Many debates in philosophy focus on whether folk or scientific psychological notions pick out cognitive natural kinds. Examples include memory, emotions and concepts. A potentially interesting type of kind is: kinds of mental representations (as opposed, for example, to kinds of psychological faculties). In this chapter we outline a proposal for a theory of representational kinds in cognitive science. We argue that the explanatory role of representational kinds in scientific theories, in conjunction with a mainstream approach to explanation in (...) cognitive science, suggest that representational kinds are multi-level. This is to say that representational kinds’ properties cluster at different levels of explanation and allow for intra- and inter-level projections. (shrink)

Starting from a recent paper by S. Kaufmann, we introduce a notion of conjunction of two conditional events and then we analyze it in the setting of coherence. We give a representation of the conjoined conditional and we show that this new object is a conditional random quantity, whose set of possible values normally contains the probabilities assessed for the two conditional events. We examine some cases of logical dependencies, where the conjunction is a conditional event; moreover, we give the (...) lower and upper bounds on the conjunction. We also examine an apparent paradox concerning stochastic independence which can actually be explained in terms of uncorrelation. We briefly introduce the notions of disjunction and iterated conditioning and we show that the usual probabilistic properties still hold. (shrink)

We study the variety generated by the three-element equivalential algebra with conjunction on the dense elements. We prove the representation theorem which let us construct the free algebras in this variety.

Is the mechanism behind presupposition projection and filtering fundamentally asymmetric or symmetric? This is a foundational question for the theory of presupposition which has been at the centre of attention in recent literature. It also bears on broader issues concerning the source of asymmetries observed in natural language: are these simply rooted in superficial asymmetries of language use ; or are they, at least in part, directly encoded in linguistic knowledge and representations? In this paper we aim to make (...) progress on these questions by exploring presupposition projection across conjunction, which has traditionally been taken as a central piece of evidence that presupposition filtering is asymmetric in general. As a number of authors have recently pointed out, however, the evidence which has typically been used to support this conclusion is muddied by independent issues concerning redundancy; additional concerns have to do with the possibility of local accommodation. We report on a series of experiments, building on previous work by Chemla and Schlenker :177–226, 2012 and Schwarz 2015), using inference and acceptability tasks, which aim to control for both of these potential confounds. In our results, we find strong evidence for left-to-right filtering across conjunctions, but no evidence for right-to-left filtering—even when right-to-left filtering would, if available, rescue an otherwise unacceptable sentence. These results suggest that presupposition filtering across conjunction is asymmetric, contra suggestions in the recent literature :157–212, 2008a.), and pave the way for the investigation of further questions about the nature of this asymmetry and presupposition projection more generally. Our results also have broader implications for the study of presupposition: we find important differences in the verdicts of acceptability versus inference tasks in testing for projected content, which has both methodological ramifications for the question of how to distinguish presupposed content, and theoretical repercussions for understanding the nature of projection and presuppositions more generally. (shrink)

Recent work in defence of direct realism has concentrated on the representationalist and disjunctivist responses to the arguments from illusion and hallucination, whilst relatively little attention has been given to the argument from causation which has been dismissed lightly as irrelevant or confused. However such charges arise from an ambiguity in the thesis which is being defended and the failure to distinguish between metaphysical and epistemological issues and between factual and conceptual claims. The argument from causation, as an argument against (...) the conjunction of metaphysical direct realism and an explanation of the perceptual process in terms of a naturalistically understood causal chain of events, has not been answered in the philosophical literature. Moreover when the process of perception is fleshed out in terms of contemporary cognitive science, the difficulties are compounded. Neither representation-friendly mainstream cognitive science, nor representation-averse radical embodied cognitive science, is compatible with a theory of perception which is at the same time both direct and robustly realist. (shrink)

If possible worlds are conjunctions of states of affairs, as in David Armstrong’s combinatorial theory, then is the empty world to be thought of as the null conjunction of states of affairs? The proposal seems plausible, and has received support from David Efird, Tom Stoneham, and Armstrong himself. However, in this paper, it is argued that the proposal faces a trilemma: either it leads to the absurd conclusion that the actual world is empty; or it reduces to a familiar representation (...) of the empty world in which the concept of a null conjunction plays no role; or it needs to make room for the null individual of certain non-classical mereologies. (shrink)

