Combinatorial Bitstring Semantics for Arbitrary Logical Fragments

Logical geometry systematically studies Aristotelian diagrams, such as the classical square of oppositions and its extensions. These investigations rely heavily on the use of bitstrings, which are compact combinatorial representations of formulas that allow us to quickly determine their Aristotelian relations. However, because of their general nature, bitstrings can be applied to a wide variety of topics in philosophical logic beyond those of logical geometry. Hence, the main aim of this paper is to present a systematic technique for assigning bitstrings to arbitrary finite fragments of formulas in arbitrary logical systems, and to study the logical and combinatorial properties of this technique. It is based on the partition of logical space that is induced by a given fragment, and sheds new light on a number of interesting issues, such as the logic-dependence of the Aristotelian relations and the subtle interplay between the Aristotelian and Boolean structure of logical fragments. Finally, the bitstring technique also allows us to systematically analyze fragments from contemporary logical systems, such as public announcement logic, which could not be done before.     

A psychoanalytically informed hospitalization‐based treatment of personality disorders

This study presents a model of psychic change in personality disorders focusing on three dimensions: felt safety, mentalization and self‐object relations. Based upon this model a hospitalization‐based therapy program was created. Four scales to measure these three dimensions on the Object Relation Interview are discussed: the Felt Safety Scale, the Reflective Functioning Scale and the Bion Grid Scale and the Differentiation‐Relatedness Scale. A naturalistic symptom outcome study of the program showed a large effect on both symptoms and personality functioning. Furthermore, trajectory based on pre‐treatment patient characteristics (i.e., anaclitic versus introjective personality styles). Importantly, we also found a relation between symptomatic and personality change and change in felt safety and object relations. At 5‐year follow‐up, patients showed sustained improvement in symptomatic distress and further improvement in terms of personality and interpersonal functioning.     

A general proof of consistency of heuristic classification for cognitive diagnosis models

The Asymptotic Classification Theory of Cognitive Diagnosis (Chiu et al., 2009, Psychometrika, 74, 633–665) determined the conditions that cognitive diagnosis models must satisfy so that the correct assignment of examinees to proficiency classes is guaranteed when non‐parametric classification methods are used. These conditions have only been proven for the Deterministic Input Noisy Output AND gate model. For other cognitive diagnosis models, no theoretical legitimization exists for using non‐parametric classification techniques for assigning examinees to proficiency classes. The specific statistical properties of different cognitive diagnosis models require tailored proofs of the conditions of the Asymptotic Classification Theory of Cognitive Diagnosis for each individual model – a tedious undertaking in light of the numerous models presented in the literature. In this paper a different way is presented to address this task. The unified mathematical framework of general cognitive diagnosis models is used as a theoretical basis for a general proof that under mild regularity conditions any cognitive diagnosis model is covered by the Asymptotic Classification Theory of Cognitive Diagnosis.