The Incompleteness of Theories of Games

We first state a few previously obtained results that lead to general undecidability and incompleteness theorems in axiomatized theories that range from the theory of finite sets to classical elementary analysis. Out of those results we prove several incompleteness theorems for axiomatic versions of the theory of noncooperative games with Nash equilibria; in particular, we show the existence of finite games whose equilibria cannot be proven to be computable.     

Parietal ERP Activity and Appetite

Recent research on brain activity suggests that visual attention increases in response to emotional images. This increase is reflected in signs of greater activity, in response to different emotional visual stimuli, in parietal and parietooccipital areas in several studies employing neuroimaging techniques and event-related potentials (ERPs). In the latter case, greater parietal and parietooccipital negativities have been observed. The objective of the present study was to examine the role of a person's level of motivation towards the emotional stimulus with respect to this ERP pattern. Two groups of stimuli were presented to 60 participants: neutral or N (photographs of taps) and appetitive or A (photographs of cakes). The level of hunger was measured via a questionnaire. Recordings were taken at PO3, PO4, P7, and P8. The largest differences, as a function of appetite, were produced between 575 and 625 ms. Multiple regression analyses were carried out to study the relationship between subjects' appetite and their ERP recordings in response to A and N stimuli. There was a significant negative association between appetite and 575–625 mean amplitude in response to stimulus A at PO3 and PO4.     

Testing the age related differentiation hypothesis through the Wechsler’s scales

According to the age differentiation hypothesis (ADH), g becomes increasingly invested in specific abilities with age: with increasing age, g should account for a decreasing proportion of the variance in any particular cognitive test. However, there is no conclusive evidence concerning this important topic. Data from the Italian, Spanish, and American standardisation samples of the WPPSI and the WISC-R were analysed in the present study for testing the ADH. No changes in the proportion of variance associated with g in the 4–16 age range were found. This pattern does not change depending on the country. Therefore, the ADH is rejected: g seems to be very stable across age, and, thus, it seems to be an equally important component of intelligence test performance from early childhood to late adolescence.     

Maternal anxiety and depression and development of prematurely born infants in the first year of life

The purpose of this study was: (a) to assess and to compare anxiety and depression symptoms in mothers of preterm neonates during hospitalization in the Neonatal Intensive Care Unit, after discharge, and at the end of the infants' first year of life; and (b) to assess the child's development at 12 months of chronological corrected age (CCA). Thirty-six mothers, with no psychiatric antecedents assessed with the SCID-NP, were evaluated by STAI and BDI. The infants were assessed with Bayley-II Scales. There was a significant decrease in clinical symptoms of state-anxiety in mothers (p = .008), comparing the period during hospitalization and after discharge of the infants. Clinical symptoms of anxiety and depression were observed in 20% of the mothers at the end of the infants' first year of age. The majority of the infants exhibited normal development on Bayley-II at 12 months CCA; however, 25% of the infants displayed cognitive problems and 40% motor problems. The mothers' anxiety and depression symptoms decreased at the end of the first year of life of the pre-term infants and the children showed predominately normal development at this phase.     

Dual Equivalent Two-valued Under-determined and Over-determined Interpretations for Łukasiewicz’s 3-valued Logic Ł3

?ukasiewicz three-valued logic ?3 is often understood as the set of all 3-valued valid formulas according to ?ukasiewicz’s 3-valued matrices. Following Wojcicki, in addition, we shall consider two alternative interpretations of ?3: “well-determined” ?3a and “truth-preserving” ?3b defined by two different consequence relations on the 3-valued matrices. The aim of this paper is to provide (by using Dunn semantics) dual equivalent two-valued under-determined and over-determined interpretations for ?3, ?3a and ?3b. The logic ?3 is axiomatized as an extension of Routley and Meyer’s basic positive logic following Brady’s strategy for axiomatizing many-valued logics by employing two-valued under-determined or over-determined interpretations. Finally, it is proved that “well determined” ?ukasiewicz logics are paraconsistent.