Is the basic mechanism behind presupposition projection fundamentally asymmetric or symmetric? This is a basic question for the theory of presupposition, which also bears on broader issues concerning the source of asymmetries observed in natural language: are these simply rooted in superficial asymmetries of language use— language use unfolds in time, which we experience as fundamentally asymmetric— or can they be, at least in part, directly referenced in linguistic knowledge and representations? In this paper we aim to make progress (...) on these questions by exploring presupposition projection across conjunction, which has typically been taken as a central piece of evidence that presupposition projection is asymmetric. As a number of authors have recently pointed out, however, whether or not this conclusion is warranted is not clear once we take into account independent issues of redundancy. Building on previous work by Chemla & Schlenker (2012) and Schwarz (2015), we approach this question experimentally by using an inference task which controls for redundancy and presupposition suspension. We find strong evidence for left-to-right filtering across conjunctions, but no evidence for right-to-left filtering, suggesting that, at least as a default, presupposition projection across conjunction is indeed asymmetric. (shrink)

The causal and simulation theories are often presented as very distinct views about declarative memory, their major difference lying on the causal condition. The causal theory states that remembering involves an accurate representation causally connected to an earlier experience. In the simulation theory, remembering involves an accurate representation generated by a reliable memory process. I investigate how to construe detailed versions of these theories that correctly classify memory errors as misremembering or confabulation. Neither causalists nor simulationists have paid attention to (...) memory-conjunction errors, which is unfortunate because both theories have problems with these cases. The source of the difficulty is the background assumption that an act of remembering has one target. I fix these theories for those cases. The resulting versions are closely related when implemented using tools of information theory, differing only on how memory transmits information about the past. The implementation provides us with insights about the distinction between confabulatory and non-confabulatory memory, where memory-conjunction errors have a privileged position. (shrink)

Is the mechanism behind presupposition projection and filtering fundamentally asymmetric or symmetric? This is a foundational question for the theory of presupposition which has been at the centre of attention in recent literature :287–316, 2008b. https://doi.org/10.1515/THLI.2008.021, Semant Pragmat 2:1–78, 2009. https://doi.org/10.3765/sp.2.3; Rothschild in Semant Pragmat 4:1–43, 2011/2015. https://doi.org/10.3765/sp.4.3 a.o.). It also bears on broader issues concerning the source of asymmetries observed in natural language: are these simply rooted in superficial asymmetries of language use ; or are they, at least in (...) part, directly encoded in linguistic knowledge and representations? In this paper we aim to make progress on these questions by exploring presupposition projection across conjunction, which has traditionally been taken as a central piece of evidence that presupposition filtering is asymmetric in general. As a number of authors have recently pointed out, however, the evidence which has typically been used to support this conclusion is muddied by independent issues concerning redundancy; additional concerns have to do with the possibility of local accommodation. We report on a series of experiments, building on previous work by Chemla and Schlenker :177–226, 2012. https://doi.org/10.1007/s11050-012-9080-7) and Schwarz Experimental perspectives on presuppositions, Springer, Cham, 2015), using inference and acceptability tasks, which aim to control for both of these potential confounds. In our results, we find strong evidence for left-to-right filtering across conjunctions, but no evidence for right-to-left filtering—even when right-to-left filtering would, if available, rescue an otherwise unacceptable sentence. These results suggest that presupposition filtering across conjunction is asymmetric, contra suggestions in the recent literature :157–212, 2008a. https://doi.org/10.1515/THLI.2008.013, 2009 a.o.), and pave the way for the investigation of further questions about the nature of this asymmetry and presupposition projection more generally. Our results also have broader implications for the study of presupposition: we find important differences in the verdicts of acceptability versus inference tasks in testing for projected content, which has both methodological ramifications for the question of how to distinguish presupposed content, and theoretical repercussions for understanding the nature of projection and presuppositions more generally. (shrink)

In this paper we shall give a characterization of D-algebras in terms of lattice ordered abelian groups. To make this paper self-contained we shall recall some notations from [4]. The symbols !; ^; _; serve as implication, conjunction, disjunction, and negation, respectively. By D we mean a set of connectives from the list above containing the implication connective !. By a D-formula we mean a formula built up in a usual way from an innite set of the propositional variables and (...) connectives from D. (shrink)

