Only countable common cause systems exist

In this paper we give a positive answer to a problem posed by G. Hofer-Szabo and M. Redei (2004) regarding the existence of infinite common cause systems (CCSs). An example of a countably infinite CCS is presented, as well as the proof that no CCSs of greater cardinality exist

Completion of the Causal Completability Problem

We give a few results concerning the notions of causal completability and causal closedness of classical probability spaces (Hofer-Szabó, Rédei & Szabó [1999], Gyenis & Rédei [2004]). Answering a question from Hofer-Szabó et al. [1999], we prove that any classical probability space has a causally closed extension. We also employ the notion of causal up-to-n-closedness (Wroński & Marczyk [2010a]) to show that any finite classical probability space with rational probabilities on the atoms of the event algebra can be extended to a finite space which is causally up-to-3-closed. Lastly, we prove that any classical probability space can be extended to a space in which all correlations between events which are logically independent modulo measure zero event have a countably infinite common cause system (for the definition of the latter notion, see Hofer-Szabó & Rédei [2004]). Collectively, these results show that it is surprisingly easy to find Reichenbach-style explanations for correlations, underlining doubts as to whether this approach can yield a philosophically relevant account of causality

A note on arbitrarily vertex decomposable graphs

A graph $G$ of order $n$ is said to be arbitrarily vertex decomposable if for each sequence $(n_{1},\ldots,n_k)$ of positive integers such that $n_{1}+\ldots+n_{k}=n$ there exists a partition $(V_{1},\ldots,V_{k})$ of the vertex set of $G$ such that for each $i \in \{1,\ldots,k\}$, $V_{i}$ induces a connected subgraph of $G$ on $n_i$ vertices. In this paper we show that if $G$ is a two-connected graph on $n$ vertices with the independence number at most $\lceil n/2\rceil$ and such that the degree sum of any pair of non-adjacent vertices is at least $n-3$, then $G$ is arbitrarily vertex decomposable. We present another result for connected graphs satisfying a similar condition, where the bound $n-3$ is replaced by $n-2$

Completion of the causal completability problem

We give a few results concerning the notions of causal completability and causal closedness of classical probability spaces (Hofer-Szabó et al. [1999]; Gyenis and Rédei [2004]). We prove that (i) any classical probability space has a causally closed extension; (ii) any finite classical probability space with positive rational probabilities on the atoms of the event algebra can be extended to a causally up-to-three-closed finite space; and (iii) any classical probability space can be extended to a space in which all correlations between events that are logically independent modulo measure zero event have a countably infinite common-cause system. Collectively, these results show that it is surprisingly easy to find Reichenbach-style ‘explanations' for correlations, underlining doubts as to whether this approach can yield a philosophically relevant account of causality

A New Notion of Causal Closedness

In recent years part of the literature on probabilistic causality concerned notions stemming from Reichenbach’s idea of explaining correlations between not directly causally related events by referring to their common causes. A few related notions have been introduced, e.g. that of a “common cause system” (Hofer-Szabó and Rédei in Int J Theor Phys 43(7/8):1819–1826, 2004) and “causal (N-)closedness” of probability spaces (Gyenis and Rédei in Found Phys 34(9):1284–1303, 2004; Hofer-Szabó and Rédei in Found Phys 36(5):745–756, 2006). In this paper we introduce a new and natural notion similar to causal closedness and prove a number of theorems which can be seen as extensions of earlier results from the literature. Most notably we prove that a finite probability space is causally closed in our sense iff its measure is uniform. We also present a generalisation of this result to a class of non-classical probability spaces

Predicting segmental substitution errors in aphasic patients with phonological and phonetic encoding impairments

This paper analyses the factors that predict substitution errors produced by four Broca's and four conduction aphasic subjects, all native speakers of Spanish, in reading and repetition tasks. Errors were elicited using a list of words where type of consonant, lexical stress and phonetic context were controlled for and where variables related to frequency of occurrence (word and syllable) and phonological neighbourhood characteristics were assigned using available online corpora. 675 substitution errors were obtained and preferential tendencies to devoice, occlusivise or spirantise were identified. Logistic regression mixed-effect models were performed on these three types of substitution errors to identify the predictors depending on the aphasic profile. While our results lent support to the hypothesis of a concomitant phonetic deficit in fluent aphasia, contrary to the classical claim, it also revealed differential patterns in the phonic behaviour of patients regarding the access to mental syllabary or syllabic position effects. Our results are discussed in relation to the phonetic vs. phonological impairments dimension in aphasia and the seriality/interactivity axis in speech architecturesEste estudio se propone identificar los factores que permiten predecir la aparición de errores segmentales de sustitución producidos por pacientes con afasia de Broca y de conducción en tareas de lectura y de repetición. El corpus utilizado para obtener los errores consistía en 240 palabras en las que las consonantes objeto de estudio -oclusivas, fricativas y africadas del español- se encontraban en distintos contextos fonéticos y acentuales. Posteriormente, se atribuyó a las palabras del corpus los valores relativos a la frecuencia léxica y silábica, así como las características relacionadas con la vecindad fonológica, empleando para ello corpus disponibles en línea. En total, se obtuvieron 675 sustituciones, en las que prevalecen tres tendencias: ensordecimiento de las oclusivas sonoras, refuerzo (oclusivización) de las fricativas y espirantización de las oclusivas. Para identificar los predictores de cualquiera de estos tres tipos de substitución en relación con el perfil clínico de afasia, se efectuó un análisis mediante el modelo mixto de regresión logística. Los resultados son globalmente congruentes con la hipótesis de un déficit fonético concomitante al déficit fonológico en la afasia de conducción, contrariamente a las predicciones de la hipótesis clásica. Sin embargo, el examen de los errores revela también patrones de tratamiento fónico distintos según el cuadro clínico, en relación con el silabario mental y la influencia de la posición silábica. Se propone una interpretación de estos resultados en el marco del espectro de déficits fonético-fonológicos en la afasia, así como en relación con la dimensión serialidad vs. interactividad que los modelos de codificación del habl