Compactness of first-order fuzzy logics

One of the nice properties of the first-order logic is the compactness of satisfiability. It state that a finitely satisfiable theory is satisfiable. However, different degrees of satisfiability in many-valued logics, poses various kind of the compactness in these logics. One of this issues is the compactness of $K$-satisfiability. Here, after an overview on the results around the compactness of satisfiability and compactness of $K$-satisfiability in many-valued logic based on continuous t-norms (basic logic), we extend the results around this topic. To this end, we consider a reverse semantical meaning for basic logic. Then we introduce a topology on $[0,1]$ and $[0,1]^2$ that the interpretation of all logical connectives are continuous with respect to these topologies. Finally using this fact we extend the results around the compactness of satisfiability in basic ogic

Classification and Retrieval of Digital Pathology Scans: A New Dataset

In this paper, we introduce a new dataset, \textbf{Kimia Path24}, for image classification and retrieval in digital pathology. We use the whole scan images of 24 different tissue textures to generate 1,325 test patches of size 1000$\times$1000 (0.5mm$\times$0.5mm). Training data can be generated according to preferences of algorithm designer and can range from approximately 27,000 to over 50,000 patches if the preset parameters are adopted. We propose a compound patch-and-scan accuracy measurement that makes achieving high accuracies quite challenging. In addition, we set the benchmarking line by applying LBP, dictionary approach and convolutional neural nets (CNNs) and report their results. The highest accuracy was 41.80\% for CNN.Comment: Accepted for presentation at Workshop for Computer Vision for Microscopy Image Analysis (CVMI 2017) @ CVPR 2017, Honolulu, Hawai

The Craig Interpolation Property in First-order G\"odel Logic

In this article, a model-theoretic approach is proposed to prove that the first-order G\"odel logic, $\mathbf{G}$, as well as its extension $\mathbf{G}^\Delta$ associated with first-order relational languages enjoy the Craig interpolation property. These results partially provide an affirmative answer to a question posed in [Aguilera, Baaz, 2017, Ten problems in G\"odel logic]