The pushmi-pullyu representation is a non-conjunctive representation with both descriptive and directive contents. Introduced by Millikan, the PPR is supposed to aid in explaining how organisms adapt behavior to environmental variance in the absence of intermediate inference. Until recently, it has led an uncontroversial theoretical life. However, Artiga has suggested that the PPR postulate conflicts with Millikan-style teleosemantics and, as a consequence, the PPR postulate should probably be set aside. I suggest here that the theoretical motivations for the PPR (...) are independent of any specific theory of naturalized content. If Artiga is right about the PPR’s incompatibility with Millikan-style teleosemantics, then that only reveals the inadequacy of Millikan-style teleosemantics. The PPR has a clear role to play in explaining the primitive systems that dominate the biosphere. However, Millikan did not want to limit the explanatory utility of the PPR to primitive systems but suggested that it has explanatory work to play in the animal signaling of complex organisms, Gibsonian affordances, as well as with distinctively human mental life and language. Contra Millikan, I suggest that the PPR has no or at best a very limited explanatory role to play in such cases. Further, the non-inferential feature of the PPR suggests that it should be understood at best as a marginal or borderline representation. (shrink)

How should we understand the claim that people comply with social norms because they possess the right kinds of beliefs and preferences? I answer this question by considering two approaches to what it is to believe (and prefer), namely: representationalism and dispositionalism. I argue for a variety of representationalism, viz. neural representationalism. Neural representationalism is the conjunction of two claims. First, what it is essential to have beliefs and preferences is to have certain neural representations. Second, neural representations (...) are often necessary to adequately explain behaviour. After having canvassed one promising way to understand what neural representations could be, I argue that the appeal to beliefs and preferences in explanations of paradigmatic cases of norm compliance should be understood as an appeal to neural representations. (shrink)

This paper is devoted to an exploration of the implications for the theory of pre-lexical syntax as developed by McCawley, and for syntactic theories in general, of an analysis of English emphatic conjunctions along the lines of Green . Among the conclusions are: The underlying representation of sentences must be much more abstract than has even been imagined previously, referring, in some as yet undiscovered way, to assumptions of the speaker about the real world, in order to account for the (...) grammatical occurrence of both terms of suppletive lexical items in otherwise identical surface strings with corresponding differences in meaning. A grammatical theory which purports to be capable of relating the sentences of a language to what they mean in a systematic way must be capable of referring directly to relevant assumptions made by the speaker of any given utterance at the time of utterance. So-called 'contrastive stress' is only one of the phenomena whose ultimate explanation depends on direct reference to such assumptions. Transformational grammars, which explicitly claim to be capable of relating in a systematic way the sentences of a language and what they mean, must be capable of referring to the sub-lexical, semantic structure of sentences, and furthermore, must be capable of doing so at an indefinite number of points in their derivation. This means that the semantic representation of a sentence must be available for reference at every stage in the derivation of the sentence. (shrink)

Several approaches to implementing symbol-like representations in neurally plausible models have been proposed. These approaches include binding through synchrony, “mesh” binding, and conjunctive binding. Recent theoretical work has suggested that most of these methods will not scale well, that is, that they cannot encode structured representations using any of the tens of thousands of terms in the adult lexicon without making implausible resource assumptions. Here, we empirically demonstrate that the biologically plausible structured representations employed in the (...) Semantic Pointer Architecture approach to modeling cognition do scale appropriately. Specifically, we construct a spiking neural network of about 2.5 million neurons that employs semantic pointers to successfully encode and decode the main lexical relations in WordNet, which has over 100,000 terms. In addition, we show that the same representations can be employed to construct recursively structured sentences consisting of arbitrary WordNet concepts, while preserving the original lexical structure. We argue that these results suggest that semantic pointers are uniquely well-suited to providing a biologically plausible account of the structured representations that underwrite human cognition. (shrink)

Barsalou has recently argued against the strategy of identifying amodal neural representations by using their cross-modal responses (i.e., their responses to stimuli from different modalities). I agree that there are indeed modal structures that satisfy this “cross-modal response” criterion (CM), such as distributed and conjunctive modal representations. However, I argue that we can distinguish between modal and amodal structures by looking into differences in their cross-modal responses. A component of a distributed cell assembly can be considered unimodal (...) because its responses to stimuli from a given modality are stable, whereas its responses to stimuli from any other modality are not (i.e., these are lost within a short time, plausibly as a result of cell assembly dynamics). In turn, conjunctive modal representations, such as superior colliculus cells in charge of sensory integration, are multimodal because they have a stable response to stimuli from different modalities. Finally, some prefrontal cells constitute amodal representations because they exhibit what has been called ‘adaptive coding’. This implies that their responses to stimuli from any given modality can be lost when the context and task conditions are modified. We cannot assign them a modality because they have no stable relation with any input type. (shrink)

