The Logic and Meaning of Plurals. Part II

In this sequel to “The logic and meaning of plurals. Part I”, I continue to present an account of logic and language that acknowledges limitations of singular constructions of natural languages and recognizes plural constructions as their peers. To this end, I present a non-reductive account of plural constructions that results from the conception of plurals as devices for talking about the many. In this paper, I give an informal semantics of plurals, formulate a formal characterization of truth for the regimented languages that results from augmenting elementary languages with refinements of basic plural constructions of natural languages, and account for the logic of plural constructions by characterizing the logic of those regimented languages.

Induction of Relational Schemas: Common Processes in Reasoning and Complex Learning

Five experiments were performed to test whether participants induced a coherent representation of the structure of a task, called a relational schema, from specific instances. Properties of a relational schema include: An explicit symbol for a relation, a binding that preserves the truth of a relation, potential for higher-order relations, omnidirectional access, potential for transfer between isomorphs, and ability to predict unseen items in isomorphic problems. However relational schemas are not necessarily coded in abstract form. Predictions from relational schema theory were contrasted with predictions from configural learning and other nonstructural theories in five experiments in which participants were taught a structure comprised of a set of initial-state,operator → end-state instances. The initial-state,operator pairs were presented and participants had to predict the correct end-state. Induction of a relational schema was achieved efficiently by adult participants as indicated by ability to predict items of a new isomorphic problem. The relational schemas induced showed the omnidirectional access property, there was efficient transfer to isomorphs, and structural coherence had a powerful effect on learning. The “learning to learn” effect traditionally associated with the learning set literature was observed, and the long-standing enigma of learning set acquisition is explained by a model composed of relational schema induction and structure mapping. Performance was better after reversal of operators than after shift to an alternate structure, even though the latter entailed more overlap with previously learned tasks in terms of the number of configural associations that were preserved. An explanation for the reversal shift phenomenon in terms of induction and mapping of a relational schema is proposed. The five experiments provided evidence supporting predictions from relational schema theory, and no evidence was found for configural or nonstructural learning theories.     

A linear conservative extension of Zermelo-Fraenkel set theory

In this paper, we develop the system LZF of set theory with the unrestricted comprehension in full linear logic and show that LZF is a conservative extension of ZF^– i.e., the Zermelo-Fraenkel set theory without the axiom of regularity. We formulate LZF as a sequent calculus with abstraction terms and prove the partial cut-elimination theorem for it. The cut-elimination result ensures the subterm property for those formulas which contain only terms corresponding to sets in ZF^–. This implies that LZF is a conservative extension of ZF^– and therefore the former is consistent relative to the latter. Hiroakira Ono     

Poor cognitive flexibility,and the experience thereof,in a subclinical sample of female students with obsessive‐compulsive symptoms

Research indicates that people with obsessive‐compulsive disorder (OCD) have poor cognitive flexibility. However, studies have largely focused on actual abilities and while individuals' emotional responses may be just as important, little is known about how those with OCD experience a situation that requires cognitive flexibility. It is furthermore largely unknown whether cognitive flexibility may also be important for people with OCD symptoms, rather than only to those with full blown disorders. This study investigates the relationship between cognitive flexibility, and the experience thereof in female students with and without OCD symptoms. It was expected that poor cognitive flexibility would be positively associated to OCD symptoms, and that those with OCD symptoms would display poor cognitive flexibility, and experience situations requiring cognitive flexibility as more difficult, than those without OCD symptoms. Participants completed a measure for OCD symptoms, a neuropsychological task to measure cognitive flexibility, and a self‐report measure assessing emotional experience of situations requiring cognitive flexibility. Positive associations between OCD symptoms and both poor cognitive flexibility and negative experience of situations requiring cognitive flexibility were found. Furthermore, those with OCD symptoms performed poorer on the cognitive flexibility task than those without OCD symptoms, and reported higher scores on the cognitive inflexibility questionnaire. Results confirm a relation between OCD symptoms and poor cognitive flexibility in a subclinical sample and identify a relation between OCD symptoms and a negative experience of situations that require cognitive flexibility. Overall findings suggest that poor cognitive flexibility may be an important part of OCD symptomatology.     

Fuzzy Identities for an Inclusive Anglohispanic Dialogue

When constructed in linear terms, cultures and identities misrepresent other people, constructing crisp boundaries that separate groups as if completely different. To demonstrate the negative impact of such views, I analyze cultural texts such as songs, films, and Web pages, showing the intercultural complexity existing in different constructions of Mexicanness as part of the dialogue arising in the political, social, and cultural interaction between Mexico and the United States. I emphasize the contrast between examples that reinforce identities that can be interpreted as fuzzy and inclusive, against those promoting and generating discrimination and exclusion.     

Learning to think in a ‘war zone’

This paper describes an experimental investigation of Winnicott's set situation as described by him in 1941. Three groups of South African infants, 7 to 9 months old, selected from white, black and institutionalized samples were tested three times in the set situation to validate Winnicott's findings and explore new ways of extending the usefulness of the set situation. The study also attempts to explore phantasy in infancy. The results show no significant differences between the black and white infants in the standard presentation, validating Winnicott's observations across different ethnic groups. However, significant differences in the institutionalized group were found, revealing considerable deviations and disturbances. In the second testing, where frustration was introduced, there were, however, significant differences in response to frustration between the black and white infants. Individual examples reveal the uniqueness of the responses to the situation. The situation provides a semi-structured infant observation which can be used as a diagnostic thermometer by professionals in the field of mental health.