to compute the number of inequivalent representations of relation algebras constructed over projective lines of order at most 10. For instance, the relation algebra constructed over the projective line of order 9 has 56,700 mutually inequivalent representations. (shrink)

This paper tries to meet the three basic constraints in the metaphysics of perception—that, following Schellenberg, I call here the particularity constraint, the indistinguishable constraint, and the phenomenological constraint—by putting forward a new combination of the two well-known contradictory views in this field: the relational view and the content view. Following other compatibilists, I do think that it is possible to reconcile the two views, recognizing that experience has both a relational and a representational dimension. However, in opposition (...) to the current ways of combining these two views, I reject the idea of gappy contents. Instead, my proposal is builds on Lewis’s famous semantic, according to which the content of sentences is best modeled as complex functions from context-index pairs to truth-values. In conformity with the content view, I want to suggest that perceptual experiences do represent complex properties or complex functions that are either veridical or falsidical of particulars in contexts and indexes. In this relativist framework, I can also accommodate the relational claim that our experience of particulars must be understood as a fundamental cognitive relation rather than as a representation. In this way, particulars also play a key role in individuating perceptual experiences. Two token experiences, e and e′, are different when one of the following conditions is met: first, if two different particulars, a and a′, are causally responsible for the token experiences e and e′, respectively, regardless of the time and location in which the perceptual experiences take place; second, if the same particular a, which is causally responsible for both e and e′, is either located in a different place or is in the same location but at a different time. (shrink)

According to the Computational/Representational Theory of Thought (CRTT ? Language of Thought Hypothesis, or LOTH), propositional attitudes, such as belief, desire, and the like, are triadic relations among subjects, propositions, and internal mental representations. These representations form a representational _system_ physically realized in the brain of sufficiently sophisticated cognitive organisms. Further, this system of representations has a combinatorial syntax and semantics, but the processes that operate on the representations are causally sensitive only to their syntax, not (...) to their semantics. On this approach, a first pass account of propositional attitudes is the following (cf. Field 1978: 37 and Fodor 1987: 17). (shrink)

Brief overview of the debates held in the workshop on scientific representation, in Prague, May 2018.

We want to highlight the strong link between learning systems such as deep learning neural networks and neutrosophy. The latter is above all a representation considering a neutral state which is at the heart of many phenomena of reality as well as mathematical and information theories. Here, we start from the recent understanding of neural networks, which considers their internal functioning and the learning that characterizes them as based on adapted representations (both of the information to be processed and (...) of the task to be performed) that are in fact optimal compressions. Compression means discriminating the similar and the different between cases by identifying representative characteristics through focusing on the most significant and rejecting of the rest. These three operations of neural processing, learning and compression owe their existence to non-linear treatments which essentially amount to distinguishing a neutral zone between two filtered zones, corresponding to the neutrosophical approach. (shrink)

Word in noise identification is facilitated by acoustic differences between target and competing sounds and temporal separation between the onset of the masker and that of the target. Younger and older adults are able to take advantage of onset delay when the masker is dissimilar to the target word, but only younger adults are able to do so when the masker is similar. We examined the neural underpinning of this age difference using cortical evoked responses to words masked by either (...) Babble or Noise when the masker preceded the target word by 100 or 600 ms in younger and older adults, after adjusting the signal-to-noise ratios to equate behavioural performance across age groups and conditions. For the 100 ms onset delay, the word in noise elicited an acoustic change complex response that was comparable in younger and older adults. For the 600 ms onset delay, the ACC was modulated by both masker type and age. In older adults, the ACC to a word in babble was not affected by the increase in onset delay whereas younger adults showed a benefit from longer delays. Hence, the age difference in sensitivity to temporal delay is indexed by early activity in the auditory cortex. These results are consistent with the hypothesis that an increase in onset delay improves stream segregation in younger adults in both noise and babble, but only in noise for older adults and that this change in stream segregation is evident in early cortical processes. (shrink)

Durante la Revolución Francesa, el trabajo político del "lado izquierdo", del cual Robespierre fue uno de los portavoces, consistió en implementar los principios de la Declaración de los Derechos del Hombre y del Ciudadano. Esto implica que el pueblo soberano puede controlar el ejercicio del poder de sus agentes. Su función es garantizar el derecho natural del hombre a la existencia, que es la condición principal de la libertad y la razón de ser de la república. During the French Revolution, (...) the political work of the "left side", of which Robespierre was one of the spokespersons, consisted in implementing the principles of the Declaration of the Rights of Man and of the Citizen. These imply that the sovereign people can control the exercise of the power of their agents. Their function is to guarantee the natural right of man to existence which is the main condition of freedom and the raison d'être of the republic. (shrink)