Skepticism and Epistemic Logic

This essay attempts to implement epistemic logic through a non-classical inference relation. Given that relation, an account of '(the individual) a knows that A' is constructed as an unfamiliar non-normal modal logic. One advantage to this approach is a new analysis of the skeptical argument.     

Optimal designs for the generalized partial credit model

Analysing ordinal data is becoming increasingly important in psychology, especially in the context of item response theory. The generalized partial credit model (GPCM) is probably the most widely used ordinal model and has found application in many large-scale educational assessment studies such as PISA. In the present paper, optimal test designs are investigated for estimating persons’ abilities with the GPCM for calibrated tests when item parameters are known from previous studies. We find that local optimality may be achieved by assigning non-zero probability only to the first and last categories independently of a person's ability. That is, when using such a design, the GPCM reduces to the dichotomous two-parameter logistic (2PL) model. Since locally optimal designs require the true ability to be known, we consider alternative Bayesian design criteria using weight distributions over the ability parameter space. For symmetric weight distributions, we derive necessary conditions for the optimal one-point design of two response categories to be Bayes optimal. Furthermore, we discuss examples of common symmetric weight distributions and investigate under what circumstances the necessary conditions are also sufficient. Since the 2PL model is a special case of the GPCM, all of these results hold for the 2PL model as well.     

Three boys and their stories: Atypical eating and primitive relations1

Eating disorders of whatever category, especially the most severe ones such as anorexia or bulimia, are often considered typical of the female sex. While this is correct concerning these two disorders, I suggest that there are other eating disorders that are more frequent among boys, especially the ones concerning atypical relations to food, notwithstanding the evidence that the already very well‐known syndromes of bulimia and anorexia are also gaining ground among males. However, similar, unspecified eating disorders do not seem to occur so often among girls. Clinical data from my private practice should be taken for granted considering these matters, since I do not yet have statistical data to back up my thesis. In examples from three clinical cases involving boys and one female vignette, I shall attempt to establish a relation between eating disorders and primitive relations with men and women. This relation goes well beyond the oft‐cited ‘contemporary’ causes of eating disorders. In addition, I shall situate these differences among symptoms of both sexes and relate them to impasses in different stages of emotional development, as well as to the extent to which girls’ identification with their mother’s sex can influence their acquisition of eating disorders.     

The Universal Group of a Heyting Effect Algebra

A Heyting effect algebra (HEA) is a lattice-ordered effect algebra that is at the same time a Heyting algebra and for which the Heyting center coincides with the effect-algebra center. Every HEA is both an MV-algebra and a Stone-Heyting algebra and is realized as the unit interval in its own universal group. We show that a necessary and sufficient condition that an effect algebra is an HEA is that its universal group has the central comparability and central Rickart properties. Presented by Daniele Mundici     

MV-Algebras and Quantum Computation

We introduce a generalization of MV algebras motivated by the investigations into the structure of quantum logical gates. After laying down the foundations of the structure theory for such quasi-MV algebras, we show that every quasi-MV algebra is embeddable into the direct product of an MV algebra and a “flat” quasi-MV algebra, and prove a completeness result w.r.t. a standard quasi-MV algebra over the complex numbers. Presented by Heinrich Wansing     

A comparison of momentary time sampling and partial-interval recording for evaluating functional relations

In the current study, momentary time sampling (MTS) and partial-interval recording (PIR) were compared to continuous-duration recording of stereotypy and to the frequency of self-injury during a treatment analysis to determine whether the recording method affected data interpretation. Five previously conducted treatment analysis data sets were analyzed by creating separate graphic displays for each measurement method (duration or frequency, MTS, and PIR). An expert panel interview and structured criterion visual inspection were used to evaluate treatment effects across measurement methods. Results showed that treatment analysis interpretations based on both discontinuous recording methods often matched those based on frequency or duration recording; however, interpretations based on MTS were slightly more likely to match those based on duration and those based on PIR were slightly more likely to match those based on frequency.     

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.     

What is Classical Mereology?

Classical mereology is a formal theory of the part-whole relation, essentially involving a notion of mereological fusion, or sum. There are various different definitions of fusion in the literature, and various axiomatizations for classical mereology. Though the equivalence of the definitions of fusion is provable from axiom sets, the definitions are not logically equivalent, and, hence, are not inter-changeable when laying down the axioms. We examine the relations between the main definitions of fusion and correct some technical errors in prominent discussions of the axiomatization of mereology. We show the equivalence of four different ways to axiomatize classical mereology, using three different notions of fusion. We also clarify the connection between classical mereology and complete Boolean algebra by giving two “neutral” axiom sets which can be supplemented by one or the other of two simple axioms to yield the full theories; one of these uses a notion of “strong complement” that helps explicate the connections between the theories.     

Execution architectures for program algebra

We investigate the notion of an execution architecture in the setting of the program algebra PGA, and distinguish two sorts of these: analytic architectures, designed for the purpose of explanation and provided with a process-algebraic, compositional semantics, and synthetic architectures, focusing on how a program may be a physical part of an execution architecture. Then we discuss in detail the Turing machine, a well-known example of an analytic architecture. The logical core of the halting problem—the inability to forecast termination behavior of programs—leads us to a few approaches and examples on related issues: forecasters and rational agents. In particular, we consider architectures suitable to run a Newcomb Paradox system and the Prisoner's Dilemma.