We show that a O-l law holds for propositional modal logic, both for structure validity and frame validity. In the case of structure validity, the result follows easily from the well-known O-l law for first-order logic. However, our proof gives considerably more information. It leads to an elegant axiomatization for almost-sure structure validity and to sharper complexity bounds. Since frame va...

In the pointfree topological context of locales and frames, real functions on a locale L are represented as localic morphisms S(L)→ L(R) (i.e. frame homomorphisms L(R) → S(L)) where S(L) stands for the frame of all sublocales of L and L(R) denotes the frame of reals. This is reminiscent of dealing with (not necessarily continuous) real functions X → R as with continuous functions D(X)→ R where ...

The structural behavior of T-frame bridges is particularly complicated and it is difficult using a general analytical method to directly acquire the internal forces in the structure. This paper presents a spatial grillage model for analysis of such bridges. The proposed model is validated by comparison with results obtained from field testing. It is shown that analysis of T-frame bridges may be...

This paper presents a hyperspectral remote sensing image analysis frame based on homogeneous-regions. In this frame, a multi-scale segmentation method based on Spectral Code Mapping (SCM) was proposed, and spatial relationship was discussed for improved classification.

This work focuses on the concept of frame of reference. Levinson (2003) suggested that spatial information encoded in one frame of reference cannot be translated into another one. While this is partially true in language, I argue for a nesting relationship between frames of reference at the conceptual level. A set of spatial concepts suggested by Lehman & Bennardo (2003) informs this investigat...

Compressed video may possess a number of artifacts, both spatial and temporal. Spatial compression artifacts arise as a result of quantization of the transform-domain coefficients, and are often manifested as blocking and ringing artifacts. Temporal limitations in compressed video occur when the encoder, in an effort to reduce bandwidth, drops frames. Omitting frames decreases the reconstructed...

In human robot dialogue, identifying intended referents from human partners’ spatial language is challenging. This is partly due to automated inference of potentially ambiguous underlying reference system (i.e., frame of reference). To improve spatial language understanding, we conducted an empirical study to investigate the prevalence of ambiguities of frame of reference. Our findings indicate...

Einstein’s general relativity with both metric and vielbein treated as independent fields is considered, demonstrating the existence of a consistent variational principle and deriving a Hamiltonian formalism that treats the spatial metric and spatial vielbein as canonical coordinates. This results in a Hamiltonian in standard form that consists of Hamiltonian and momentum constraints as well as...

Einstein’s general relativity with both metric and vielbein treated as independent fields is considered, demonstrating the existence of a consistent variational principle and deriving a Hamiltonian formalism that treats the spatial metric and spatial vielbein as canonical coordinates. This results in a Hamiltonian in standard form that consists of Hamiltonian and momentum constraints as well as...

Research in the field of spatial cognition has advocated a frame of reference (FOR) -based cognitive representation system to account for human’s spatial reasoning and navigation capacities. It has been argued that such mental models may also contribute to the underlying mechanisms of Theory of Mind (ToM). In the present study, we investigated how people made rapid judgments about the number of...