一阶形式系统K~*及其完备性

模糊命题演算的形式系统L＊已经在模糊逻辑与模糊推理的结合研究中得到了成功的应用.本文考虑与系统L＊相应的一阶逻辑理论,建立了一阶形式系统K＊,并证明了这个系统的完备性.     

An approach to deciding the observational equivalence of Algol-like languages

We prove that the observational equivalence of third-order finitary (i.e. recursion-free) Idealized Algol (IA) is decidable using Game Semantics. By modelling the state explicitly in our games, we show that the denotation of a term M of this fragment of IA is a compactly innocent strategy-with-state, i.e. the strategy is generated by a finite view function f_M. Given any such f_M, we construct a real-time deterministic pushdown automaton (DPDA) that recognizes the complete plays of the knowing-strategy denotation of M. Since such plays characterize observational equivalence, and there is an algorithm for deciding whether any two DPDAs recognize the same language, we obtain a procedure for deciding the observational equivalence of third-order finitary IA. Restricted to second-order terms, the DPDA representation cuts down to a deterministic finite automaton; thus our approach gives a new proof of Ghica and McCusker’s regular-expression characterization for this fragment. Our algorithmic representation of program meanings, which is compositional, provides a foundation for model-checking a wide range of behavioural properties of IA and other cognate programming languages. Another result concerns second-order IA with full recursion: we show that observational equivalence for this fragment is undecidable.     

Restorations of punctured languages and similarity of languages

Punctured languages are languages whose words are partial words in the sense that the letters at some positions are unknown. We investigate to which extent restoration of punctured languages is possible if the number of unknown positions or the proportion of unknown positions per word, respectively, is bounded, and we study their relationships for different boundings. The considered restoration classes coincide with similarity classes according to some kind of similarity for languages. Thus all results we can also formulate in the language of similarity. We show some hierarchies of similarity classes for each class from the Chomsky hierarchy and prove the existence of linear languages which are not δ ‐similar to any regular language for any δ < ½. For δ ≥ ½ this is unknown but it could only be possible in the case of non‐slender linear languages. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A New Modal Lindström Theorem

We prove new Lindstr?m theorems for the basic modal propositional language, and for some related fragments of first-order logic. We find difficulties with such results for modal languages without a finite-depth property, high-lighting the difference between abstract model theory for fragments and for extensions of first-order logic. In addition we discuss new connections with interpolation properties, and the modal invariance theorem. Mathematics Subject Classification (2000): Primary 03B45; Secondary 03C95     

Finite turns and the regular closure of linear context-free languages

Turn bounded pushdown automata with different conditions for beginning a new turn are investigated. Their relationships with closures of the linear context-free languages under regular operations are studied. For example, automata with an unbounded number of turns that have to empty their pushdown store up to the initial symbol in order to start a new turn are characterized by the regular closure of the linear languages. Automata that additionally have to re-enter the initial state are (almost) characterized by the Kleene star closure of the linear languages. For both a bounded and an unbounded number of turns, requiring to empty the pushdown store is a strictly stronger condition than requiring to re-enter the initial state. Several new language families are obtained which form a double-stranded hierarchy. Closure properties of these families under AFL operations are derived. The regular closure of the linear languages share the strong closure properties of the context-free languages, i.e., the family is a full AFL. Interestingly, three natural new language families are not closed under intersection with regular languages and inverse homomorphism. Finally, an algorithm is presented parsing languages from the new families in quadratic time.     

Effect of ionic strength on the formal potential of the glass electrode in various saline media

We examined the variation with ionic strength (I, adjusted with KCl, KNO₃, KBr, NaCl or NaClO₄) of the formal potential (E_const) for glass electrodes exhibiting a Nernstian response (i.e. E_cell=E_const−s log [H⁺]). For this purpose, we investigated the different factors included in the formal potential, so we obtained reported values for the liquid junction potential as a function of ionic strength and determined the logarithm of the activity coefficient for the proton in various saline media, using Pitzer equations.     