It, is shown that Birkhoff –von Neumann quantum logic (i.e., an orthomodular lattice or poset) possessing an ordering set of probability measures S can be isomorphically represented as a family of fuzzy subsets of S or, equivalently, as a family of propositional functions with arguments ranging over S and belonging to the domain of infinite-valued Łukasiewicz logic. This representation endows BvN quantum logic with a new pair of partially defined binary operations, different from the order-theoretic ones: Łukasiewicz intersection and union (...) of fuzzy sets in the first case and Łukasiewicz conjunction and disjunction in the second. Relations between old and new operations are studied and it is shown that although they coincide whenever new operations are defined, they are not identical in general. The hypothesis that quantum-logical conjunction and disjunction should be represented by Łukasiewicz operations, not by order-theoretic join and meet is formulated and some of its possible consequences are considered. (shrink)

This paper surveys the various forms of Deduction Theorem for a broad range of relevant logics. The logics range from the basic system B of Routley-Meyer through to the system R of relevant implication, and the forms of Deduction Theorem are characterized by the various formula representations of rules that are either unrestricted or restricted in certain ways. The formula representations cover the iterated form,A 1 .A 2 . ... .A n B, the conjunctive form,A 1&A 2 (...) & ...A n B, the combined conjunctive and iterated form, enthymematic version of these three forms, and the classical implicational form,A 1&A 2& ...A n B. The concept of general enthymeme is introduced and the Deduction Theorem is shown to apply for rules essentially derived using Modus Ponens and Adjunction only, with logics containing either (A B)&(B C) .A C orA B .B C .A C. (shrink)

In this essay, I compare the meaning of political representation in Hobbes? Leviathan and Corneille's Cinna. For both authors, a monarch is a ?representer? and representation is a necessary condition of effective sovereignty. However, the term ?representation? means something entirely different in Hobbes and in Corneille. For the former, it means acting and speaking in the name of a multitude and in its absence; for the latter, it means acting and speaking in the presence of a political public, with the (...) intention to impress this audience. I would like to argue that our late modern (or postmodern) conception of sovereignty can be seen as being (unconsciously) based on the conjunction of Hobbes? and Corneille's different notions of representation. (shrink)

Alors que la plupart des recherches sur la psychologie sociale des représentations soulignent les aspects symboliques et communicationnels de ces dernières, une tendance subsiste qui consiste à concevoir les processus représentationnels en termes uniquement cognitifs comme si l'essentiel d'une représentation était articulé à une tentative de re-présenter le monde environnant. L'accent mis sur cette fonction des représentations, qui décalquerait en quelque sorte le monde extérieur, a instillé un courant anti-représentationnel qui a desservi la notion de représentation elle-même. Sur ce point, (...) deux aspects sont lacunaires : on ne peut rendre compte de la capacité ontogénétique de la représentation et on ne peut saisir sa fonction symbolique. La genèse des représentations montre qu'elles sont organisées en triades dialogiques ego/alter/objet articulées à des constructions entre personnes, relations ego/alter et monde. En saisissant cette genèse dialogique, on peut consolider les fonctions expressives et dialogiques des représentations qui, conjuguées à sa fonction épistémique sont partie intégrante du processus de construction des savoirs.While current research on the social psychology of representations emphasizes the symbolic and communicative aspects of representation, there remains a tendency to conceive representational processes in purely cognitive terms, as if all that is involved in representation is an attempt to re-present the reality of the world outside. This accent on the representational function qua mental replica of the outside world has engendered an anti-representational stance whose most radical consequence has been the dismissal of the notion of representation. This paper argues that this view fails on two accounts: it cannot provide an ontogenetic account of representation and it is unable to engage with its symbolic function. The genesis of representation shows that its foundations are dialogical triads between self-other-object, which shape it as a symbolic construction of persons, self-other relations and world. Understanding this dialogical genesis consolidates the expressive and dialogical functions of representation which, in conjunction with the epistemic function, are integral to the process of construction of knowledge. (shrink)

We give an extension of the Jónsson‐Tarski representation theorem for both normal and non‐normal modal algebras so that it preserves countably many infinite meets and joins. In order to extend the Jónsson‐Tarski representation to non‐normal modal algebras we consider neighborhood frames instead of Kripke frames just as Došen's duality theorem for modal algebras, and to deal with infinite meets and joins, we make use of Q‐filters, which were introduced by Rasiowa and Sikorski, instead of prime filters. By means of the (...) extended representation theorem, we show that every predicate modal logic, whether it is normal or non‐normal, has a model defined on a neighborhood frame with constant domains, and we give a completeness theorem for some predicate modal logics with respect to classes of neighborhood frames with constant domains. Similarly, we show a model existence theorem and a completeness theorem for infinitary modal logics which allow conjunctions of countably many formulas. (shrink)

