The d-Logic of the Rational Numbers: A Fruitful Construction

We present a geometric construction that yields completeness results for modal logics including K4, KD4, GL and GL _n with respect to certain subspaces of the rational numbers. These completeness results are extended to the bimodal case with the universal modality.     

On a Definition of a Variety of Monadic ℓ-Groups

In this paper we expand previous results obtained in [2] about the study of categorical equivalence between the category IRL ₀ of integral residuated lattices with bottom, which generalize MV-algebras and a category whose objects are called c-differential residuated lattices. The equivalence is given by a functor ${{\mathsf{K}^\bullet}}$ , motivated by an old construction due to J. Kalman, which was studied by Cignoli in [3] in the context of Heyting and Nelson algebras. These results are then specialized to the case of MV-algebras and the corresponding category ${MV^{\bullet}}$ of monadic MV-algebras induced by “Kalman’s functor” ${\mathsf{K}^\bullet}$ . Moreover, we extend the construction to ?-groups introducing the new category of monadic ?-groups together with a functor ${\Gamma ^\sharp}$ , that is “parallel” to the well known functor ${\Gamma}$ between ? and MV-algebras.     

Dynamic Modalities

A new modal logic containing four dynamic modalities with the following informal reading is introduced: ${\square^\forall}$ – always necessary, ${\square^\exists}$ – sometimes necessary, and their duals – ${\diamondsuit^\forall}$ – always possibly, and ${\diamondsuit^\exists}$ – sometimes possibly. We present a complete axiomatization with respect to the intended formal semantics and prove decidability via fmp.     

A motor similarity effect in object memory

In line with theories of embodied cognition (e.g., Versace et al. European Journal of Cognitive Psychology, 21, 522–560, 2009), several studies have suggested that the motor system used to interact with objects in our environment is involved in object recognition (e.g., Helbig, Graf, & Kiefer Experimental Brain Research, 174, 221-228, 2006). However, the role of the motor system in immediate memory for objects is more controversial. The objective of the present study was to investigate the role of the motor system in object memory by manipulating the similarity between the actions associated to series of objects to be retained in memory. In Experiment 1, we showed that lists of objects associated to dissimilar actions were better recalled than lists associated to similar actions. We then showed that this effect was abolished when participants were required to perform a concurrent motor suppression task (Experiment 2) and when the objects to be memorized were unmanipulable (Experiment 3). The motor similarity effect provides evidence for the role of motor affordances in object memory.     

Constructing formal semantics from an ontological perspective. The case of second-order logics

In a first part, I defend that formal semantics can be used as a guide to ontological commitment. Thus, if one endorses an ontological view \(O\) and wants to interpret a formal language \(L\) , a thorough understanding of the relation between semantics and ontology will help us to construct a semantics for \(L\) in such a way that its ontological commitment will be in perfect accordance with \(O\) . Basically, that is what I call constructing formal semantics from an ontological perspective. In the rest of the paper, I develop rigorously and put into practice such a method, especially concerning the interpretation of second-order quantification. I will define the notion of ontological framework: it is a set-theoretical structure from which one can construct semantics whose ontological commitments correspond exactly to a given ontological view. I will define five ontological frameworks corresponding respectively to: (i) predicate nominalism, (ii) resemblance nominalism, (iii) armstrongian realism, (iv) platonic realism, and (v) tropism. From those different frameworks, I will construct different semantics for first-order and second-order languages. Notably I will present different kinds of nominalist semantics for second-order languages, showing thus that we can perfectly quantify over properties and relations while being ontologically committed only to individuals. I will show in what extent those semantics differ from each other; it will make clear how the disagreements between the ontological views extend from ontology to logic, and thus why endorsing an ontological view should have an impact on the kind of logic one should use.     

Boolean Skeletons of MV-algebras and ?-groups

Let ?? be Mundici??s functor from the category ${\mathcal{LG}}$ whose objects are the lattice-ordered abelian groups (?-groups for short) with a distinguished strong order unit and the morphisms are the unital homomorphisms, onto the category ${\mathcal{MV}}$ of MV-algebras and homomorphisms. It is shown that for each strong order unit u of an ?-group G, the Boolean skeleton of the MV-algebra ??(G, u) is isomorphic to the Boolean algebra of factor congruences of G.     

