We introduce the horizontal and vertical topologies on the product of topological spaces, and study their relationship with the standard product topology. We show that the modal logic of products of topological spaces with horizontal and vertical topologies is the fusion ${\bf S4}\oplus {\bf S4}$ . We axiomatize the modal logic of products of spaces with horizontal, vertical, and standard product topologies. We prove that both of these logics are complete for the product of rational numbers ${\Bbb Q}\times {\Bbb Q}$ (...) with the appropriate topologies. (shrink)

We introduce the horizontal and vertical topologies on the product of topological spaces, and study their relationship with the standard product topology. We show that the modal logic of products of topological spaces with horizontal and vertical topologies is the fusion S4 ⊕ S4. We axiomatize the modal logic of products of spaces with horizontal, vertical, and standard product topologies.We prove that both of these logics are complete for the product of rational numbers ℚ × ℚ with the appropriate topologies.

We introduce the horizontal and vertical topologies on the product of topological spaces, and study their relationship with the standard product topology. We show that the modal logic of products of topological spaces with horizontal and vertical topologies is the fusion S4 ⊕ S4. We axiomatize the modal logic of products of spaces with horizontal, vertical, and standard product topologies.We prove that both of these logics are complete for the product of rational numbers ℚ × ℚ with the appropriate topologies.

Sumner B. (Barney) Twiss, who died in 2023, was for ten years a General Editor of the Journal of Religious Ethics (JRE). He was a frequent contributor of articles, a member of the JRE Editorial Board, and a member of the journal's Board of Trustees. In this article, colleagues and students reflect on some of his many contributions, not only to the JRE but to the broader discursive fields of comparative religious ethics and human rights.

Several extensions of the basic modal language are characterized in terms of interpolation. Our main results are of the following form: Language ℒ' is the least expressive extension of ℒ with interpolation. For instance, let ℳ be the extension of the basic modal language with a difference operator [7]. First-order logic is the least expressive extension of ℳ with interpolation. These characterizations are subsequently used to derive new results about hybrid logic, relation algebra and the guarded fragment.

Teachers´ attitudes toward their students have been associated with differential teachers´ expectations and, in turn, with students´ educational pathways. Theories of social cognition can explain the link between attitudes and behavior. In this regard, the distinction between implicit and explicit attitudes is worth to be considered, whereby implicit attitudes are automatically activated when the attitude object is present and guide automatic behavior. In contrast, explicit attitudes infer deliberation and reflection, hence affecting controlled behavior. As teachers often are required to act (...) immediately in situations that do not allow for thoughtful reflection due to time restraints, teachers´ implicit attitudes concerning different student groups with shared characteristics, such as gender or ethnicity, may be especially important when considering teachers´ behavior in relation to students´ educational pathways. This notion is reflected by an increased interest in adopting implicit methodology in the educational domain. Over the last 10 years, several studies have been conducted in different countries, involving in- and preservice teachers and investigating their attitudes toward different student groups. Estimates of effects have varied and may be affected by sampling bias. To systematically review and integrate data from different studies, this meta-analysis focuses on teachers´ implicit attitudes. Following the systematic search of the database and initial screening, 43 articles were identified from which 22, describing 34 studies, were retained for the meta-analysis after further inspection. First analyses revealed an estimated average effect size of 0.56 for implicit attitudes in favor of non-marginalized groups. As there was a large extent of heterogeneity between studies, several moderator variables, were investigated. Results showed that the employed implicit measure and stimulus materials as well as the student target group affected the effect sizes. Low or non-significant relationships were reported between implicit and explicit attitudes. Findings are discussed in terms of theory and future research. (shrink)

In this paper we study the expressive power and definability for modal languages interpreted on topological spaces. We provide topological analogues of the van Benthem characterization theorem and the Goldblatt–Thomason definability theorem in terms of the well-established first-order topological language.

We consider second-order propositional modal logic (SOPML), an extension of the basic modal language with propositional quantifiers introduced by Kit Fine in 1970. We determine the precise expressive power of SOPML by giving analogues of the Van Benthem–Rosen theorem and the Goldblatt Thomason theorem. Furthermore, we show that the basic modal language is the bisimulation invariant fragment of SOPML, and we characterize the bounded fragment of first-order logic as being the intersection of first-order logic and SOPML.