Linguistic Issues in Language Technology (LiLT) is an open-access journal that focuses on the relationships between linguistic insights and language technology. In conjunction with machine learning and statistical techniques, deeper and more sophisticated models of language and speech are needed to make significant progress in both existing and newly emerging areas of computational language analysis. The vast quantity of electronically accessible natural language data (text and speech, annotated and unannotated, formal and informal) provides unprecedented opportunities for data-intensive analysis of linguistic (...) phenomena, which can in turn enrich computational methods. Taking an eclectic view on methodology, LiLT provides a forum for this work. In this volume, contributors offer new perspectives on semantic representations for textual inference. (shrink)

Constructs developed for the semantics of artificial languages are often proposed as the proper description of aspects of the semantics of natural languages. Most of us are familiar with the claims that conjunction, disjunction, negation, and material implication in standard versions of propositional calculus describe the meaning of “and”, “or”, “not”, and “if …, then …” in English. The argument for such claims is not only that these constructs account for meanings in English but that they offer the advantage of (...) well-understood formal apparatus for the explication of meaning in natural language. The argument against such claims is that explications based on this apparatus leave important aspects of the meaning of “and”, “or”, “not”, and “if …, then …” unexplicated. It is charged that the advantage of a well-understood formalism is secured at the expense of truth. Many of the most significant issues in philosophic logic are or depend on questions about whether constructs from artificial languages provide adequate semantic descriptions for natural languages. (shrink)

This paper reports on a case study which aims to recreate the hearing voices symptom in schizophrenia. The case study was submitted for a co-curricular module at King’s College London by a first-year undergraduate Music student, Bethany James, and was created using the web application, Mahara. The core of the case study consists of a soundscape of both everyday and unusual sounds, in conjunction with an original musical composition. The paper describes the case study and discusses it using chaos narrative (...) as an analytical lens. The paper argues that the case study effectively evokes the hearing voices symptom, conveying a lucid sense of the experience to non-sufferers and thus potentially creating use value for clinicians and care workers. (shrink)

Purely parallel neural networks can model object recognition in brief displays – the same conditions under which illusory conjunctions have been demonstrated empirically. Correcting errors of illusory conjunction is the “tag-assignment” problem for a purely parallel processor: the problem of assigning a spatial tag to nonspatial features, feature combinations, and objects. This problem must be solved to model human object recognition over a longer time scale. Our model simulates both the parallel processes that may underlie illusory conjunctions and the serial (...) processes that may solve the tag-assignment problem in normal perception. One component of the model extracts pooled features and another provides attentional tags that correct illusory conjunctions. Our approach addresses two questions: How can objects be identified from simultaneously attended features in a parallel, distributed representation? How can the spatial selectional requirements of such an attentional process be met by a separation of pathways for spatial and nonspatial processing? Our analysis of these questions yields a neurally plausible simulation of tag assignment based on synchronizing feature processing activity in a spatial focus of attention. (shrink)

The prominence of Bayesian modeling of cognition has increased recently largely because of mathematical advances in specifying and deriving predictions from complex probabilistic models. Much of this research aims to demonstrate that cognitive behavior can be explained from rational principles alone, without recourse to psychological or neurological processes and representations. We note commonalities between this rational approach and other movements in psychology – namely, Behaviorism and evolutionary psychology – that set aside mechanistic explanations or make use of optimality assumptions. (...) Through these comparisons, we identify a number of challenges that limit the rational program's potential contribution to psychological theory. Specifically, rational Bayesian models are significantly unconstrained, both because they are uninformed by a wide range of process-level data and because their assumptions about the environment are generally not grounded in empirical measurement. The psychological implications of most Bayesian models are also unclear. Bayesian inference itself is conceptually trivial, but strong assumptions are often embedded in the hypothesis sets and the approximation algorithms used to derive model predictions, without a clear delineation between psychological commitments and implementational details. Comparing multiple Bayesian models of the same task is rare, as is the realization that many Bayesian models recapitulate existing (mechanistic level) theories. Despite the expressive power of current Bayesian models, we argue they must be developed in conjunction with mechanistic considerations to offer substantive explanations of cognition. We lay out several means for such an integration, which take into account the representations on which Bayesian inference operates, as well as the algorithms and heuristics that carry it out. We argue this unification will better facilitate lasting contributions to psychological theory, avoiding the pitfalls that have plagued previous theoretical movements. (shrink)

