Explorations and comparisons of actual, ideal, and ought forgiveness definitions : a Q-methodological study /

Numerous definitions of forgiveness have been proposed in the literature (e.g.. North, 1987; Enright, Freedman & Rique, 1998), most ofwhich are based on religious or philosophical notions, rather than on empirical evidence. Definitions employed by researchers have typically set very high standards for forgiveness. This research was designed to investigate the possibility that these definitions describe an ideal of forgiveness and may not reflect laypersons' beliefe and experiences. Using Higgins' Self-Discrepancy Theory as a fiamework, three types of forgiveness beliefs were investigated: actual, ideal, and ought Q-methodology (which permits intensive study ofphenomena in small samples) was employed to examine and compare participants' beliefs about forgiveness across these domains. Thirty participants (20 women), 25 to 78 years of age, were recruited firom the community. They were asked to sort a set of66 statements about forgiveness according to their level of agreement with each statement This process was repeated three times, with the goal of modelling participants' actual experiences, their ideals, and how they believed forgiveness ought to be. Three perspectives on forgiveness emerged across the domains: forgiveness as motivated by religious beliefs, reconciliation-focussed forgiveness, and conflicted forgiveness. These perspectives indicated that, for many participants, the definitions presented in the literature may coincide with their beliefs about how forgiveness would ideally be and should be, as well as with their experiences of forgiveness; however, a large number of participants' experiences of, and beliefs about, forgiveness do not conform to the standards set out in the literature, and to exclude these participants' experiences and beliefs would mean overlooking what forgiveness means to a large portion of people. Results of this study indicate that researchers need to keep an open mind about what forgiveness may mean to their participants.

Monte Carlo study of the XY-model on quasi-periodic lattices

Monte Carlo Simulations were carried out using a nearest neighbour ferromagnetic XYmodel, on both 2-D and 3-D quasi-periodic lattices. In the case of 2-D, both the unfrustrated and frustrated XV-model were studied. For the unfrustrated 2-D XV-model, we have examined the magnetization, specific heat, linear susceptibility, helicity modulus and the derivative of the helicity modulus with respect to inverse temperature. The behaviour of all these quatities point to a Kosterlitz-Thouless transition occuring in temperature range Te == (1.0 -1.05) JlkB and with critical exponents that are consistent with previous results (obtained for crystalline lattices) . However, in the frustrated case, analysis of the spin glass susceptibility and EdwardsAnderson order parameter, in addition to the magnetization, specific heat and linear susceptibility, support a spin glass transition. In the case where the 'thin' rhombus is fully frustrated, a freezing transition occurs at Tf == 0.137 JlkB , which contradicts previous work suggesting the critical dimension of spin glasses to be de > 2 . In the 3-D systems, examination of the magnetization, specific heat and linear susceptibility reveal a conventional second order phase transition. Through a cumulant analysis and finite size scaling, a critical temperature of Te == (2.292 ± 0.003) JI kB and critical exponents of 0:' == 0.03 ± 0.03, f3 == 0.30 ± 0.01 and I == 1.31 ± 0.02 have been obtained.

L-Fuzzy Structured Query Language

Lattice valued fuzziness is more general than crispness or fuzziness based on the unit interval. In this work, we present a query language for a lattice based fuzzy database. We define a Lattice Fuzzy Structured Query Language (LFSQL) taking its membership values from an arbitrary lattice L. LFSQL can handle, manage and represent crisp values, linear ordered membership degrees and also allows membership degrees from lattices with non-comparable values. This gives richer membership degrees, and hence makes LFSQL more flexible than FSQL or SQL. In order to handle vagueness or imprecise information, every entry into an L-fuzzy database is an L-fuzzy set instead of crisp values. All of this makes LFSQL an ideal query language to handle imprecise data where some factors are non-comparable. After defining the syntax of the language formally, we provide its semantics using L-fuzzy sets and relations. The semantics can be used in future work to investigate concepts such as functional dependencies. Last but not least, we present a parser for LFSQL implemented in Haskell.