Herbrand Theorems for Substructural Logics

Herbrand and Skolemization theorems are obtained for a broad family of first-order substructural logics. These logics typically lack equivalent prenex forms, a deduction theorem, and reductions of semantic consequence to satisfiability. The Herbrand and Skolemization theorems therefore take various forms, applying either to the left or right of the consequence relation, and to restricted classes of formulas.

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.

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.

Realizing public announcements by justifications

Modal public announcement logics study how beliefs change after public announcements. However, these logics cannot express the reason for a new belief. Justification logics fill this gap since they can formally represent evidence and justifications for an agent's belief. We present OPAL(K) and JPAL(K) , two alternative justification counterparts of Gerbrandy–Groeneveld's public announcement logic PAL(K) . We show that PAL(K) is the forgetful projection of both OPAL(K) and JPAL(K) . We also establish that JPAL(K) partially realizes PAL(K) . The question whether a similar result holds for OPAL(K) is still open.

Skolemization for Substructural Logics

The usual Skolemization procedure, which removes strong quantifiers by introducing new function symbols, is in general unsound for first-order substructural logics defined based on classes of complete residuated lattices. However, it is shown here (following similar ideas of Baaz and Iemhoff for first-order intermediate logics in [1]) that first-order substructural logics with a semantics satisfying certain witnessing conditions admit a “parallel” Skolemization procedure where a strong quantifier is removed by introducing a finite disjunction or conjunction (as appropriate) of formulas with multiple new function symbols. These logics typically lack equivalent prenex forms. Also, semantic consequence does not in general reduce to satisfiability. The Skolemization theorems presented here therefore take various forms, applying to the left or right of the consequence relation, and to all formulas or only prenex formulas.