Human language is a salient example of a neurocognitive system that is specialized to process complex dependencies between sensory events distributed in time, yet how this system evolved and specialized remains unclear. Artificial Grammar Learning (AGL) studies have generated a wealth of insights into how human adults and infants process different types of sequencing dependencies of varying complexity. The AGL paradigm has also been adopted to examine the sequence processing abilities of nonhuman animals. We critically evaluate this growing literature in (...) species ranging from mammals (primates and rats) to birds (pigeons, songbirds, and parrots) considering also cross‐species comparisons. The findings are contrasted with seminal studies in human infants that motivated the work in nonhuman animals. This synopsis identifies advances in knowledge and where uncertainty remains regarding the various strategies that nonhuman animals can adopt for processing sequencing dependencies. The paucity of evidence in the few species studied to date and the need for follow‐up experiments indicate that we do not yet understand the limits of animal sequence processing capacities and thereby the evolutionary pattern. This vibrant, yet still budding, field of research carries substantial promise for advancing knowledge on animal abilities, cognitive substrates, and language evolution. (shrink)

We prove ExpTime-membership of the satisfiability problem for loosely ∀-guarded first-order formulas with a bounded number of variables and an unbounded number of constants. Guarded fragments with constants are interesting by themselves and because of their connection to hybrid logic.

This paper provides several examples of how modal logic can be used in studying the XML document navigation language XPath. More specifically, we derive complete axiomatizations, computational complexity and expressive power results for XPath fragments from known results for corresponding logics. A secondary aim of the paper is to introduce XPath in a way that makes it accessible to an audience of modal logicians.

In this paper we argue that hybrid logic is the deductive setting most natural for Kripke semantics. We do so by investigating hybrid axiomatics for a variety of systems, ranging from the basic hybrid language (a decidable system with the same complexity as orthodox propositional modal logic) to the strong Priorean language (which offers full first-order expressivity).We show that hybrid logic offers a genuinely first-order perspective on Kripke semantics: it is possible to define base logics which extend automatically to a (...) wide variety of frame classes and to prove completeness using the Henkin method. In the weaker languages, this requires the use of non-orthodox rules. We discuss these rules in detail and prove non-eliminability and eliminability results. We also show how another type of rule, which reflects the structure of the strong Priorean language, can be employed to give an even wider coverage of frame classes. We show that this deductive apparatus gets progressively simpler as we work our way up the expressivity hierarchy, and conclude the paper by showing that the approach transfers to first-order hybrid logic. (shrink)

Artificial grammar learning (AGL) is used to study how human adults, infants, animals or machines learn various sorts of rules defined over sounds or visual items. Ten Cate et al. introduce the topic and provide a critical synthesis of this important interdisciplinary area of research. They identify the questions that remain open and the challenges that lie ahead, and argue that the limits of human, animal and machine learning abilities have yet to be found.

Dynamic predicate logic (DPL), presented in [5] as a formalism for representing anaphoric linking in natural language, can be viewed as a fragment of a well known formalism for reasoning about imperative programming [6]. An interesting difference from other forms of dynamic logic is that the distinction between formulas and programs gets dropped: DPL formulas can be viewed as programs. In this paper we show that DPL is in fact the basis of a hierarchy of formulas-as-programs languages.

Dynamic predicate logic (DPL), presented in [5] as a formalism for representing anaphoric linking in natural language, can be viewed as a fragment of a well known formalism for reasoning about imperative programming [6]. An interesting difference from other forms of dynamic logic is that the distinction between formulas and programs gets dropped: DPL formulas can be viewed as programs. In this paper we show that DPL is in fact the basis of a hierarchy of formulas-as-programs languages.

This paper provides several examples of how modal logic can be used in studying the XML document navigation language XPath. More specifically, we derive complete axiomatizations, computational complexity and expressive power results for XPath fragments from known results for corresponding logics. A secondary aim of the paper is to introduce XPath in a way that makes it accessible to an audience of modal logicians.

The implementation of inclusive policies is largely dependent on teachers´ willingness to accommodate students with special educational needs (SEN) in mainstream classrooms, which is affected by their perceived competence and attitudes. This study investigated attitudes of pre- and in-service teachers toward students with two types of SEN: challenging behavior and learning difficulties. The three components of attitude (affective, cognitive, and behavioral) were assessed using indirect and direct measures. Results revealed that teachers held negative implicit attitudes toward challenging behavior and learning (...) difficulties, however implicit attitudes did not vary as a function of the type of SEN. Ratings of the stereotypical dimensions warmth and competence and overall ratings of scholastic achievement were affected by professional status and type of SEN. Professional status, implicit attitudes and stereotypical knowledge together explained 52 and 43% of the variance in teachers´ ratings of academic proficiency for students with challenging behavior and learning difficulties, respectively. Results are interpreted within the theoretical framework and implications for teacher training are discussed. (shrink)

Edited in collaboration with FoLLI, the Association of Logic, Language and Information, this book represents the thoroughly refereed post-proceedings of the 6th International Tbilisi Symposium on Logic, Language, and Computation, TbiLLC 2005, held in Batumi, Georgia. The 19 revised full papers presented were carefully reviewed and selected from numerous presentations at the symposium. The papers present current research in all aspects of linguistics, logic and computation.

