A Finite Model Property for Gödel Modal Logics

A new semantics with the finite model property is provided and used to establish decidability for Gödel modal logics based on (crisp or fuzzy) Kripke frames combined locally with Gödel logic. A similar methodology is also used to establish decidability, and indeed co-NP-completeness for a Gödel S5 logic that coincides with the one-variable fragment of first-order Gödel logic.

Multi-modal glioblastoma segmentation: man versus machine

BACKGROUND AND PURPOSE Reproducible segmentation of brain tumors on magnetic resonance images is an important clinical need. This study was designed to evaluate the reliability of a novel fully automated segmentation tool for brain tumor image analysis in comparison to manually defined tumor segmentations. METHODS We prospectively evaluated preoperative MR Images from 25 glioblastoma patients. Two independent expert raters performed manual segmentations. Automatic segmentations were performed using the Brain Tumor Image Analysis software (BraTumIA). In order to study the different tumor compartments, the complete tumor volume TV (enhancing part plus non-enhancing part plus necrotic core of the tumor), the TV+ (TV plus edema) and the contrast enhancing tumor volume CETV were identified. We quantified the overlap between manual and automated segmentation by calculation of diameter measurements as well as the Dice coefficients, the positive predictive values, sensitivity, relative volume error and absolute volume error. RESULTS Comparison of automated versus manual extraction of 2-dimensional diameter measurements showed no significant difference (p = 0.29). Comparison of automated versus manual segmentation of volumetric segmentations showed significant differences for TV+ and TV (p<0.05) but no significant differences for CETV (p>0.05) with regard to the Dice overlap coefficients. Spearman's rank correlation coefficients (ρ) of TV+, TV and CETV showed highly significant correlations between automatic and manual segmentations. Tumor localization did not influence the accuracy of segmentation. CONCLUSIONS In summary, we demonstrated that BraTumIA supports radiologists and clinicians by providing accurate measures of cross-sectional diameter-based tumor extensions. The automated volume measurements were comparable to manual tumor delineation for CETV tumor volumes, and outperformed inter-rater variability for overlap and sensitivity.

A Hennessy-Milner Property for Many-Valued Modal Logics

A Hennessy-Milner property, relating modal equivalence and bisimulations, is defined for many-valued modal logics that combine a local semantics based on a complete MTL-chain (a linearly ordered commutative integral residuated lattice) with crisp Kripke frames. A necessary and sufficient algebraic condition is then provided for the class of image-finite models of these logics to admit the Hennessy-Milner property. Complete characterizations are obtained in the case of many-valued modal logics based on BL-chains (divisible MTL-chains) that are finite or have universe [0,1], including crisp Lukasiewicz, Gödel, and product modal logics.