Succinctness in subsystems of the spatial mu-calculus

In this paper we systematically explore questions of succinctness in modal logics employed in spatial reasoning. We show that the closure operator, despite being less expressive, is exponentially more succinct than the limit-point operator, and that the $\mu$-calculus is exponentially more succinct than the equally-expressive tangled limit operator. These results hold for any class of spaces containing at least one crowded metric space or containing all spaces based on ordinals below $\omega^\omega$, with the usual limit operator. We also show that these results continue to hold even if we enrich the less succinct language with the universal modality

On the relative succinctness of some modal logics

The aim of this thesis is to compare several extensions of multimodal logic in terms of their representational succinctness on different classes of models. Succinctness is a natural refinement on the notion of expressivity. Intuitively, given two logics L1 and L2, we say that L1 expresses more succinctly than L2 some properties of a class of models if the L1-formulae expressing the properties in question are significantly shorter than all the equivalent L2-formulae. The precise technical interpretation of "significantly shorter" depends on the case at hand and may mean "exponentially shorter", "nonelementary shorter", etc. This work was motivated by the question of whether public announcement logic (PAL) is exponentially more succinct than multimodal logic (ML) on the class S5 of Kripke models with underlying structures in which all relations are reflexive, symmetric, and transitive. Using techniques based on a generalisation of Ehrenfeucht-Fra��ss�e games called Adler- Immerman games, we show that extending ML in two di�erent ways: by allowing formulae [

Eosinophilic granuloma of the skull bone: a case report Langenharns cell granulomatosis

Eosinophilic granuloma is a rare benign tumor which is a variety of histiocytosis-X with unknown etiology. Eosinophilic granuloma occurs as single or multiple lesions of bone destruction. The eosinophilic granuloma of the skull can be asymptomatic or presented with pain and swelling. We present a clinical case of 20-years-old female patient who has entered the Neurosurgery clinic of “St. Marina” University Hospital with clinical manifestation of growing and painful tumor formation in the left frontal area for several weeks. MRI scan discovered evidence of a tumor formation on the left frontal side of the skull, suspicious for an eosinophilic granuloma. Under general anesthesia, an operative treatment was performed. Total extirpation of the tumor mass was achieved and cranioplasty with titanium mesh of the bone defect was performed. Posteratively, the patient had a good cosmetic effect, she was mobilized on the first day after the intervention and discharged from the hospital on the 5th day. Surgery-related complications were not observed. In the postoperative period the patient was followed-up by a hematologist. It is important and recommended for clinicians to include eosinophilic granuloma in the differential diganosis of bone lesions in patients because of the possible expansion of the disease if untreated. A follow-up of a year is necessary for possible recurrence

Multiple proliferating trichilemmal cysts of the skalp: a case report. Multiple proliferating pilar tumors of the scalp

Proliferating trichilemmal cyst, also known as proliferating pilar scalp tumor, is a rare benign tumor of the hair follicle. While trichilemmal cysts are common intradermal or subcutaneous cysts, occuring in 5–10% of the population, only 2% will develop into proliferative trichilemmal cyst. The differential diagnosis should include lesions such as malignant proliferating trichilemmal tumor and squamous cell carcinoma. Surgical treatment is the only effective method for treating these rare cysts. We present a case report of a 78-years-old female patient who hasentered the Neurosurgery clinic of “St. Marina” University Hospital with clinical manifestation of rapidly growing from several months subcutaneous formation on the head and the presence of two smaller ones. MRI scan discovered three subcutaneous tumor formations suspicious for trichilem cysts, one of which was gigantic in size. After clinical discussion, under general anesthesia an operative treatment was performed with total extirpation of the cysts. Postoperatively, surgery-related complications were not observed. The patient was mobilized and verticalized on the day after intervention and discharged on the 5th day. As a result, a good cosmetic effect was obtained. Proliferating trichilemmal cyst is an uncommon neoplasm, and reporting of these lesions are important due to the good clinical evolution compared to the malignant macroscopic and microscopic feature of these tumor formations

Kinesitherapy in patients with ligament injuries of the ankle

The high incidence of ligament injury and the tendency to develop secondary motor deficiency allows selection and application of modern methods and techniques, to overcome ankle dysfunction more quickly and permanently theresult has been proven by numerous authors and clinical experiences, . The aim of this study is to examine the effect of the kinesitherapy method, in improving the functional status of patients with ligamentous injuries of the talocrural joint based on modern principles of manual mobilization and stretching. Material and methods: The study involved 13 patients with ligamentous injuries of the talocrural joint. In order to have homogeneity of the research, the patients were selected according to multiple criteria: to be between 20 and 50 years old; have not been diagnosed with other inflammatory condition (unilaterally and or bilaterally); not to have severe cardiovascular and respiratory failure. The subjects underwent a specialized kinesitherapy method, based on the current principles of kinesitherapy in ligamentous injuries of the talocrural joint. For the purposes of the research, a complex of diagnostic methods was applied, and the results of which are evaluated on the 1st day, the 15th day and the 1st month from the beginning of the treatment are shown on the worksheet. Assessed: motor capabilities with manual-muscle test (MMT), centimetry, ankle mobility test (goniometry). Results and discussion: The presence of a positive change in all parameters has been observed after the application of specialized kinesitherapy in all examined persons. The applied specialized kinesitherapy method stabilizes the functional possibilities for motor recovery in patients with ligamentous injuries of the talocrural joint. Conclusion: In conclusion, observed improvement is associated with the continuous application of the method with respect to the modern principles of kinesitherapy and the application of specialized techniques for mobilization of the talocrural joint

On the relative succinctness of modal logics with union, intersection and quantification

International audienceno abstrac

Succinctness in subsystems of the spatial mu-calculus

In this paper we systematically explore questions of succinctness in modal logics employed in spatial reasoning. We show that the closure operator, despite being less expressive, is exponentially more succinct than the limit-point operator, and that the mu-calculus is exponentially more succinct than the equally-expressive tangled limit operator. These results hold for any class of spaces containing at least one crowded metric space or containing all spaces based on ordinals below omega(omega), with the usual limit operator. We also show that these results continue to hold even if we enrich the less succinct language with the universal modality

A modal logic for Pawlak's approximation spaces with rough cardinality n

International audienceThe natural modal logic corresponding to Pawlak's approximation spaces is S5, based on the box modality [R]A (and the diamond modality 〈R〉A=¬[R]¬A), where R is the corresponding indiscernibility relation of the approximation space S=(W,R). However the expressive power of S5 is too weak and, for instance, we cannot express that the space S has exactly n equivalence classes (we say that S is roughly-finite and n is the rough cardinality of S). For this reason we extend the modal logic S5 with a new box modality [S]A, where S is the complement of R i.e. the discernibility relation of W. We propose a complete axiomatization, in this new language, of the logic ROUGH^n corresponding to the class of approximation spaces with rough cardinality n. We prove that the satisfiability problem for ROUGH^n is NP-complete