Is nevtral NEUTRAL? Visual similarity effects in the early phases of written-word recognition

For simplicity, contemporary models of written-word recognition and reading have unspecified feature/letter levels—they predict that the visually similar substituted-letter nonword PEQPLE is as effective at activating the word PEOPLE as the visually dissimilar substituted-letter nonword PEYPLE. Previous empirical evidence on the effects of visual similarly across letters during written-word recognition is scarce and nonconclusive. To examine whether visual similarity across letters plays a role early in word processing, we conducted two masked priming lexical decision experiments (stimulus-onset asynchrony = 50 ms). The substituted-letter primes were visually very similar to the target letters (u/v in Experiment 1 and i/j in Experiment 2; e.g., nevtral–NEUTRAL). For comparison purposes, we included an identity prime condition (neutral–NEUTRAL) and a dissimilar-letter prime condition (neztral-NEUTRAL). Results showed that the similar-letter prime condition produced faster word identification times than the dissimilar-letter prime condition. We discuss how models of written-word recognition should be amended to capture visual similarity effects across letters.     

On the axiomatization of finiteK-frames

We find a short way to construct a formula which axiomatizes a given finite frame of the modal logicK, in the sense that for each finite frameA, we construct a formula ωA which holds in those and only those frames in which every formula true inA holds. To obtain this result we find, for each finite model \(\mathfrak{A}\) and each natural numbern, a formula ω \(\mathfrak{A}\) which holds in those and only those models in which every formula true in \(\mathfrak{A}\) , and involving the firstn propositional letters, holds.     

Effects of parafoveal word length and orthographic features on initial fixation landing positions in reading

Previous research has demonstrated that readers use word length and word boundary information in targeting saccades into upcoming words while reading. Previous studies have also revealed that the initial landing positions for fixations on words are affected by parafoveal processing. In the present study, we examined the effects of word length and orthographic legality on targeting saccades into parafoveal words. Long (8?C9 letters) and short (4?C5 letters) target words, which were matched on lexical frequency and initial letter trigram, were paired and embedded into identical sentence frames. The gaze-contingent boundary paradigm (Rayner, 1975) was used to manipulate the parafoveal information available to the reader before direct fixation on the target word. The parafoveal preview was either identical to the target word or was a visually similar nonword. The nonword previews contained orthographically legal or orthographically illegal initial letters. The results showed that orthographic preprocessing of the word to the right of fixation affected eye movement targeting, regardless of word length. Additionally, the lexical status of an upcoming saccade target in the parafovea generally did not influence preprocessing.     

Word skipping during sentence reading: effects of lexicality on parafoveal processing

Two experiments examined how lexical status affects the targeting of saccades during reading by using the boundary technique to vary independently the content of a letter string when seen in parafoveal preview and when directly fixated. Experiment 1 measured the skipping rate for a target word embedded in a sentence under three parafoveal preview conditions: full preview (e.g., brain–brain), pseudohomophone preview (e.g., brane–brain), and orthographic nonword control preview (e.g., brant–brain); in the first condition, the preview string was always an English word, while in the second and third conditions, it was always a nonword. Experiment 2 investigated three conditions where the preview string was always a word: full preview (e.g., beach–beach), homophone preview (e.g., beech–beach), and orthographic control preview (e.g., bench–beach). None of the letter string manipulations used to create the preview conditions in the experiments disrupted sublexical orthographic or phonological patterns. In Experiment 1, higher skipping rates were observed for the full (lexical) preview condition, which consisted of a word, than for the nonword preview conditions (pseudohomophone and orthographic control). In contrast, Experiment 2 showed no difference in skipping rates across the three types of lexical preview conditions (full, homophone, and orthographic control), although preview type did influence reading times. This pattern indicates that skipping not only depends on the presence of disrupted sublexical patterns of orthography or phonology, but also is critically dependent on processes that are sensitive to the lexical status of letter strings in the parafovea.     

On Birkhoff’s Common Abstraction Problem

In his milestone textbook Lattice Theory, Garrett Birkhoff challenged his readers to develop a ??common abstraction?? that includes Boolean algebras and latticeordered groups as special cases. In this paper, after reviewing the past attempts to solve the problem, we provide our own answer by selecting as common generalization of ${\mathcal{B} \mathcal{A}}$ and ${\mathcal{L} \mathcal{G}}$ their join ${\mathcal{B} \mathcal{A} \vee \mathcal{L} \mathcal{G}}$ in the lattice of subvarieties of ${\mathcal{F} \mathcal{L}}$ (the variety of FL-algebras); we argue that such a solution is optimal under several respects and we give an explicit equational basis for ${\mathcal{B} \mathcal{A} \vee \mathcal{L} \mathcal{G}}$ relative to ${\mathcal{F} \mathcal{L}}$ . Finally, we prove a Holland-type representation theorem for a variety of FL-algebras containing ${\mathcal{B} \mathcal{A} \vee \mathcal{L} \mathcal{G}}$ .     

