A Fibred Tableau Calculus for Modal Logics of Agents

In previous works we showed how to combine propositional multimodal logics using Gabbay's \emph{fibring} methodology. In this paper we extend the above mentioned works by providing a tableau-based proof technique for the combined/fibred logics. To achieve this end we first make a comparison between two types of tableau proof systems, (\emph{graph} $\&$ \emph{path}), with the help of a scenario (The Friend's Puzzle). Having done that we show how to uniformly construct a tableau calculus for the combined logic using Governatori's labelled tableau system \KEM. We conclude with a discussion on \KEM's features.

Calculation of line integrals in boundary integral methods

We propose quadrature rules for the approximation of line integrals possessing logarithmic singularities and show their convergence. In some instances a superconvergence rate is demonstrated.

A finite integral transform technique for solving the diffusion-reaction equation with Michaelis-Menten kinetics

An approximate analytical technique employing a finite integral transform is developed to solve the reaction diffusion problem with Michaelis-Menten kinetics in a solid of general shape. A simple infinite series solution for the substrate concentration is obtained as a function of the Thiele modulus, modified Sherwood number, and Michaelis constant. An iteration scheme is developed to bring the approximate solution closer to the exact solution. Comparison with the known exact solutions for slab geometry (quadrature) and numerically exact solutions for spherical geometry (orthogonal collocation) shows excellent agreement for all values of the Thiele modulus and Michaelis constant.

Two estimates concerning asymptotics of the minimizations of a Ginzburg-Landau functional

We prove two asymptotical estimates for minimizers of a Ginzburg-Landau functional of the form integral(Omega) [1/2 \del u\(2) + 1/4 epsilon(2) (1 - \u\(2))(2) W (x)] dx.

Is the irritable bladder associated with anterior compartment relaxation? A critical look at the 'integral theory of pelvic floor dysfunction'

The 'integral theory of pelvic floor dysfunction', first proposed by Petros and Ulmsten in 1990, claims that anterior vaginal wall relaxation is associated with symptoms of urgency, frequency, nocturia and urge incontinence. A retrospective study was designed to test this hypothesis. Imaging data and urodynamic reports from 272 women suffering from symptoms of lower urinary tract dysfunction were evaluated. Opening of the retrovesical angle, bladder neck descent, urethral rotation and descent of a cystocele during Valsalva were used to quantify anterior vaginal wall laxity None of the tested parameters were associated with symptoms and signs of detrusor overactivity. On the contrary, patients with higher grades of urethral and bladder descent were less likely to suffer from nocturia and urge incontinence and were less likely to leave sensory urgency and detrusor instability diagnosed on urodynamic testing. The findings of this study therefore do not support this hypothesis of the 'integral theory'.

Theory and applications of fuzzy Volterra integral equations

Formulations of fuzzy integral equations in terms of the Aumann integral do not reflect the behavior of corresponding crisp models. Consequently, they are ill-adapted to describe physical phenomena, even when vagueness and uncertainty are present. A similar situation for fuzzy ODEs has been obviated by interpretation in terms of families of differential inclusions. The paper extends this formalism to fuzzy integral equations and shows that the resulting solution sets and attainability sets are fuzzy and far better descriptions of uncertain models involving integral equations. The investigation is restricted to Volterra type equations with mildly restrictive conditions, but the methods are capable of extensive generalization to other types and more general assumptions. The results are illustrated by integral equations relating to control models with fuzzy uncertainties.

A refinement calculus for logic programs

Existing refinement calculi provide frameworks for the stepwise development of imperative programs from specifications. This paper presents a refinement calculus for deriving logic programs. The calculus contains a wide-spectrum logic programming language, including executable constructs such as sequential conjunction, disjunction, and existential quantification, as well as specification constructs such as general predicates, assumptions and universal quantification. A declarative semantics is defined for this wide-spectrum language based on executions. Executions are partial functions from states to states, where a state is represented as a set of bindings. The semantics is used to define the meaning of programs and specifications, including parameters and recursion. To complete the calculus, a notion of correctness-preserving refinement over programs in the wide-spectrum language is defined and refinement laws for developing programs are introduced. The refinement calculus is illustrated using example derivations and prototype tool support is discussed.

Enriched behavioral prediction equation and its impact on structured learning and the dynamic calculus

This theoretical note describes an expansion of the behavioral prediction equation, in line with the greater complexity encountered in models of structured learning theory (R. B. Cattell, 1996a). This presents learning theory with a vector substitute for the simpler scalar quantities by which traditional Pavlovian-Skinnerian models have hitherto been represented. Structured learning can be demonstrated by vector changes across a range of intrapersonal psychological variables (ability, personality, motivation, and state constructs). Its use with motivational dynamic trait measures (R. B. Cattell, 1985) should reveal new theoretical possibilities for scientifically monitoring change processes (dynamic calculus model; R. B. Cattell, 1996b), such as encountered within psycho therapeutic settings (R. B. Cattell, 1987). The enhanced behavioral prediction equation suggests that static conceptualizations of personality structure such as the Big Five model are less than optimal.

Induction in the timed interval calculus

The Timed Interval Calculus, a timed-trace formalism based on set theory, is introduced. It is extended with an induction law and a unit for concatenation, which facilitates the proof of properties over trace histories. The effectiveness of the extended Timed Interval Calculus is demonstrated via a benchmark case study, the mine pump. Specifically, a safety property relating to the operation of a mine shaft is proved, based on an implementation of the mine pump and assumptions about the environment of the mine. (C) 2002 Elsevier Science B.V. All rights reserved.