We introduce the horizontal and vertical topologies on the product of topological spaces, and study their relationship with the standard product topology. We show that the modal logic of products of topological spaces with horizontal and vertical topologies is the fusion S4 ⊕ S4. We axiomatize the modal logic of products of spaces with horizontal, vertical, and standard product topologies.We prove that both of these logics are complete for the product of rational numbers ℚ × ℚ with the appropriate topologies.

Background Genuine uncertainty on superiority of one intervention over the other is called equipoise. Physician-investigators in randomized controlled trials need equipoise at least in studies with more than minimal risks. Ideally, this equipoise is also present in patient-participants. In pediatrics, data on equipoise are lacking. We hypothesize that 1) lack of equipoise at enrolment among parents may reduce recruitment; 2) lack of equipoise during participation may reduce retention in patients assigned to a less favoured treatment-strategy. Methods We compared preferences of (...) parents/patients at enrolment, documented by a questionnaire, with preferences developed during follow-up by an interview-study to investigate equipoise of child-participants and parents in the BeSt-for-Kids-study. This trial in new-onset Juvenile Idiopathic Arthritis-patients consists of three strategies. One strategy comprises initial treatment with a biological disease-modifying-antirheumatic-drug, currently not standard-of-care. Semi-structured interviews were conducted with 23 parents and 7 patients, median 11 months after enrolment. Results Initially most parents and children were not in equipoise. Parents/patients who refused participation, regularly declined due to specific preferences. Many participating families preferred the biological-first-strategy. They participated to have a chance for this initial treatment, and would even consider stopping trial-participation when not randomized for it. Their conviction of superiority of the biological-first strategy was based on knowledge from internet and close relations. According to four parents, the physician-investigator preferred the biological-first-strategy, but the majority stated that she had no preferred strategy. In phase 2, preferences tended to change to the treatment actually received. Conclusions Lack of equipoise during enrolment did not reduce study recruitment, mainly due to the fact that preferred treatment was only available within the study. Still, when developing a trial it is important to evaluate whether the physicians’ research question is in line with preferences of the patient-group. By exploring so-called ‘informed patient-group’-equipoise, successful recruitment may be enhanced and bias avoided. In our study, lack of equipoise during trial-participation did not reduce retention in those assigned to a less favoured option. We observed a change for preference towards treatment actually received, possibly explained by comparable outcomes in all three arms. (shrink)

The human blood coagulation system comprises a series of linked glycoproteins that upon activation induce the generation of downstream enzymes ultimately forming fibrin. This process is primarily important to arrest bleeding (hemostasis). Hemostasis is a typical example of a molecular machine, where the assembly of substrates, enzymes, protein cofactors and calcium ions on a phospholipid surface markedly accelerates the rate of coagulation. Excess, pathological, coagulation activity occurs in “thrombosis”, the formation of an intravascular clot, which in the most dramatic form (...) precipitates in the microvasculature as disseminated intravascular coagulation. Thrombosis occurs according to a biochemical machine model in the case of atherothrombosis on a ruptured atherosclerotic plaque, but may develop at a slower rate in venous thrombosis, illustrating that the coagulation machinery can act at different velocities. The separate coagulation enzymes are also important in other biological processes, including inflammation for which the rapid conversion of one coagulation factor by the other is not a prerequisite. The latter role of coagulation enzymes may be related to the old and probably maintained function of the coagulation machine in innate immunity. BioEssays 25:1220–1228, 2003. © 2003 Wiley Perioicals, Inc. (shrink)

Mueller et al. discuss the role of acoustic cues in detecting language structure more generally. Across languages, there are clear links between acoustic cues and syntactic structure. They show that AGL experiments implementing analogous links demonstrate that prosodic cues, as well as various auditory biases, facilitate the learning of structural rules. Some of these biases, e.g. for auditory grouping, are also present in other species.