In this paper we will try to find resemblances of the operation of human consciousness with systems with the intention to simulate it mathematically. Also we will try to do the same for the non-conscious operations and try to synthesize the human mind in form of system with subsystems.

S4.2 is the modal logic of directed partial pre-orders and/or the modal logic of reflexive and transitive relational frames with a final cluster. It holds a distinguished position in philosophical...

Weak filters were introduced by K. Schlechta in the ’90s with the aim of interpreting defaults via a generalized ‘most’ quantifier in first-order logic. They arguably represent the largest class of structures that qualify as a ‘collection of large subsets’ of a given index set |$I$|⁠, in the sense that it is difficult to think of a weaker, but still plausible, definition of the concept. The notion of weak ultrafilter naturally emerges and has been used in epistemic logic and other (...) knowledge representation (KR) applications. We provide a comprehensive exposition of weak filters and ultrafilters, comparing them with their classical counterparts that have found very important applications in logic, set theory and topology. Weak (ultra)filters capture the ‘majorities’ of social choice theory (which coincide with the commonsense understanding of a ‘large subset’) and in that respect, they outperform classical (ultra)filters in their role as ‘collections of large subsets’. Yet, they lack some of the elegant properties of classical (ultra)filters that make them an almost perfect match for logical theories. We investigate the extent to which some important classical results carry through in this new setting, and we focus on genuinely weak filters and genuinely weak ultrafilters. For weak ultrafilters, we proceed to provide concrete examples, answer questions of existence and characterize their construction. The class of weak (ultra)filters represents a genuine contribution of KR to set theory that might be of some interest to set theorists too and we initiate this study by providing a glimpse on natural set-theoretic questions. (shrink)

We examined if cancer patients' health-related quality of life (HRQoL) scores on the European Organisation for Research and Treatment of Cancer (EORTC) QLQ-C30 are affected by the specific time point, before or during treatment, at which the questionnaire is completed, and whether this could bias the overall treatment comparison analyses. A 'completion-time window' variable was created on three closed EORTC randomised control trials in lung (non-small cell lung cancer, NSCLC) and colorectal cancer (CRC) to indicate when the QLQ-30 was completed (...) relative to chemotherapy cycle dates, defined as 'before', 'on' and 'after'. HRQoL mean scores were calculated using a linear mixed model. Statistically significant differences (P < 0.05) were observed on 6 and 5 scales for 'on' and 'after' comparisons in the NSCLC and two-group CRC trial, respectively. As for the three-group CRC trial, several statistical differences were observed in the 'before' to 'on' and the 'on' to 'after' comparisons. For all three trials, including the 'completion-time window' variable in the model resulted in a better fit, but no substantial changes in the treatment effects were noted. We showed that considering the exact timing of completion within specified windows resulted in statistical and potentially clinically significant differences, but it did not alter the conclusions of treatment comparison in these studies. (shrink)