In this paper, we establish the first-order definability of sequents with consistent variable occurrence on bi-approximation semantics by means of the Sahlqvist–van Benthem algorithm. Then together with the canonicity results in Suzuki (2011), this allows us to establish a Sahlqvist theorem for substructural logic. Our result is not limited to substructural logic but is also easily applicable to other lattice-based logics.

In this paper, we extend the canonicity methodology in Ghilardi & Meloni (1997) to arbitrary lattice expansions, and syntactically describe canonical inequalities for lattice expansions consisting of -meet preserving operations, -multiplicative operations, adjoint pairs, and constants. This approach gives us a uniform account of canonicity for substructural and lattice-based logics. Our method not only covers existing results, but also systematically accounts for many canonical inequalities containing nonsmooth additive and multiplicative uniform operations. Furthermore, we compare our technique with the approach in (...) Dunn et al. (2005) and Gehrke et al. (2005). (shrink)

In this paper, we give a possible characterization of the distributivity on bi-approximation semantics. To this end, we introduce new notions of special elements on polarities and show that the distributivity is first-order definable on bi-approximation semantics. In addition, we investigate the dual representation of those structures and compare them with bi-approximation semantics for intuitionistic logic. We also discuss that two different methods to validate the distributivity—by the splitters and by the adjointness—can be explicated with the help of the axiom (...) of choice as well. (shrink)

This paper reports on a quiz robot experiment in which we explore similarities and differences in human participant speech, gaze, and bodily conduct in responding to a robot’s speech, gaze, and bodily conduct across two languages. Our experiment involved three-person groups of Japanese and English-speaking participants who stood facing the robot and a projection screen that displayed pictures related to the robot’s questions. The robot was programmed so that its speech was coordinated with its gaze, body position, and gestures in (...) relation to transition relevance places, key words, and deictic words and expressions in both languages. Contrary to findings on human interaction, we found that the frequency of English speakers’ head nodding was higher than that of Japanese speakers in human-robot interaction. Our findings suggest that the coordination of the robot’s verbal and non-verbal actions surrounding TRPs, key words, and deictic words and expressions is important for facilitating HRI irrespective of participants’ native language. Keywords: coordination of verbal and non-verbal actions; robot gaze comparison between English and Japanese; human-robot interaction ; transition relevance place ; conversation analysis. (shrink)