We discuss the role of synchrony of activationin higher-level cognitive processes. Inparticular, we analyze the question of whethersynchrony of activation provides a mechanismfor compositional representation in neuralsystems. We will argue that synchrony ofactivation does not provide a mechanism forcompositional representation in neural systems.At face value, one can identify a level ofcompositional representation in the models thatintroduce synchrony of activation for thispurpose. But behavior in these models isalways produced by means conjunctiverepresentations in the form of coincidencedetectors. Therefore, models that rely onsynchrony (...) of activation lack the systematicityand productivity of true compositional systems.As a result, they cannot distinguish betweentype and token representations, which resultsin misrepresentations of spatial relations andpropositions. Furthermore, higher-levelcognitive processes will likely integrateinformation from widely distributed areas inthe brain, which puts severe restrictions onthe underlying neural dynamics if synchrony ofactivation is to play a role in theseprocesses. We will briefly discuss theserestrictions in the case of feature binding invisual cognition. (shrink)

Contemporary arguments for forms of psycho-physical dualism standardly depart from phenomenal aspects of consciousness. Conceptual aspects of conscious experience, as opposed to phenomenal or visual/perceptual ones, are often taken to be within the scope of functionalist, reductionist, or physicalist theories. I argue that the particular conceptual structure of human consciousness makes this asymmetry unmotivated. The argument for a form of dualism defended here proceeds from the empirical premise that conceptual structure in a linguistic creature like us is a combinatorial and (...) compositional system that implicates a distinction between simple and complex, or 'atomic' and 'molecular' concepts. The argument is that conceptual atoms, qua atoms, are irreducible to anything else. If so, and if the atoms are essentially semantic, a form of dualism follows: though positively inviting naturalistic inquiry into the semantic and mental aspects of nature, it requires that we look at the mental as a primitive domain of nature. Schematically, then, the argument is as follows: Human consciousness/thought is conceptually structured. The human conceptual system is a 'particulate' system at a syntactic and semantic level of representation. This implies the existence of conceptual 'particles', concepts that have no further semantic decomposition. A conceptual atom cannot be explained in terms of anything that does not involve its own intrinsic properties. Physicalism as normally conceived is inconsistent with and. (shrink)

Cet article explore la viabilité de la conjonction de trois thèses : (1) qu’il existe des valeurs objectives ; (2) que certaines émotions ont pour fonction de les représenter ; (3) que de telles émotions représentent ces valeurs de manière fiable. Nous cherchons plus particulièrement à réconcilier la troisième thèse avec l’observation que les émotions ont un aspect subjectif ou personnel qu’il n’est pas possible d’éliminer. -/- This article explores the viability of the conjunction of three claims: (1) that there (...) are objective values; (2) that some emotions have the function of representing them; (3) that such emotions represent these values reliably. In particular, we will be concerned with the project of reconciling (3) with the simple observation that emotions have a subjective or personal aspect that cannot be ignored. (shrink)

Monoidal t-norm based logic $\mathbf {MTL}$ is the weakest t-norm based residuated fuzzy logic, which is a $[0,1]$ -valued propositional logical system having a t-norm and its residuum as truth function for conjunction and implication. Monadic fuzzy predicate logic $\mathbf {mMTL\forall }$ that consists of the formulas with unary predicates and just one object variable, is the monadic fragment of fuzzy predicate logic $\mathbf {MTL\forall }$, which is indeed the predicate version of monoidal t-norm based logic $\mathbf {MTL}$. The main (...) aim of this paper is to give an algebraic proof of the completeness theorem for monadic fuzzy predicate logic $\mathbf {mMTL\forall }$ and some of its axiomatic extensions. Firstly, we survey the axiomatic system of monadic algebras for t-norm based residuated fuzzy logic and amend some of them, thus showing that the relationships for these monadic algebras completely inherit those for corresponding algebras. Subsequently, using the equivalence between monadic fuzzy predicate logic $\mathbf {mMTL\forall }$ and S5-like fuzzy modal logic $\mathbf {S5(MTL)}$, we prove that the variety of monadic MTL-algebras is actually the equivalent algebraic semantics of the logic $\mathbf {mMTL\forall }$, giving an algebraic proof of the completeness theorem for this logic via functional monadic MTL-algebras. Finally, we further obtain the completeness theorem of some axiomatic extensions for the logic $\mathbf {mMTL\forall }$, and thus give a major application, namely, proving the strong completeness theorem for monadic fuzzy predicate logic based on involutive monoidal t-norm logic $\mathbf {mIMTL\forall }$ via functional representation of finitely subdirectly irreducible monadic IMTL-algebras. (shrink)