The mental wormhole: Internal attention shifts without regard for distance

Attention operates perceptually on items in the environment, and internally on objects in visuospatial working memory. In the present study, we investigated whether spatial and temporal constraints affecting endogenous perceptual attention extend to internal attention. A retro-cue paradigm in which a cue is presented beyond the range of iconic memory and after stimulus encoding was used to manipulate shifts of internal attention. Participants?? memories were tested for colored circles (Experiments 1, 2, 3a, 4) or for novel shapes (Experiment 3b) and their locations within an array. In these experiments, the time to shift internal attention (Experiments 1 and 3) and the eccentricity of encoded objects (Experiments 2?C4) were manipulated. Our data showed that, unlike endogenous perceptual attention, internal shifts of attention are not modulated by stimulus eccentricity. Across several timing parameters and stimuli, we found that shifts of internal attention require a minimum quantal amount of time regardless of the object eccentricity at encoding. Our findings are consistent with the view that internal attention operates on objects whose spatial information is represented in relative terms. Although endogenous perceptual attention abides by the laws of space and time, internal attention can shift across spatial representations without regard for physical distance.     

The importance of context information for the spatial specificity of gaze cueing

In three experiments, we investigated the spatial allocation of attention in response to central gaze cues. In particular, we examined whether the allocation of attentional resources is influenced by context information—that is, the presence or absence of reference objects (i.e., placeholders) in the periphery. On each trial, gaze cues were followed by a target stimulus to which participants had to respond by keypress or by performing a target-directed saccade. Targets were presented either in an empty visual field (Exps. 1 and 2) or in previewed location placeholders (Exp. 3) and appeared at one of either 18 (Exp. 1) or six (Exps. 2 and 3) possible positions. The spatial distribution of attention was determined by comparing response times as a function of the distance between the cued and target positions. Gaze cueing was not specific to the exact cued position, but instead generalized equally to all positions in the cued hemifield, when no context information was provided. However, gaze direction induced a facilitation effect specific to the exact gazed-at position when reference objects were presented. We concluded that the presence of possible objects in the periphery to which gaze cues could refer is a prerequisite for attention shifts being specific to the gazed-at position.     

A Completeness Proof of Kiczuk’s Logic of Physical Change

In this paper the class of minimal models C ^ZI for Kiczuk’s system of physical change ZI is provided and soundness and completeness proofs of ZI with respect to these models are given. ZI logic consists of propositional logic von Wright’s And Then and six specific axioms characterizing the meaning of unary propositional operator “Zm”, read “there is a change in the fact that”. ZI is intended to be a logic which provides a formal account for describing two kinds of process change: the change from one state of the process to its other state (e.g., transmitting or absorbing energy with greater or less than the usual intensity) and the perishing of the process (e.g., cessation of the energetic activity of the sun).     

Endurantism and Paradox

Mereological challenges have recently been raised against the endurantist. For instance, Barker and Dowe (2003) have argued that eternalist endurantism entails (1) persisting objects are both 3D and 4D, and that (2) the lives of persisting objects last longer than they actually do. They also argue that presentist endurantism also entails, albeit in a tensed way, that (3) the lives of persisting objects last longer than they actually do. While they’ve further argued (2005) that the objections raised by McDaniel (2003) and Beebee and Rush (2003) fail, here I show that such objections are tenable without requiring further significant metaphysical commitments; I argue that such endurantist defences are tenable, contra to prior analyses.     

Color and cognitive penetrability

Several psychological experiments have suggested that concepts can influence perceived color (e.g., Delk and Fillenbaum in Am J Psychol 78(2):290–293, 1965, Hansen et al. in Nat Neurosci 9(11):1367–1368, 2006, Olkkonen et al. in J Vis 8(5):1–16, 2008). Observers tend to assign typical colors to objects even when the objects do not have those colors. Recently, these findings were used to argue that perceptual experience is cognitively penetrable (Macpherson 2012). This interpretation of the experiments has far-reaching consequences: it implies that the way we think of objects determines how we see them, thus threatening the role of perception in justifying beliefs. In this paper, I show that the psychological findings can be accounted for without admitting cognitive penetrability. An underestimated but key feature of the experiments is that observers had to judge colors in borderline cases, in conditions of reduced acuity, or on the basis of color-concepts instead of matching. Such judgments are sensitive to the form of bias that Tversky and Kahneman (Science 185:1124–1131, 1974) have termed ‘anchoring’. Adopting a suggestion from Raffman (Philos Rev 103(1):41–74, 1994), I argue that the way subjects in the experiments think of the objects could affect their color judgments without altering their color experiences.     