The representation of Takeuti's\begin{array}{*{20}c} \parallel \\ \_ \\ \end{array} -operator

Gaisi Takeuti has recently proposed a new operation on orthomodular latticesL, \(\begin{array}{*{20}c} \parallel \\ \_ \\ \end{array} \) :P(L)»L. The properties of \(\begin{array}{*{20}c} \parallel \\ \_ \\ \end{array} \) suggest that the value of \(\begin{array}{*{20}c} \parallel \\ \_ \\ \end{array} \) (A) (A) \( \subseteq \) L) corresponds to the degree in which the elements ofA behave classically. To make this idea precise, we investigate the connection between structural properties of orthomodular latticesL and the existence of two-valued homomorphisms onL.     

Algebraic Functions

Let A be an algebra. We say that the functions f ₁, . . . , f _m : A ⁿ ?? A are algebraic on A provided there is a finite system of term-equalities ${{\bigwedge t_{k}(\overline{x}, \overline{z}) = s_{k}(\overline{x}, \overline{z})}}$ satisfying that for each ${{\overline{a} \in A^{n}}}$ , the m-tuple ${{(f_{1}(\overline{a}), \ldots , f_{m}(\overline{a}))}}$ is the unique solution in A ^m to the system ${{\bigwedge t_{k}(\overline{a}, \overline{z}) = s_{k}(\overline{a}, \overline{z})}}$ . In this work we present a collection of general tools for the study of algebraic functions, and apply them to obtain characterizations for algebraic functions on distributive lattices, Stone algebras, finite abelian groups and vector spaces, among other well known algebraic structures.     

Finite axiomatization for some intermediate logics

LetN. be the set of all natural numbers (except zero), and letD _n ^* = {k ∈N ∶k|n} ∪ {0} wherek¦n if and only ifn=k.x f or somex∈N. Then, an ordered setD _n ^* = 〈D _n ^* , ? _n , wherex? _ny iffx¦y for anyx, y∈D _n ^* , can easily be seen to be a pseudo-boolean algebra. In [5], V.A. Jankov has proved that the class of algebras {D _n ^* ∶n∈B}, whereB =,{k ∈N∶ ? \(\mathop \exists \limits_{n \in N} \) (n > 1 ≧n ² k)is finitely axiomatizable. The present paper aims at showing that the class of all algebras {D _n ^* ∶n∈B} is also finitely axiomatizable. First, we prove that an intermediate logic defined as follows: $$LD = Cn(INT \cup \{ p_3 \vee [p_3 \to (p_1 \to p_2 ) \vee (p_2 \to p_1 )]\} )$$ finitely approximatizable. Then, defining, after Kripke, a model as a non-empty ordered setH = 〈K, ?〉, and making use of the set of formulas true in this model, we show that any finite strongly compact pseudo-boolean algebra ? is identical with. the set of formulas true in the Kripke modelH _B = 〈P(?), ?〉 (whereP(?) stands for the family of all prime filters in the algebra ?). Furthermore, the concept of a structure of divisors is defined, and the structure is shown to beH D _n ^* = 〈P (D _n ^* ), ?〉for anyn∈N. Finally, it is proved that for any strongly compact pseudo-boolean algebraU satisfying the axiomp ₃∨ [p ₃→(p₁→p₂)∨(p₂→p₁)] there is a structure of divisorsD _* ⁿ such that it is possible to define a strong homomorphism froomiH D _n ^* ontoH D _U . Exploiting, among others, this property, it turns out to be relatively easy to show that \(LD = \mathop \cap \limits_{n \in N} E(\mathfrak{D}_n^* )\) .     

Asymmetric binding in serial memory for verbal and spatial information

As the number of studies showing that items can be retained as bound representations in memory increases, researchers are beginning to investigate how the different features are bound together. In the present study, we examined the relative importances of the verbal and spatial features in serial memory for visual stimuli. Participants were asked to memorize the order of series of letters presented visually in different locations on the computer screen. The results showed that manipulating the phonological similarity of the letters affected recall of their spatial locations, but that increasing the complexity of the spatial pattern had no effect on recall of the letters. This finding was observed in both order reconstruction (Exps. 1 and 2) and probe serial recall (Exps. 3 and 4), suggesting that verbal–spatial binding in serial memory for visual information is asymmetric.     

Neuter is not Common in Dutch: Eye Movements Reveal Asymmetrical Gender Processing

Native speakers of languages with transparent gender systems can use gender cues to anticipate upcoming words. To examine whether this also holds true for a non-transparent two-way gender system, i.e. Dutch, eye movements were monitored as participants followed spoken instructions to click on one of four displayed items on a screen (e.g., Klik op $de_{COM}$ rode appel $_{COM}$ , ‘Click on the $_\mathrm{COM}$ red apple $_\mathrm{COM}$ ’). The items contained the target, a colour- and/or gender-matching competitor, and two unrelated distractors. A mixed-effects regression analysis revealed that the presence of a colour-matching and/or gender-matching competitor significantly slowed the process of finding the target. The gender effect, however, was only observed for common nouns, reflecting the fact that neuter gender-marking cannot disambiguate as all Dutch nouns become neuter when used as diminutives. The gender effect for common nouns occurred before noun onset, suggesting that gender information is, at least partially, activated automatically before encountering the noun.     