A mixture preorder is a preorder on a mixture space (such as a convex set) that is compatible with the mixing operation. In decision theoretic terms, it satisfies the central expected utility axiom of strong independence. We consider when a mixture preorder has a multi-representation that consists of real-valued, mixture-preserving functions. If it does, it must satisfy the mixture continuity axiom of Herstein and Milnor (1953). Mixture continuity is sufficient for a mixture-preserving multi-representation when the dimension of the mixture space (...) is countable, but not when it is uncountable. Our strongest positive result is that mixture continuity is sufficient in conjunction with a novel axiom we call countable domination, which constrains the order complexity of the mixture preorder in terms of its Archimedean structure. We also consider what happens when the mixture space is given its natural weak topology. Continuity (having closed upper and lower sets) and closedness (having a closed graph) are stronger than mixture continuity. We show that continuity is necessary but not sufficient for a mixture preorder to have a mixture-preserving multi-representation. Closedness is also necessary; we leave it as an open question whether it is sufficient. We end with results concerning the existence of mixture-preserving multi-representations that consist entirely of strictly increasing functions, and a uniqueness result. (shrink)

On a longtemps rendu compte des comportements de déplacements des hommes dans l’espace par un terme renvoyant à une logique collective et de masse, celui de migration . L’intégration dans l’observation et la compréhension de toute la palette des motifs de déplacements et l’individualisation croissante des pratiques ont amené l’usage d’un terme plus générique, emprunté aux sciences sociales et notamment à ceux qui s’intéressent à la fluidité dans l’espace social, celui de mobilité. Ce glissement n’est pas purement sémantique : il (...) exprime le passage de l’empire de la nécessité aux capacités stratégiques et aux désirs des acteurs, de la représentation aréolaire d’un territoire rassemblant une « société locale » « contenant » les déplacements de ses membres à des représentations réticulaires , multi-territoriales . Sur tous ces points, les enquêtes initiées dans les années 1960 par les ingénieurs pour alimenter leurs modèles de trafic nous ont permis, grâce à l’élaboration d’indicateurs, de concepts, de représentations nouvelles, de comprendre en profondeur la dynamique et les rôles respectifs des rationalités individuelles et de la formation de normes sociales dans le champ spécifique de la mobilité quotidienne. C’est de cette construction dont nous rendons compte dans cet article, qui livre aussi à partir des quelques résultats saillants des recherches conduites, les convictions fortes en matière de dynamique de la mobilité qui s’en dégagent et les paradigmes qu’il conviendrait de mieux explorer.Spatial behaviour was studied in the past through group concepts, such as residential or regular migrations from home to work. The will to understand travel behaviour for the full range of trip purposes and the growing personalisation of behaviour leads to adopt the term of mobility from social sciences. This change is not purely semantic. It expresses the transition from a vision based on the needs to the consideration of the strategic capabilities of the persons, from areola-based representations of a local society to network and archipelago-based representations of individual behaviours. We have used, in conjunction with the international community of travel behaviour analysts, the travel surveys introduced in the sixties to feed traffic models, to build concepts, indicators and representations of travel behaviour, to understand in depth the transformations of mobility patterns and to analyze the roles of individual rationality and social norms. The paper relates this history, highlights some key results and strong beliefs, and questions the need to explore new paradigms. (shrink)

Visual representations of the whole earth permeate modern cultures, shaping how societies imagine globalization and planetary ecological derangement. To explore the complex ways in which these images configure human attitudes toward environments, this essay attends to a series of hegemonic representations of the earth from diverse situations and stages of modernity in conjunction with ideas drawn from Martin Heidegger’s ontological philosophy. I proceed from the insight that for Heidegger modernity is not a singular condition, but entails two contrary (...) determinations of being: “machination,” in which detached subjects reshape an objectified world, and “enordering,” in which fungible and flexible resources circulate endlessly around a closed global space. Taking up these divergent concepts, my argument accentuates basic differences in how the earth has been disclosed in representation over the course of modern history. Through close analyses of world maps from the early modern Netherlands; chalkboard globes from nineteenth-century schoolrooms; and the contemporary geospatial application Google Earth, I show how global visions both articulate and complicate Heidegger’s thinking of machination and enordering. Far from being the culmination of a singular modernity, images of the earth reveal and reinforce a discordant global condition, riven by clashing, equally total disclosures of the world. (shrink)

Various representation results have been established for logics of belief revision, in terms of remainder sets, epistemic entrenchment, systems of spheres and so on. In this paper I present another representation for logics of belief revision, as an algebra of theories. I show that an algebra of theories, enriched with a set of rejection operations, provides a suitable algebraic framework to characterize the theory change operations of systems of belief revision. The theory change operations arise as power operations of the (...) conjunction and disjunction connectives of the underlying logic. (shrink)