On the notions of indiscernibility and indeterminacy in the light of the Galois–Grothendieck theory

We analyze the notions of indiscernibility and indeterminacy in the light of the Galois theory of field extensions and the generalization to \(K\) -algebras proposed by Grothendieck. Grothendieck’s reformulation of Galois theory permits to recast the Galois correspondence between symmetry groups and invariants as a Galois–Grothendieck duality between \(G\) -spaces and the minimal observable algebras that discern (or separate) their points. According to the natural epistemic interpretation of the original Galois theory, the possible \(K\) -indiscernibilities between the roots of a polynomial \(p(x)\in K[x]\) result from the limitations of the field \(K\) . We discuss the relation between this epistemic interpretation of the Galois–Grothendieck duality and Leibniz’s principle of the identity of indiscernibles. We then use the conceptual framework provided by Klein’s Erlangen program to propose an alternative ontologic interpretation of this duality. The Galoisian symmetries are now interpreted in terms of the automorphisms of the symmetric geometric figures that can be placed in a background Klein geometry. According to this interpretation, the Galois–Grothendieck duality encodes the compatibility condition between geometric figures endowed with groups of automorphisms and the ‘observables’ that can be consistently evaluated at such figures. In this conceptual framework, the Galoisian symmetries do not encode the epistemic indiscernibility between individuals, but rather the intrinsic indeterminacy in the pointwise localization of the figures with respect to the background Klein geometry.     

Decidability of General Extensional Mereology

The signature of the formal language of mereology contains only one binary predicate P which stands for the relation “being a part of”. Traditionally, P must be a partial ordering, that is, ${\forall{x}Pxx, \forall{x}\forall{y}((Pxy\land Pyx)\to x=y)}$ and ${\forall{x}\forall{y}\forall{z}((Pxy\land Pyz)\to Pxz))}$ are three basic mereological axioms. The best-known mereological theory is “general extensional mereology”, which is axiomatized by the three basic axioms plus the following axiom and axiom schema: (Strong Supplementation) ${\forall{x}\forall{y}(\neg Pyx\to \exists z(Pzy\land \neg Ozx))}$ , where Oxy means ${\exists z(Pzx\land Pzy)}$ , and (Fusion) ${\exists x\alpha \to \exists z\forall y(Oyz\leftrightarrow \exists x(\alpha \land Oyx))}$ , for any formula α where z and y do not occur free. In this paper, I will show that general extensional mereology is decidable, and will also point out that the decidability of the first-order approximation of the theory of complete Boolean algebras can be shown in the same way.     

Working memory for relations among objects

Across many areas of study in cognition, the capacity of working memory (WM) is widely agreed to be roughly three to five items: three to five objects (i.e., bound collections of object features) in the literature on visual WM or three to five role bindings (i.e., objects in specific relational roles) in the literature on memory and reasoning. Three experiments investigated the capacity of observers’ WM for the spatial relations among objects in a visual display, and the results suggest that the “items” in WM are neither simply objects nor simply role bindings. The results of Experiment 1 are most consistent with a model that treats an “item” in visual WM as an object, along with the roles of all its relations to one other object. Experiment 2 compared observers’ WM for object size with their memory for relative size and provided evidence that observers compute and store objects’ relations per se (rather than just absolute size) in WM. Experiment 3 tested and confirmed several more nuanced predictions of the model supported by Experiment 1. Together, these findings suggest that objects are stored in visual WM in pairs (along with all the relations between the objects in a pair) and that, from the perspective of WM, a given object in one pair is not the same “item” as that same object in a different pair.     

Medieval Disputationes de obligationibus as Formal Dialogue Systems

Formal dialogue systems model rule-based interaction between agents and as such have multiple applications in multi-agent systems and AI more generally. Their conceptual roots are in formal theories of natural argumentation, of which Hamblin’s formal systems of argumentation in Hamblin (Fallacies. Methuen, London, 1970, Theoria 37:130–135, 1971) are some of the earliest examples. Hamblin cites the medieval theory of obligationes as inspiration for his development of formal argumentation. In an obligatio, two agents, the Opponent and the Respondent, engage in an alternating-move dialogue, where the Respondent’s actions are governed by certain rules, and the goal of the dialogue is establishing the consistency of a proposition. We implement obligationes in the formal dialogue system framework of Prakken (Knowl Eng Rev 21(2):163–188, 2006) using Dynamic Epistemic Logic (van Ditmarsch et al. in Dynamic epistemic logic, Synthese Library Series. Springer, Berlin, 2007). The result is a new type of inter-agent dialogue, for consistency-checking, and analyzing obligationes in this way also sheds light on interpretational and historical questions concerning their use and purpose in medieval academia.     

