In this article, we study logics of unknown truths and false beliefs under neighborhood semantics. We compare the relative expressivity of the two logics. It turns out that they are incomparable over various classes of neighborhood models, and the combination of the two logics are equally expressive as standard modal logic over any class of neighborhood models. We propose morphisms for each logic, which can help us explore the frame definability problem, show a general soundness and completeness result, and generalize some results in the literature. We axiomatize the two logics over various classes of neighborhood frames. Most importantly, by adopting the intersection semantics and the subset semantics in the literature, we extend the results to the case of public announcements, which gives us the desired reduction axioms and has good applications related to Moore sentences, successful formulas and self-refuting formulas. Also, we can say something about the comparative merits of the intersection semantics and the subset semantics.
A complete understanding of visual phonetic perception (lipreading) requires linking perceptual effects to physical stimulus properties. However, the talking face is a highly complex stimulus, affording innumerable possible physical measurements. In the search for isomorphism between stimulus properties and phoneticeffects, second-order isomorphism was examined between theperceptual similarities of video-recorded perceptually identified speech syllables and the physical similarities among the stimuli. Four talkers produced the stimulus syllables comprising 23 initial consonants followed by one of three vowels. Six normal-hearing participants identified the syllables in a visual-only condition. Perceptual stimulus dissimilarity was quantified using the Euclidean distances between stimuli in perceptual spaces obtained via multidimensional scaling. Physical stimulus dissimilarity was quantified using face points recorded in three dimensions by an optical motion capture system. The variance accounted for in the relationship between the perceptual and the physical dissimilarities was evaluated using both the raw dissimilarities and the weighted dissimilarities. With weighting and the full set of 3-D optical data, the variance accounted for ranged between 46% and 66% across talkers and between 49% and 64% across vowels. The robust second-order relationship between the sparse 3-D point representation of visible speech and the perceptual effects suggests that the 3-D point representation is a viable basis for controlled studies of first-order relationships between visual phonetic perception and physical stimulus attributes. 相似文献
