Dynamic algebras: Examples,constructions, applications

Dynamic algebras combine the classes of Boolean (B 0) and regular (R ; *) algebras into a single finitely axiomatized variety (B R ) resembling an R-module with scalar multiplication . The basic result is that * is reflexive transitive closure, contrary to the intuition that this concept should require quantifiers for its definition. Using this result we give several examples of dynamic algebras arising naturally in connection with additive functions, binary relations, state trajectories, languages, and flowcharts. The main result is that free dynamic algebras are residually finite (i.e. factor as a subdirect product of finite dynamic algebras), important because finite separable dynamic algebras are isomorphic to Kripke structures. Applications include a new completeness proof for the Segerberg axiomatization of prepositional dynamic logic, and yet another notion of regular algebra.Dept. of Computer Science, Stanford, CA 94305 This research was supported by the National Science Foundation under NSF grant no. MCS78-04338. Preparation of the present version was supported by the National Science Foundation under NSF grant number CCR-8814921.This paper originally appeared as Technical Memo #138, Laboratory for Computer Science, MIT, July 1979, and was subsequently revised, shortened, retitled, and published as [Pra80b]. After more than a decade of armtwisting I. Németi and H. Andréka finally persuaded the author to publish TM#138 itself on the ground that it contained a substantial body of interesting material that for the sake of brevity had been deleted from the STOC-80 version. The principal changes here to TM#138 are the addition of footnotes and the sections at the end on retrospective citations and reflections.     

Kathleen Wallace and the Network Self

Kathleen Wallace makes an important contribution to the theoretical frameworks available to understanding the nature of selves. Drawing on the theory of natural complexes proposed by Justus Buchler, Wallace proposes the “cumulative network model” (CNM) of selves. This article provides an overview of CNM, suggests its relation to recent New Materialist theories of agency, ideas of power, and the American philosophical tradition, and proposes that it can serve as a new resource in discussions of pressing problems faced in today’s world.     

Life's little (and big) lessons: identity statuses and meaning-making in the turning point narratives of emerging adults

A longitudinal study examined relations between 2 approaches to identity development: the identity status model and the narrative life story model. Turning point narratives were collected from emerging adults at age 23 years. Identity statuses were collected at several points across adolescence and emerging adulthood, as were measures of generativity and optimism. Narratives were coded for the sophistication of meaning-making reported, the event type in the narrative, and the emotional tone of the narrative. Meaning-making was defined as connecting the turning point to some aspect of or understanding of oneself. Results showed that less sophisticated meaning was associated particularly with the less advanced diffusion and foreclosure statuses, and that more sophisticated meaning was associated with an overall identity maturity index. Meaning was also positively associated with generativity and optimism at age 23, with stories focused on mortality experiences, and with a redemptive story sequence. Meaning was negatively associated with achievement stories. Results are discussed in terms of the similarities and differences in the 2 approaches to identity development and the elaboration of meaning-making as an important component of narrative identity.     

Distractibility after frontal lobe lesions: behavioral and event-related brain potential evidence

The authors used a semantic priming paradigm to investigate the distractibility phenomenon of patients with frontal lobe lesions (FLPs). They tested two distractibility categories: an inhibition category requiring inhibition of an automatic response and a distraction category caused by irrelevant, unexpected stimuli. Fifteen FLPs were compared with 2 matched control groups: 14 posterior-lesion patients and 15 normal controls. Both behavioral and event-related brain potential (ERP) measures were used. The results suggest that, although there were differences in performance between the FLP group and the control groups, there was no evidence that the FLPs had difficulty specifically with the inhibition category. The most consistent ERP result was that the FLP group had longer N100 latencies than either control group. On the basis of these results, the authors hypothesize that FLPs have difficulty focusing on and starting to process a new stimulus. The authors also discuss the unique contribution ERP evidence has made to cognitive studies.     

The effect of oral vocabulary on reading visually novel words: a comparison of the dual-route-cascaded and triangle frameworks

Dual-route-cascaded (DRC) (e.g. Coltheart & Rastle, Journal of Experimental Psychology: Human Perception and Performance 20 (1994) 1197) and triangle framework (e.g. Seidenberg & McClelland, Psychological Review 96 (1989) 523) predictions were tested regarding the effect of having a word in oral vocabulary prior to reading that same word. Over two sessions, at intervals of 2--3 days, 44 Grade 1 (6--7-year-old) children were aurally familiarized with the sound and meaning of ten novel words (semantic oral instantiation), and with just the sound of another ten novel words (non-semantic oral instantiation). Two to three days later non-word naming performance was significantly more accurate for aurally trained novel words compared to pseudohomophones, which were in turn advantaged over untrained non-words. The semantic manipulation had no effect. Experiment 2 manipulated articulation during (non-semantic) training. Forty Grade 1 children participated. Again, aurally trained items were named more accurately and quickly than equivalently trained pseudohomophones, which were in turn advantaged over untrained non-words. The articulation manipulation had no effect. The results suggest that word-specific phonological information is represented in the reading system independently of semantic or articulatory influences. The results are interpreted as being problematic for both the DRC and triangle frameworks, but more so for the latter.     

Playing an action video game reduces gender differences in spatial cognition

We demonstrate a previously unknown gender difference in the distribution of spatial attention, a basic capacity that supports higher-level spatial cognition. More remarkably, we found that playing an action video game can virtually eliminate this gender difference in spatial attention and simultaneously decrease the gender disparity in mental rotation ability, a higher-level process in spatial cognition. After only 10 hr of training with an action video game, subjects realized substantial gains in both spatial attention and mental rotation, with women benefiting more than men. Control subjects who played a non-action game showed no improvement. Given that superior spatial skills are important in the mathematical and engineering sciences, these findings have practical implications for attracting men and women to these fields.     

Towards a Theological Metaphysics of Death

Death is an inescapable event. It defines our existence as mortal. It is both a marker of our finitude and a portal to a deeper mystery: what awaits us in, through, and beyond this moment of ending? In thinking about death in the context of a theological dialogue, I identify two key questions: the phenomenological ‘What is death?’ and the philosophical ‘What is the meaning of death?’ as the beginning points of reflection. In general, it is the function of religion to provide some sort of answer to these questions, to give death both coherent definition and adequate understanding. The primary religious response is to articulate appropriate beliefs. But in their intellectual formation and construction, beliefs draw on metaphysics—the structures of logic, language, conceptuality and general worldview presuppositions by which we render all things intelligible and communicable. In this article I shall undertake an exploration of Christian viewpoints on death, which will require noting antecedents and corollaries in Judaism, then discuss possible metaphysical readings of death, that is, philosophical understandings of death that lie within and under, as it were, the otherwise stated religious beliefs about death. The aim of this article is not to present a fully developed ‘theological metaphysics of death’ as such; rather, in the context of an inter-religious dialogical engagement, to raise issues and perspectives from a Christian point of view that might contribute to a wider, more encompassing, theistically oriented understanding of death.     

Inhibition of return to social signals of fear

The present study examined whether inhibition of return (IOR) is modulated by the fear relevance of the cue. Experiment 1 found similar magnitude of IOR was produced by neutral and fear faces and luminance matched cues. To allow a more sensitive measure of endogenously directed attention, Experiment 2 removed a central reorienting cue and more precisely measured the time course of IOR. At stimulus onset asynchronies (SOAs) of 500, 1,000 and 1,500 ms, fear face and luminance matched cues resulted in similar IOR. These findings suggest that IOR is triggered by event onsets and disregards event value. Views of IOR as an adaptive "foraging facilitator," whereby attention is guided to promote optimal sampling of important environmental events, are discussed.