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.

Landmark Detection for Fusion of Fundus and MRI Towards a Patient-Specific Multi-Modal Eye Model

Ophthalmologists typically acquire different image modalities to diagnose eye pathologies. They comprise e.g., Fundus photography, Optical Coherence Tomography (OCT), Computed Tomography (CT) and Magnetic Resonance Imaging (MRI). Yet, these images are often complementary and do express the same pathologies in a different way. Some pathologies are only visible in a particular modality. Thus, it is beneficial for the ophthalmologist to have these modalities fused into a single patient-specific model. The presented article’s goal is a fusion of Fundus photography with segmented MRI volumes. This adds information to MRI which was not visible before like vessels and the macula. This article’s contributions include automatic detection of the optic disc, the fovea, the optic axis and an automatic segmentation of the vitreous humor of the eye.

Justifying induction on modal μ-formulae

We define a rank function for formulae of the propositional modal μ-calculus such that the rank of a fixed point is strictly bigger than the rank of any of its finite approximations. A rank function of this kind is needed, for instance, to establish the collapse of the modal μ-hierarchy over transitive transition systems. We show that the range of the rank function is ωω. Further we establish that the rank is computable by primitive recursion, which gives us a uniform method to generate formulae of arbitrary rank below ωω.

Modal interpolation via nested sequents

The main method of proving the Craig Interpolation Property (CIP) constructively uses cut-free sequent proof systems. Until now, however, no such method has been known for proving the CIP using more general sequent-like proof formalisms, such as hypersequents, nested sequents, and labelled sequents. In this paper, we start closing this gap by presenting an algorithm for proving the CIP for modal logics by induction on a nested-sequent derivation. This algorithm is applied to all the logics of the so-called modal cube.