Robustly complete synthesis of sampled-data control for continuous-time nonlinear systems with reach-and-stay objectives

Formal methods are becoming favorable for control and verification of safety-critical systems because of the rigorous model-based computation. Relying on an over-approximated model of the original system behaviors, formal control synthesis algorithms are not often complete, which means that a controller cannot necessarily be synthesized even if there exists one. The main result of this paper shows that, for continuous-time nonlinear systems, a sample-and-hold control strategy for a reach-and-stay specification can be synthesized whenever such a strategy exists for the same system with its dynamics perturbed by small disturbances. Control synthesis is carried out by a fixed-point algorithm that adaptively partitions the system state space into a finite number of cells. In each iteration, the reachable set from each cell after one sampling time is over-approximated within a precision determined by the bound of the disturbances. To meet such a requirement, we integrate validated high-order Taylor expansion of the system solution over one sampling period into every fixed-point iteration and provide a criterion for choosing the Taylor order and the partition precision. Two nonlinear system examples are given to illustrate the effectiveness of the proposed method.     

Complexing equilibria and redox potentials in the system Ag(II)/Ag(I)-1,10-phenanthroline in propylene carbonate

Predominance areas of various equilibria were identified and complex formation constants of Ag(I) with 1,10-phenanthroline were determined as well as the solubility product of the complex salt for Ag(phen)₂ClO₄ in propylene carbonate. The solubility product of AgNO₃ in propylene carbonate was estimated. The value of the formal potential of the system Ag(phen) ₂ ²⁺ /Ag(phen) ₂ ⁺ inPC was determined by chronovoltammetry. Differences in the stability of analogous complexes in water andPC are discussed.

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Die Gleichgewichtskonstante der Komplexierung und die Redoxpotentiale im System Ag(II)/Ag(I)-1,10-Phenantrolin in Propylencarbonat

Zusammenfassung Die Gebiete der Dominanz der einzelnen Gleichgewichte, die Bildungskonstanten ₁ und ₂ der Komplexe Ag(I) mit 1,10-Phenantrolin und der Wert des Löslichkeitsproduktes Ag(phen)₂ClO₄ in Propylencarbonat wurden bestimmt. Das Löslichkeitsprodukt von AgNO₃ in Propylencarbonat wurde abgeschätzt. Die Werte des formalen Potentials des Systems Ag(phen) ₂ ²⁺ /Ag(phen) ₂ ⁺ inPC wurden mit Hilfe cyclischer Voltametrie ermittelt. Es wurden weiterhin die Unterschiede in der Stabilität analoger Komplexe in Wasser und in Propylencarbonat diskutiert.

     

Complexing equilibria and redox potentials of the Ag(II)/Ag(I) system in the presence of 2,2′:6′,2″-terpyridine in water

Summary The conditional protonation constants (=0.1) for 2,2:6,2-terpyridine, logK ₁=4.93, logK ₂=3.69, were determined by thepH-metric method. The compositions of complexes of Ag²⁺ and Ag⁺ ions with 2,2:6,2-terpyridine (tp) were studied and equilibria of the complex formation process were described. The values of conditional complex formation constants are as follows: for Ag(tp) ₂ ⁺ :log₀₁=5.79, log₀₂=9.68, for Ag(tp) ₂ ²⁺ :log₀₂=25.31, while the conditional constant of the Ag(tp)NO₃ precipitate formation is:K _SO=2.45·10⁴. Using coulometric and chronovoltamperometric measurements, the redox systems being formed in the complex solutions of Ag(II) and Ag(I) were determined and described including their formal potentials.

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Komplexibildungsgleichgewichte und Redoxpotentiale des Systems Ag(II)/Ag(I) in Gegenwart von 2,2:6,2-Terpyridin in Wasser

Zusammenfassung Mit Hilfe derpH-metrischen Methode wurden die konditionalen Protonationskonstanten (=0.1) von 2,2:6,2-Terpyridin bestimmt: logK ₁=4.93, logK ₂=3.69. Es wurde auch die Zusammensetzung der Komplexe von Ag(II) und Ag(I) mit 2,2:6,2-Terpyridin(tp) bestimmt sowie die Gleichgewichte der komplexbildung beschrieben. Die Werte der Konditionalkomplexbildungskonstanten sind: für Ag(tp) ₂ ⁺ :log₀₁=5.79, log₀₂=9.68, für Ag(tp) ₂ ²⁺ :log₀₂=25.31 und für das Löslichkeitsprodukt Ag(tp)NO₃:K _SO ^–1 =4.08·10^–5. Die in Komplexlösungen von Ag(II) und Ag(I) vorliegenden Redoxsysteme wurden mittels cyclischer Voltametrie und Coulometrie untersucht und die Formalpotentialwerte dieser Systeme in Wasser bestimmt.