We give a proof-theoretic as well as a semantic characterization of a logic in the signature with conjunction, disjunction, negation, and the universal and existential quantifiers that we suggest has a certain fundamental status. We present a Fitch-style natural deduction system for the logic that contains only the introduction and elimination rules for the logical constants. From this starting point, if one adds the rule that Fitch called Reiteration, one obtains a proof system for intuitionistic logic in the given signature; (...) if instead of adding Reiteration, one adds the rule of Reductio ad Absurdum, one obtains a proof system for orthologic; by adding both Reiteration and Reductio, one obtains a proof system for classical logic. Arguably neither Reiteration nor Reductio is as intimately related to the meaning of the connectives as the introduction and elimination rules are, so the base logic we identify serves as a more fundamental starting point and common ground between proponents of intuitionistic logic, orthologic, and classical logic. The algebraic semantics for the logic we motivate proof-theoretically is based on bounded lattices equipped with what has been called a weak pseudocomplementation. We show that such lattice expansions are representable using a set together with a reflexive binary relation satisfying a simple first-order condition, which yields an elegant relational semantics for the logic. This builds on our previous study of representations of lattices with negations, which we extend and specialize for several types of negation in addition to weak pseudocomplementation; in an appendix, we further extend this representation to lattices with implications. Finally, we discuss adding to our logic a conditional obeying only introduction and elimination rules, interpreted as a modality using a family of accessibility relations. (shrink)

Kierkegaard's preoccupation with a separation between the ‘inner’ and the ‘outer’ runs through his work and is widely thought to belong to his rejection of Hegel's idealist monism. Focusing on The Concept of Irony and Either/Or, I argue that although Kierkegaard believes in various metaphysical distinctions between inside and outside, he nonetheless understands the task of the philosopher as that of making outside and inside converge in a representation. Drawing on Hegel's philosophy of art, I show that Kierkegaard's project in (...) both of these books is the aesthetic project of revealing the inner essence of something in its outward appearance. Kierkegaard's portrait of Socrates in The Concept of Irony is a phenomenology of the spirit of irony. My interpretation adds a new dimension to our understanding of Kierkegaard's aesthetics and his relation to Hegel; it presents him as a follower of Plato, whom he is usually thought to have dismissed; and it uncovers a deep connection between Kierkegaard's first two books, which are never read in conjunction. (shrink)

Popular culture could be understood as a political battleground where conflicting meanings are inscribed into the “ordinary objects” that constitute that public sphere. This is also true for science fiction television series. This article critically examines how political matters and ethical agencies are represented within The Expanse, a series that takes place within a speculative twenty-fourth century milky way. Firstly, I will situate The Expanse within its generic “system of reference.” Then, I will illustrate how political matters are represented as (...) conjoined with the ethical. While the ethical refers to actions of persons, politics refers to fictional conceptions of what Tristan Garcia’s terms we-ourselves, understood as conflicting and overlapping conceptions of “we.” The conjunction between the political and the ethical in The Expanse is spatiotemporal: the characters, the events they are entangled in, and the spaces that connect discrete events develop through fictional and literal time. I argue that the science fictional representations of “we-ourselves,” and the specific spatiotemporal representational capacities of the television series format, can be understood through the application of Mikhail Bakhtin’s concepts of the chronotope and the dialogic. That is, The Expanse’s we-representations are chronotopic and the refractive rhetoric of television is dialogic. (shrink)

The common view of the transition between subitizing and numerosity estimation regimes is that there is a hard bound on the subitizing range, and beyond this range, people estimate. However, this view does not adequately address the behavioral signatures of enumeration under conditions of attentional load or in the immediate post-subitizing range. The possibility that there might exist a numerosity range where both processes of subitizing and estimation operate in conjunction has so far been ignored. Here, we investigate this new (...) proposal, that people strategically combine the processes of subitizing and estimation to maximize accuracy and precision, given time or attentional constraints. We present a process-level account of how subitizing and estimation can be combined through strategic deployment of attention to maximize the precision of perceived numerosity given time constraints. We then describe a computational model of this account and apply it in two experimental simulations to demonstrate how it can explain key findings in prior enumeration research. While recent modeling work has argued that the behavioral signatures of enumeration can best be explained through a single numerosity system with a single form of representation, we argue that our model demonstrates how the traditional two-systems view of numerical representation accounts for behavioral data through coordination with a unified attentional mechanism, rather than a unified representation. (shrink)