An unforgettable apple: Memory and attention for forbidden objects

Are we humans drawn to the forbidden? From jumbo-sized soft drinks to illicit substances, the influence of prohibited ownership on subsequent demand has made this question a pressing one. We know that objects that we ourselves own have a heightened psychological saliency, relative to comparable objects that are owned by others, but do these kinds of effects extend from self-owned to “forbidden” objects? To address this question, we developed a modified version of the Turk shopping paradigm in which “purchased” items were assigned to various recipients. Participants sorted everyday objects labeled as “self-owned”, “other-owned,” and either “forbidden to oneself” (Experiment 1) or “forbidden to everyone” (Experiment 2). Subsequent surprise recognition memory tests revealed that forbidden objects with high (Experiment 1) but not with low (Experiment 2) self-relevance were recognized as well as were self-owned objects, and better than other-owned objects. In a third and final experiment, we used event-related potentials (ERPs) to determine whether self-owned and self-forbidden objects, which showed a common memory advantage, are in fact treated the same at a neurocognitive–affective level. We found that both object types were associated with enhanced cognitive analysis, relative to other-owned objects, as measured by the P300 ERP component. However, we also found that self-forbidden objects uniquely triggered an enhanced response preceding the P300, in an ERP component (the N2) that is sensitive to more rapid, affect-related processing. Our findings thus suggest that, whereas self-forbidden objects share a common cognitive signature with self-owned objects, they are unique in being identified more quickly at a neurocognitive level.     

Infants’ discrimination of crossed and uncrossed horizontal disparity

In a series of preferential-looking experiments, infants 5 to 6 months of age were tested for their responsiveness to crossed and uncrossed horizontal disparity. In Experiments 1 and 2, infants were presented with dynamic random dot stereograms displaying a square target defined by either a 0.5° crossed or a 0.5° uncrossed horizontal disparity and a square control target defined by a 0.5° vertical disparity. In Experiment 3, infants were presented with the crossed and the uncrossed horizontal disparity targets used in Experiments 1 and 2. According to the results, the participants looked more often at the crossed (Experiment 1), as well as the uncrossed (Experiment 2), horizontal disparity targets than at the vertical disparity target. These results suggest that the infants were sensitive to both crossed and uncrossed horizontal disparity information. Moreover, the participants exhibited a natural visual preference for the crossed over the uncrossed horizontal disparity (Experiment 3). Since prior research established natural looking and reaching preferences for the (apparently) nearer of two objects, this finding is consistent with the hypothesis that the infants were able to extract the depth relations specified by crossed (near) and uncrossed (far) horizontal disparity.     

Erfassung der sozialen Ungleichheit in empirischen Untersuchungen

Background

The interrelationship between social inequality and health problems is well known. This paper evaluates how current empirical studies in the context of social psychiatry, psychosomatics and medical sociology respond to this issue in terms of taking characteristics of socio-economic status (SES) into account.

Material and methods

All empirical studies published in the German journals Psychotherapie, Psychosomatik und Medizinische Psychologie and Psychiatrische Praxis in 2005 and 2006 were evaluated regarding the use of characteristics of SES.

Results

Of the 113 studies examined, 70 (62%) covered characteristics of the SES. The majority included characteristics of both formal and professional education, but often in only few categories. Some studies used a combination of formal and professional education. Half of the studies included categories of occupational status or gainful employment, also often in few categories and 11% of studies included net family income. Three studies formed an index of social class using the categories lower class, middle class and upper class.

Conclusion

Determination of characteristics of SES can be improved both quantitatively and qualitatively. Comparability of population studies can be improved by an increased orientation on demographic standards.     

On the Theorem of Correspondence

In a recent paper, Mammen (Integrative Psychological and Behavioral Science, 50, 196–233, 2016a) brought novel arguments into the discussion concerning the importance of being able to single out and track objects through space and time. Mammen offered a formal account of two basic, yet distinct, ways in which we as human beings encounter objects in the real world, that is, sense and choice categories. In this paper I discuss aspects of his theory and in particular the Theorem of Correspondence. I shall attempt to argue that Mammen’s formal account is indeed a novel and powerful analytical generic tool allowing us to see the important relevance in different domains of being able to establish choice categories. Meanwhile, I will attempt to show that evidence from the so-called multiple object tracking studies -- even though these use highly artificial stimuli -- provide compelling evidence in support of Mammen’s formal account.