Definability and decidability of binary predicates for time granularity

In this paper we study the definability and decidability of binary predicates for time granularity in monadic languages interpreted over finitely and infinitely layered structures. We focus our attention on the equi-level (respectively equi-column) predicate constraining two time points to belong to the same layer (respectively column) and on the horizontal (respectively vertical) successor predicate relating a time point to its successor within a given layer (respectively column). We give a number of positive and negative results by reduction to/from a wide spectrum of decidable/undecidable problems.     

Illness Perception and Well-Being Among Persons with Multiple Sclerosis and Their Caregivers

This study jointly examined illness beliefs held by persons with multiple sclerosis (PwMS) and caregivers in relation to well-being. A group of 68 PwMS and their caregivers completed the Revised Illness Perception Questionnaire, Psychological Well-being Scales, Satisfaction with Life Scale and Positive Affect and Negative Affect Schedule. Findings revealed that PwMS’ well-being was primarily predicted by their own illness beliefs, and that also caregivers’ well-being was primarily predicted by their own beliefs. Across the two groups, well-being was positively associated with their belief that they understood the disease, and inversely associated with their representations of negative emotions. In addition, among PwMS, well-being was inversely associated with the number of symptoms they specifically attributed to their illness, while among caregivers, well-being was positively associated with beliefs that treatment could control the disease. Based on the study findings, psychoeducational and cognitive-behavioral strategies are suggested to promote well-being among PwMS and caregivers.     

Modal Deduction in Second-Order Logic and Set Theory - II

In this paper, we generalize the set-theoretic translation method for poly-modal logic introduced in [11] to extended modal logics. Instead of devising an ad-hoc translation for each logic, we develop a general framework within which a number of extended modal logics can be dealt with. We first extend the basic set-theoretic translation method to weak monadic second-order logic through a suitable change in the underlying set theory that connects up in interesting ways with constructibility; then, we show how to tailor such a translation to work with specific cases of extended modal logics.     

Dimensionality of the Latent Structure and Item Selection Via Latent Class Multidimensional IRT Models

With reference to a questionnaire aimed at assessing the performance of Italian nursing homes on the basis of the health conditions of their patients, we investigate two relevant issues: dimensionality of the latent structure and discriminating power of the items composing the questionnaire. The approach is based on a multidimensional item response theory model, which assumes a two-parameter logistic parameterization for the response probabilities. This model represents the health status of a patient by latent variables having a discrete distribution and, therefore, it may be seen as a constrained version of the latent class model. On the basis of the adopted model, we implement a hierarchical clustering algorithm aimed at assessing the actual number of dimensions measured by the questionnaire. These dimensions correspond to disjoint groups of items. Once the number of dimensions is selected, we also study the discriminating power of every item, so that it is possible to select the subset of these items which is able to provide an amount of information close to that of the full set. We illustrate the proposed approach on the basis of the data collected on 1,051 elderly people hosted in a sample of Italian nursing homes.     

A general tableau method for propositional interval temporal logics: Theory and implementation

In this paper, we focus our attention on tableau methods for propositional interval temporal logics. These logics provide a natural framework for representing and reasoning about temporal properties in several areas of computer science. However, while various tableau methods have been developed for linear and branching time point-based temporal logics, not much work has been done on tableau methods for interval-based ones. We develop a general tableau method for Venema's CDT logic interpreted over partial orders (BCDT⁺ for short). It combines features of the classical tableau method for first-order logic with those of explicit tableau methods for modal logics with constraint label management, and it can be easily tailored to most propositional interval temporal logics proposed in the literature. We prove its soundness and completeness, and we show how it has been implemented.