Finitely generated free Heyting algebras via Birkhoff duality and coalgebra

Algebras axiomatized entirely by rank 1 axioms are algebras for a functor and thus the free algebras can be obtained by a direct limit process. Dually, the final coalgebras can be obtained by an inverse limit process. In order to explore the limits of this method we look at Heyting algebras which have mixed rank 0-1 axiomatizations. We will see that Heyting algebras are special in that they are almost rank 1 axiomatized and can be handled by a slight variant of the rank 1 coalgebraic methods

LiMo0.15V2.85O8 AS CATHODE FOR ALL-SOLID-STATE BATTERY

For the obtained sample, the thermal stability and the temperature dependence of the electrical conductivity were studied. The impedance spectroscopy and pulse potentiometry methods, as well as voltammetry have been used to study the all-solid-state LiMo0.15V2.85O8 | Li+ solid-state electrolyte | LiMo0.15V2.85O8. It is shown that lithium-vanadium oxide has good adhesion to the lithium-cationic solid electrolyte, is characterized by the ability for reversible intercalation of lithium cations and does not degrade during cycling.Растворным методом синтезирован литий-ванадиевый оксид состава LiMo0.15V2.85O8. Соединение охарактеризовано методами рентгенофазового анализа, растровой электронной микроскопии и спектроскопии комбинационного рассеяния. Для образца изучена термическая стабильность и температурная зависимость электропроводности. Методами импеданса, импульсной потенциометрии и вольтамперометрии проведены изучения твердофазной электрохимической ячейки LiMo0.15V2.85O8 |Li+ твёрдый электролит| LiMo0.15V2.85O8. Показано, что литий-ванадиевый оксид обладает хорошей адгезией к литий-катионному твёрдому электролиту, характеризуется способностью к обратимому внедрению катионов лития и не деградирует при циклировании

Modal Logics of Topological Relations

Logical formalisms for reasoning about relations between spatial regions play a fundamental role in geographical information systems, spatial and constraint databases, and spatial reasoning in AI. In analogy with Halpern and Shoham's modal logic of time intervals based on the Allen relations, we introduce a family of modal logics equipped with eight modal operators that are interpreted by the Egenhofer-Franzosa (or RCC8) relations between regions in topological spaces such as the real plane. We investigate the expressive power and computational complexity of logics obtained in this way. It turns out that our modal logics have the same expressive power as the two-variable fragment of first-order logic, but are exponentially less succinct. The complexity ranges from (undecidable and) recursively enumerable to highly undecidable, where the recursively enumerable logics are obtained by considering substructures of structures induced by topological spaces. As our undecidability results also capture logics based on the real line, they improve upon undecidability results for interval temporal logics by Halpern and Shoham. We also analyze modal logics based on the five RCC5 relations, with similar results regarding the expressive power, but weaker results regarding the complexity

Complete axiomatization of the stutter-invariant fragment of the linear time µ-calculus

The logic µ(U) is the fixpoint extension of the "Until"-only fragment of linear-time temporal logic. It also happens to be the stutter-invariant fragment of linear-time µ-calculus µ(◊). We provide complete axiomatizations of µ(U) on the class of finite words and on the class of ω-words. We introduce for this end another logic, which we call µ(◊_Γ), and which is a variation of µ(◊) where the Next time operator is replaced by the family of its stutter-invariant counterparts. This logic has exactly the same expressive power as µ(U). Using already known results for µ(◊), we first prove completeness for µ(◊_Γ), which finally allows us to obtain completeness for µ(U)