Semilattice-based dualities

The paper discusses regularisation of dualities. A given duality between (concrete) categories, e.g. a variety of algebras and a category of representation spaces, is lifted to a duality between the respective categories of semilattice representations in the category of algebras and the category of spaces. In particular, this gives duality for the regularisation of an irregular variety that has a duality. If the type of the variety includes constants, then the regularisation depends critically on the location or absence of constants within the defining identities. The role of schizophrenic objects is discussed, and a number of applications are given. Among these applications are different forms of regularisation of Priestley, Stone and Pontryagin dualities.     

Pierre de La Ramée et le déclin de la rhétorique

This article provides a basic general introduction to Ramus, and evaluates his role in the history of logic and rhetoric, especially with relation to the study of argumentation. The author agrees with Ong and other historians of logic that Ramus is not to be taken seriously as a logician, and that his undoubted importance in the history of ideas is to be found elsewhere.Ramus advocates a belief in nature, experience and reason, and rejects the reliance on the authority of ancient philosophers, above all Aristotle, though experience does not mean scientific experiment and, paradoxically, includes the example of great philosophers and writers. In the end Ramus is seen as responsible for substituting for ancient classical rhetoric an entirely ornamental rhetoric of figures which was to take over education (with the exception of the Jesuit schools) almost until our own day. This curtailing and diminishing of rhetoric is seen as a degeneration. Ancient five-part rhetoric had been concerned with convincing and persuading: Aristotle distinguished the analytic, scientific reasoning of logic, from dialectic which was based on opinion and probability and had close links with rhetoric; by the time of Cicero and Quintilian, who addressed themselves to jurists and politicians, logic has given way to dialectic. In the Middle Ages and the Renaissance the two become assimilated; the evolution of this is traced here through the thirteenth-century Summulae logicales of Peter of Spain to the fifteenth-century German humanist logician Rudolph Agricola, who influenced Ramus partly through the intermediary of Johann Sturm. Ramus took over their topical theories but restricted them to logic/dialectic, and left rhetoric with little more than tropes and figures. He believed that there was only one method for teaching all the arts, and one dialectic common to them all. The distinction between analytical and dialectical has disappeared, with far-reaching consequences for the study of argumentation. Over the centuries logic has lost its connection with controversy and persuasion. With the development of the post-Cartesian, post-Baconian emphasis on the clarity of scientific discourse, and the mid-nineteenth-century interest in mathematical and formal logic, the process was complete. Argumentation, or the new rhetoric, aims to fill the gap thus created.

     

Adaptations in driver deceleration behaviour with automatic incident detection: A naturalistic driving study

Traffic congestion and crash rates can be reduced by introducing variable speed limits (VSLs) and automatic incident detection (AID) systems. Previous findings based on loop detector measurements have revealed that drivers reduce their speeds while approaching traffic congestion when the AID system is active. Notwithstanding these behavioural effects, most microscopic traffic flow models assessing the impact of VSLs do not describe driver response accurately.This study analyses the main factors that influence driver deceleration behaviour while approaching traffic congestion with and without VSLs. The Dutch VSL database was linked to the driver behaviour data collected in the UDRIVE naturalistic driving study. Driver engagement in secondary tasks and glance behaviour were extracted from the video data. Linear mixed-effects models predicting the characteristics of deceleration events were estimated.The results show that the maximum deceleration is high when approaching a slower leader, when driving at high speeds and short distance headways, and close to the beginning of traffic congestion. The minimum time headway is short when driving at high speeds and changing lanes. Certain drivers showed higher decelerations and shorter time headways than others. Controlled for these main factors, smaller maximum decelerations were found when the VSLs were present and visible, and when the gantries were within close proximity. These factors could be incorporated into microscopic traffic simulations to evaluate the impact of AID systems on traffic congestion more realistically. Further research is needed to clarify the link between engagement in secondary tasks, glance behaviour and deceleration behaviour.     

Perception as abduction: turning sensor data into meaningful representation

This article presents a formal theory of robot perception as a form of abduction. The theory pins down the process whereby low-level sensor data is transformed into a symbolic representation of the external world, drawing together aspects such as incompleteness, top-down information flow, active perception, attention, and sensor fusion in a unifying framework. In addition, a number of themes are identified that are common to both the engineer concerned with developing a rigorous theory of perception, such as the one on offer here, and the philosopher of mind who is exercised by questions relating to mental representation and intentionality.     