Resolution of Algebraic Systems of Equations in the Variety of Cyclic Post Algebras

There is a constructive method to define a structure of simple k-cyclic Post algebra of order p, L _p,k , on a given finite field F(p ^k ), and conversely. There exists an interpretation ??₁ of the variety ${\mathcal{V}(L_{p,k})}$ generated by L _p,k into the variety ${\mathcal{V}(F(p^k))}$ generated by F(p ^k ) and an interpretation ??₂ of ${\mathcal{V}(F(p^k))}$ into ${\mathcal{V}(L_{p,k})}$ such that ??₂??₁(B) =  B for every ${B \in \mathcal{V}(L_{p,k})}$ and ??₁??₂(R) =  R for every ${R \in \mathcal{V}(F(p^k))}$ . In this paper we show how we can solve an algebraic system of equations over an arbitrary cyclic Post algebra of order p, p prime, using the above interpretation, Gröbner bases and algorithms programmed in Maple.     

Dependence and Independence

We introduce an atomic formula ${\vec{y} \bot_{\vec{x}}\vec{z}}$ intuitively saying that the variables ${\vec{y}}$ are independent from the variables ${\vec{z}}$ if the variables ${\vec{x}}$ are kept constant. We contrast this with dependence logic ${\mathcal{D}}$ based on the atomic formula = ${(\vec{x}, \vec{y})}$ , actually equivalent to ${\vec{y} \bot_{\vec{x}}\vec{y}}$ , saying that the variables ${\vec{y}}$ are totally determined by the variables ${\vec{x}}$ . We show that ${\vec{y} \bot_{\vec{x}}\vec{z}}$ gives rise to a natural logic capable of formalizing basic intuitions about independence and dependence. We show that ${\vec{y} \bot_{\vec{x}}\vec{z}}$ can be used to give partially ordered quantifiers and IF-logic an alternative interpretation without some of the shortcomings related to so called signaling that interpretations using = ${(\vec{x}, \vec{y})}$ have.     

Epistemic Operators in Dependence Logic

The properties of the ${\forall^{1}}$ quantifier defined by Kontinen and Väänänen in [13] are studied, and its definition is generalized to that of a family of quantifiers ${\forall^{n}}$ . Furthermore, some epistemic operators δ ⁿ for Dependence Logic are also introduced, and the relationship between these ${\forall^{n}}$ quantifiers and the δ ⁿ operators are investigated. The Game Theoretic Semantics for Dependence Logic and the corresponding Ehrenfeucht- Fraissé game are then adapted to these new connectives. Finally, it is proved that the ${\forall^{1}}$ quantifier is not uniformly definable in Dependence Logic, thus answering a question posed by Kontinen and Väänänen in the above mentioned paper.     

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.     

Probability Propagation in Generalized Inference Forms

Probabilistic inference forms lead from point probabilities of the premises to interval probabilities of the conclusion. The probabilistic version of Modus Ponens, for example, licenses the inference from \({P(A) = \alpha}\) and \({P(B|A) = \beta}\) to \({P(B)\in [\alpha\beta, \alpha\beta + 1 - \alpha]}\) . We study generalized inference forms with three or more premises. The generalized Modus Ponens, for example, leads from \({P(A_{1}) = \alpha_{1}, \ldots, P(A_{n})= \alpha_{n}}\) and \({P(B|A_{1} \wedge \cdots \wedge A_{n}) = \beta}\) to an according interval for P(B). We present the probability intervals for the conclusions of the generalized versions of Cut, Cautious Monotonicity, Modus Tollens, Bayes’ Theorem, and some SYSTEM O rules. Recently, Gilio has shown that generalized inference forms “degrade”—more premises lead to less precise conclusions, i.e., to wider probability intervals of the conclusion. We also study Adam’s probability preservation properties in generalized inference forms. Special attention is devoted to zero probabilities of the conditioning events. These zero probabilities often lead to different intervals in the coherence and the Kolmogorov approach.     

Indistinguishability, Choices, and Logics of Agency

This paper deals with structures ${\langle{\bf T}, I\rangle}$ in which T is a tree and I is a function assigning each moment a partition of the set of histories passing through it. The function I is called indistinguishability and generalizes the notion of undividedness. Belnap’s choices are particular indistinguishability functions. Structures ${\langle{\bf T}, I\rangle}$ provide a semantics for a language ${\mathcal{L}}$ with tense and modal operators. The first part of the paper investigates the set-theoretical properties of the set of indistinguishability classes, which has a tree structure. The significant relations between this tree and T are established within a general theory of trees. The aim of second part is testing the expressive power of the language ${\mathcal{L}}$ . The natural environment for this kind of investigations is Belnap’s seeing to it that (stit). It will be proved that the hybrid extension of ${\mathcal{L}}$ (with a simultaneity operator) is suitable for expressing stit concepts in a purely temporal language.