This paper presents Automath encodings (which are also valid in LF/λP) of various kinds of foundations of mathematics. Then it compares these encodings according to their size, to find out which foundation is the simplest.
The systems analyzed in this way are two kinds of set theory (ZFC and NF), two systems based on Church's higher order logic (Isabelle/Pure and HOL), three kinds of type theory (the calculus of constructions, Luo's extended calculus of constructions, and Martin-Löf's predicative type theory) and one foundation based on category theory.
The conclusions of this paper are that the simplest system is type theory (the calculus of constructions), but that type theories that know about serious mathematics are not simple at all. In that case the set theories are the simplest. If one looks at the number of concepts needed to explain such a system, then higher order logic is the simplest, with twenty-five concepts. On the other side of the scale, category theory is relatively complex, as is Martin-Löf's type theory.
(The full Automath sources of the contexts described in this paper are one the web at http://www.cs.ru.nl/~freek/zfc-etc/.) 相似文献
The present commentary addresses the main results obtained in the Butler and Klein [Butler, B. C., & Klein, R. (2009). Inattentional blindness for ignored words: Comparison of explicit and implicit memory tasks. Consciousness and Cognition, 18, 811–819.] study and discusses them in relation to the Perceptual Load Theory of Lavie [Lavie, N. (1995). Perceptual load as a necessary condition for selective attention. Journal of Experimental Psychology: Human Perception and Performance, 21, 451–68.]. The authors claim that the use of implicit indexes of conceptual distractor processing in high-load situations would be an important addition to the load literature, which would benefit the research field regardless of their positive or negative findings. 相似文献
Two eye-tracking studies assessed effects of grammatical and conceptual gender cues in generic role name processing in German. Participants read passages about a social or occupational group introduced by way of a generic role name (e.g., Soldaten/soldiers, Künstler/artists). Later in the passage the gender of this group was specified by the anaphoric expression diese Männer/these men or diese Frauen/these women. Testing masculine generic role names of male, female or neutral conceptual gender (Exp. 1) showed that a gender mismatch between the role name’s conceptual gender and the anaphor significantly slowed reading immediately before and after the anaphoric noun. A mismatch between the antecedent’s grammatical gender and the anaphor slowed down the reading of the anaphoric noun itself. Testing grammatically gender-unmarked role names (Exp. 2) revealed a general male bias in participants’ understanding, irrespective of grammatical or conceptual gender. The experiments extend previous findings on gender effects to non-referential role names and generic contexts. Theoretical aspects of gender and plural reference as well as gender information in mental models are discussed. 相似文献
Semantic understanding of numbers and related concepts can be dissociated from rote knowledge of arithmetic facts. However, distinctions among different kinds of semantic representations related to numbers have not been fully explored. Working with numbers and arithmetic requires representing semantic information that is both analogue (e.g., the approximate magnitude of a number) and symbolic (e.g., what / means). In this article, the authors describe a patient (MC) who exhibits a dissociation between tasks that require symbolic number knowledge (e.g., knowledge of arithmetic symbols including numbers, knowledge of concepts related to numbers such as rounding) and tasks that require an analogue magnitude representation (e.g., comparing size or frequency). MC is impaired on a variety of tasks that require symbolic number knowledge, but her ability to represent and process analogue magnitude information is intact. Her deficit in symbolic number knowledge extends to a variety of concepts related to numbers (e.g., decimal points, Roman numerals, what a quartet is) but not to any other semantic categories that we have tested. These findings suggest that symbolic number knowledge is a functionally independent component of the number processing system, that it is category specific, and that it is anatomically and functionally distinct from magnitude representations. 相似文献
Cross-cultural studios on stress are confounded by conceptual, methodological and applied problems. Although several comprehensive definitions of stress have been offered, the conceptual schema from which the definitions emerge reflect a Western perspective and are not always relevant when transposed into other cultures. The word stress itself is not easily translated into other languages which creates a problem for research workers in non-Western cultures. While studies in India of Westernized executives in organizations using Western models have offered valuable insights into problems related to organizational structures, executive stress, etc., they do not tell us a great deal about the nature and experience of stress in the rest of the population. A brief history of stress research is offered with a concentration on stress research in India. Conceptual and methodological issues are discussed leading to an assessment of the difficulties of stress research in India. 相似文献