Proof-Theoretic Modal PA-Completeness III: The Syntactic Proof

This paper is the final part of the syntactic demonstration of the Arithmetical Completeness of the modal system G; in the preceding parts [9] and [10] the tools for the proof were defined, in particular the notion of syntactic countermodel. Our strategy is: PA-completeness of G as a search for interpretations which force the distance between G and a GL-LIN-theorem to zero. If the GL-LIN-theorem S is not a G-theorem, we construct a formula H expressing the non G-provability of S, so that ⊢_GL-LIN ∼ H and so that a canonical proof T of ∼ H in GL-LIN is a syntactic countermodel for S with respect to G, which has the height θ(T) equal to the distance d(S, G) of S from G. Then we define the interpretation ξ of S which represents the proof-tree T in PA. By induction on θ(T), we prove that ⊢_PA S^ξ and d(S, G) > 0 imply the inconsistency of PA. This revised version was published online in June 2006 with corrections to the Cover Date.     

Effect of stride length on overarm throwing delivery: A linear momentum response

Changing stride length during overhand throwing delivery is thought to alter total body and throwing arm linear momentums, thereby altering the proportion of throwing arm momentum relative to the total body. Using a randomized cross-over design, nineteen pitchers (15 collegiate and 4 high school) were assigned to pitch two simulated 80-pitch games at ±25% of their desired stride length. An 8-camera motion capture system (240 Hz) integrated with two force plates (960 Hz) and radar gun tracked each throw. Segmental linear momentums in each plane of motion were summed yielding throwing arm and total body momentums, from which compensation ratio’s (relative contribution between the two) were derived. Pairwise comparisons at hallmark events and phases identified significantly different linear momentum profiles, in particular, anteriorly directed total body, throwing arm, and momentum compensation ratios (P ⩽ .05) as a result of manipulating stride length. Pitchers with shorter strides generated lower forward (anterior) momentum before stride foot contact, whereas greater upward and lateral momentum (toward third base) were evident during the acceleration phase. The evidence suggests insufficient total body momentum in the intended throwing direction may potentially influence performance (velocity and accuracy) and perhaps precipitate throwing arm injuries.     

Second order inductive logic and Wilmers' principle

We extend the framework of Inductive Logic to Second Order languages and introduce Wilmers' Principle, a rational principle for probability functions on Second Order languages. We derive a representation theorem for functions satisfying this principle and investigate its relationship with the first order principles of Regularity and Super Regularity.     

Reflecting rules: A note on generalizing the deduction theorem

The purpose of this brief note is to prove a limitative theorem for a generalization of the deduction theorem. I discuss the relationship between the deduction theorem and rules of inference. Often when the deduction theorem is claimed to fail, particularly in the case of normal modal logics, it is the result of a confusion over what the deduction theorem is trying to show. The classic deduction theorem is trying to show that all so-called ‘derivable rules’ can be encoded into the object language using the material conditional. The deduction theorem can be generalized in the sense that one can attempt to encode all types of rules into the object language. When a rule is encoded in this way I say that it is reflected in the object language. What I show, however, is that certain logics which reflect a certain kind of rule must be trivial. Therefore, my generalization of the deduction theorem does fail where the classic deduction theorem didn't.     

Peer Assessment of Aviation Performance: Inconsistent for Good Reasons

Research into expertise is relatively common in cognitive science concerning expertise existing across many domains. However, much less research has examined how experts within the same domain assess the performance of their peer experts. We report the results of a modified think‐aloud study conducted with 18 pilots (6 first officers, 6 captains, and 6 flight examiners). Pairs of same‐ranked pilots were asked to rate the performance of a captain flying in a critical pre‐recorded simulator scenario. Findings reveal (a) considerable variance within performance categories, (b) differences in the process used as evidence in support of a performance rating, (c) different numbers and types of facts (cues) identified, and (d) differences in how specific performance events affect choice of performance category and gravity of performance assessment. Such variance is consistent with low inter‐rater reliability. Because raters exhibited good, albeit imprecise, reasons and facts, a fuzzy mathematical model of performance rating was developed. The model provides good agreement with observed variations.