Commutativeness of Fundamental Groups of Topological Groups
In this article we prove that fundamental groups based at the unit point of topological groups are commutative [11].
Compacidad Y Decibilidad De Logicas Monadicas Con Cuantificadores Cardinales.
Compactness and Löwenheim-Skolem properties in categories of pre-institutions
The abstract model-theoretic concepts of compactness and Löwenheim-Skolem properties are investigated in the "softer" framework of pre-institutions [18]. Two compactness results are presented in this paper: a more informative reformulation of the compactness theorem for pre-institution transformations, and a theorem on natural equivalences with an abstract form of the first-order pre-institution. These results rely on notions of compact transformation, which are introduced as arrow-oriented generalizations...
Compactness in Metric Spaces
In this article, we mainly formalize in Mizar [2] the equivalence among a few compactness definitions of metric spaces, norm spaces, and the real line. In the first section, we formalized general topological properties of metric spaces. We discussed openness and closedness of subsets in metric spaces in terms of convergence of element sequences. In the second section, we firstly formalize the definition of sequentially compact, and then discuss the equivalence of compactness, countable compactness,...
Comparing the succinctness of monadic query languages over finite trees
We study the succinctness of monadic second-order logic and a variety of monadic fixed point logics on trees. All these languages are known to have the same expressive power on trees, but some can express the same queries much more succinctly than others. For example, we show that, under some complexity theoretic assumption, monadic second-order logic is non-elementarily more succinct than monadic least fixed point logic, which in turn is non-elementarily more succinct than monadic datalog. Succinctness...
Comparing the succinctness of monadic query languages over finite trees
We study the succinctness of monadic second-order logic and a variety of monadic fixed point logics on trees. All these languages are known to have the same expressive power on trees, but some can express the same queries much more succinctly than others. For example, we show that, under some complexity theoretic assumption, monadic second-order logic is non-elementarily more succinct than monadic least fixed point logic, which in turn is non-elementarily more succinct than monadic datalog. Succinctness...
Completeness, functional completeness and relative completeness.
Completeness of cut-free type theories.
Completeness properties of classical theories of finite type and the normal form theorem [Book]
Completeness Theorem for a First Order Linear-time Logic
Complexité de la réduction en logique combinatoire
Complexity of the decidability of one class of formulas in quantifier-free set theory with a set-union operator.
Complexity of the decidability of the unquantified set theory with a rank operator.
Complexity of -term reductions
Computational complexity of a statistical theoremhood testing procedure for propositional calculus with pseudo-random inputs
Computational Interrpretations of Logics
Concerning basic notions of the measurement theory
Congruences parfaites et quasi-parfaites
Conservation Rules of Direct Sum Decomposition of Groups
In this article, conservation rules of the direct sum decomposition of groups are mainly discussed. In the first section, we prepare miscellaneous definitions and theorems for further formalization in Mizar [5]. In the next three sections, we formalized the fact that the property of direct sum decomposition is preserved against the substitutions of the subscript set, flattening of direct sum, and layering of direct sum, respectively. We referred to [14], [13] [6] and [11] in the formalization.
Considering uncertainty and dependence in Boolean, quantum and fuzzy logics
A degree of probabilistic dependence is introduced in the classical logic using the Frank family of -norms known from fuzzy logics. In the quantum logic a degree of quantum dependence is added corresponding to the level of noncompatibility. Further, in the case of the fuzzy logic with -states, (resp. -states) the consideration turned out to be fully analogous to (resp. considerably different from) the classical situation.