Spatial distance effects on incremental semantic interpretation of abstract sentences: Evidence from eye tracking

A large body of evidence has shown that visual context information can rapidly modulate language comprehension for concrete sentences and when it is mediated by a referential or a lexical-semantic link. What has not yet been examined is whether visual context can also modulate comprehension of abstract sentences incrementally when it is neither referenced by, nor lexically associated with, the sentence. Three eye-tracking reading experiments examined the effects of spatial distance between words (Experiment 1) and objects (Experiment 2 and 3) on participants’ reading times for sentences that convey similarity or difference between two abstract nouns (e.g., ‘Peace and war are certainly different...’). Before reading the sentence, participants inspected a visual context with two playing cards that moved either far apart or close together. In Experiment 1, the cards turned and showed the first two nouns of the sentence (e.g., ‘peace’, ‘war’). In Experiments 2 and 3, they turned but remained blank. Participants’ reading times at the adjective (Experiment 1: first-pass reading time; Experiment 2: total times) and at the second noun phrase (Experiment 3: first-pass times) were faster for sentences that expressed similarity when the preceding words/objects were close together (vs. far apart) and for sentences that expressed dissimilarity when the preceding words/objects were far apart (vs. close together). Thus, spatial distance between words or entirely unrelated objects can rapidly and incrementally modulate the semantic interpretation of abstract sentences.     

A family of Gödel hybrid logics

In this paper, we define a family of fuzzy hybrid logics that are based on Gödel logic. It is composed of two infinite-valued versions called ${\mathsf{GH}}_{\infty }$ and ${\mathsf{WGH}}_{\infty }$, and a sequence of finitary valued versions ${({\mathsf{GH}}_n)}_{0<n<\infty }$. We define decision procedures for both ${\mathsf{WGH}}_{\infty }$ and ${({\mathsf{GH}}_n)}_{0<n<\infty }$ that are based on particular sequents and on a set of proof rules dealing with such sequents. As these rules are strongly invertible the procedures naturally allow one to generate countermodels. Therefore we prove the decidability and the finite model property for these logics. Finally, from the decision procedure of ${\mathsf{WGH}}_{\infty }$, we design a sound and complete sequent calculus for this logic.     

Coinductive models and normal forms for modal logics (or how we learned to stop worrying and love coinduction)

We present a coinductive definition of models for modal logics and show that it provides a homogeneous framework in which it is possible to include different modal languages ranging from classical modalities to operators from hybrid and memory logics. Moreover, results that had to be proved separately for each different language—but whose proofs were known to be mere routine—now can be proved in a general way. We show, for example, that we can have a unique definition of bisimulation for all these languages, and prove a single invariance-under-bisimulation theorem.We then use the new framework to investigate normal forms for modal logics. The normal form we introduce may have a smaller modal depth than the original formula, and it is inspired by global modalities like the universal modality and the satisfiability operator from hybrid logics. These modalities can be extracted from under the scope of other operators. We provide a general definition of extractable modalities and show how to compute extracted normal forms. As it is the case with other classical normal forms—e.g., the conjunctive normal form of propositional logic—the extracted normal form of a formula can be exponentially bigger than the original formula, if we require the two formulas to be equivalent. If we only require equi-satisfiability, then every modal formula has an extracted normal form which is only polynomially bigger than the original formula, and it can be computed in polynomial time.     

Leibniz Filters Revisited

Leibniz filters play a prominent role in the theory of protoalgebraic logics. In [3] the problem of the definability of Leibniz filters is considered. Here we study the definability of Leibniz filters with parameters. The main result of the paper says that a protoalgebraic logic S has its strong version weakly algebraizable iff it has its Leibniz filters explicitly definable with parameters.     

Special issue: Combining probability and logic

This editorial explains the scope of the special issue and provides a thematic introduction to the contributed papers.     

Modernist Creativity and the Construction of Reality in Einstein and Kandinsky

In this article, I limn the remarkable ascent of Albert Einstein and Wassily Kandinsky into our cultural pantheon. I depict how both figures mastered and transcended their respective fields, and how they called into question long-established disciplinary assumptions and practices. I also demonstrate how the creative works of Einstein and Kandinsky constructed, and were constructed by, the reality we now call “modern.”     

The Disappearing “Advantage of Abstract Examples in Learning Math”

When teaching a novel mathematical concept, should we present learners with abstract or concrete examples? In this experiment, we conduct a critical replication and extension of a well-known study that argued for the general advantage of abstract examples (Kaminski, Sloutsky, & Heckler, 2008a). We demonstrate that theoretically motivated yet minor modifications of the learning design put this argument in question. A key finding from this study is that participants who trained with improved concrete examples performed as well as, or better than, participants who trained with abstract examples. We argue that the previously reported “advantage of abstract examples” manifested not because abstract examples are advantageous in general, but because the concrete condition employed suboptimal examples.     

Intuitive mapping between nonsymbolic quantity and observed action across development

Adults’ concurrent processing of numerical and action information yields bidirectional interference effects consistent with a cognitive link between these two systems of representation. This link is in place early in life: infants create expectations of congruency across numerical and action-related stimuli (i.e., a small [large] hand aperture associated with a smaller [larger] numerosity). Although these studies point to a developmental continuity of this mapping, little is known about the later development and thus how experience shapes such relationships. We explored how number–action intuitions develop across early and later childhood using the same methodology as in adults. We asked 3-, 6-, and 8-year-old children, as well as adults, to relate the magnitude of an observed action (a static hand shape, open vs. closed, in Experiment 1; a dynamic hand movement, opening vs. closing, in Experiment 2) to either a small or large nonsymbolic quantity (numerosity in Experiment 1 and numerosity and/or object size in Experiment 2). From 6 years of age, children started performing in a systematic congruent way in some conditions, but only 8-year-olds (added in Experiment 2) and adults performed reliably above chance in this task. We provide initial evidence that early intuitions guiding infants’ mapping between magnitude across nonsymbolic number and observed action are used in an explicit way only from late childhood, with a mapping between action and size possibly being the most intuitive. An initial coarse mapping between number and action is likely modulated with extensive experience with grasping and related actions directed to both arrays and individual objects.     

Interpolation and Amalgamation; Pushing the Limits. Part II

This is the second part of the paper [Part I] which appeared in the previous issue of this journal.