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

Novel Missense Mitochondrial ND4L Gene Mutations in Friedreich's Ataxia

AbstractObjective(s)The mitochondrial defects in Friedreich's ataxia have been reported in many researches. Mitochondrial DNA is one of the candidates for defects in mitochondrion, and complex I is the first and one of the largest catalytic complexes of oxidative phosphorylation (OXPHOS) system. Materials and MethodsWe searched the mitochondrial ND4L gene for mutations by TTGE and sequencing on 30 FRDA patients and 35 healthy controls.ResultsWe found 3 missense mutations [m.10506A>G (T13A), m.10530G>A (V21M), and m.10653G>A (A62T)] in four patients whose m.10530G>A and m.10653G>A were not reported previously. In two patients, heteroplasmic m.10530G>A mutation was detected. They showed a very early ataxia syndrome. Our results showed that the number of mutations in FRDA patients was higher than that in the control cases (P= 0.0287).ConclusionAlthough this disease is due to nuclear gene mutation, the presence of these mutations might be responsible for further mitochondrial defects and the increase of the gravity of the disease. Thus, it should be considered in patients with this disorder