On Fork Arrow Logic and its Expressive Power

We compare fork arrow logic, an extension of arrow logic, and its natural first-order counterpart (the correspondence language) and show that both have the same expressive power. Arrow logic is a modal logic for reasoning about arrow structures, its expressive power is limited to a bounded fragment of first-order logic. Fork arrow logic is obtained by adding to arrow logic the fork modality (related to parallelism and synchronization). As a result, fork arrow logic attains the expressive power of its first-order correspondence language, so both can express the same input–output behavior of processes.     

On Ultrafilter Logic and Special Functions

Logics for generally were introduced for handling assertions with vague notions,such as generally, most, several, etc., by generalized quantifiers, ultrafilter logic being an interesting case. Here, we show that ultrafilter logic can be faithfully embedded into a first-order theory of certain functions, called coherent. We also use generic functions (akin to Skolem functions) to enable elimination of the generalized quantifier. These devices permit using methods for classical first-order logic to reason about consequence in ultrafilter logic.Presented by André Fuhrmann     

Squares in Fork Arrow Logic

In this paper we show that the class of fork squares has a complete orthodox axiomatization in fork arrow logic (FAL). This result may be seen as an orthodox counterpart of Venema's non-orthodox axiomatization for the class of squares in arrow logic. FAL is the modal logic of fork algebras (FAs) just as arrow logic is the modal logic of relation algebras (RAs). FAs extend RAs by a binary fork operator and are axiomatized by adding three equations to RAs equational axiomatization. A proper FA is an algebra of relations where the fork is induced by an injective operation coding pair formation. In contrast to RAs, FAs are representable by proper ones and their equational theory has the expressive power of full first-order logic. A square semantics (the set of arrows is U×U for some set U) for arrow logic was defined by Y. Venema. Due to the negative results about the finite axiomatizability of representable RAs, Venema provided a non-orthodox finite axiomatization for arrow logic by adding a new rule governing the applications of a difference operator. We address here the question of extending the type of relational structures to define orthodox axiomatizations for the class of squares. Given the connections between this problem and the finitization problem addressed by I. Németi, we suspect that this cannot be done by using only logical operations. The modal version of the FA equations provides an orthodox axiomatization for FAL which is complete in view of the representability of FAs. Here we review this result and carry it further to prove that this orthodox axiomatization for FAL also axiomatizes the class of fork squares.     

Anxiety sensitivity and fear of pain in patients with recurring headaches.

Anxiety sensitivity (AS) plays an important role in the cognitive, affective and behavioral profiles of patients with chronic pain related to musculoskeletal injury. However, investigators have not considered whether these findings extend to patients with other classes of chronic pain. The primary purpose of this investigation was to address this issue in 72 patients with recurring headaches who completed a self-report questionnaire inventory during a treatment visit to an outpatient neurology clinic. The mean ASI score for the group (mean = 24; SD = 11) was relatively high. When patients were classified on the basis of ASI scores, 20 (28%) met criteria for high, 41 (57%) for medium and 11 (15%) for low AS. Multivariate analysis of variance confirmed that these groups differed on specific aspects of their cognitive, affective, and behavioral profiles. High AS patients reported greater depression, trait anxiety, pain-related escape/avoidance behavior and fearful appraisals of pain than did patients with medium or low AS. High AS patients also indicated greater cognitive disruption in response to pain than did patients with low AS. Groups did not differ in headache severity, physiological reactivity, change in lifestyle, anger, nor did they differ in use of over-the-counter or prescribed analgesics. Multiple regression analysis identified AS, pain-related cognitive disruption, and sensory pain experience as significant predictors of fear of pain. Lifestyle changes attributed to headache were, on the other hand, predicted by headache severity, physiological and cognitive anxiety and escape/avoidance behavior. These results provide further evidence of the important association between AS and fear responses of patients with chronic pain syndromes. Implications and future directions are discussed.     

Changes in syllabus tone affect warmth (but not competence) ratings of both male and female instructors

The syllabus is often the first meaningful piece of information that students receive about a course. Previous research has indicated that students form more positive impressions of a course instructor after reading a syllabus that has been manipulated to convey information in a friendly, rather than unfriendly, tone (Harnish and Bridges in Soc Psychol Educ 14:319–330, 2011). While a friendly syllabus leads to increased perceptions of instructor warmth and approachability, it is unclear from this previous research whether a friendly syllabus may also lead to decreases in the perceived competence of the instructor. Thus, we aimed to clarify whether changes in syllabus tone affect perceptions of instructor competency. We also wished to explore the possibility of gender bias affecting these syllabus-based impressions of instructors, and to examine whether differences in syllabus tone impact the impressions formed of male and female instructors in the same way. Participants read a friendly or unfriendly course syllabus from either a male, female, or gender-unspecified instructor. Regardless of instructor gender, participants receiving the friendly syllabus perceived the instructor as being more approachable, more caring, and more motivating, but not any more or less competent, compared to those receiving the unfriendly syllabus. While instructors will be relieved to know that efforts to appear friendly on a course syllabus do not appear to negatively impact student perceptions of instructor competence, more research is needed to examine the potential role of gender bias on students’ initial impressions of instructors.