Multiplication and comultiplication of beliefs

Multiplication and comultiplication of beliefs represent a generalisation of multiplication and comultiplication of probabilities as well as of binary logic AND and OR. Our approach follows that of subjective logic, where belief functions are expressed as opinions that are interpreted as being equivalent to beta probability distributions. We compare different types of opinion product and coproduct, and show that they represent very good approximations of the analytical product and coproduct of beta probability distributions. We also define division and codivision of opinions, and compare our framework with other logic frameworks for combining uncertain propositions. (C) 2004 Elsevier Inc. All rights reserved.

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.

An investigation of pretend play, mental state terms and false belief understanding: In search of a metarepresentational link

The aim of this study was to investigate the association between false belief comprehension, the exhibition of pretend play and the use of mental state terms in pre-school children. Ferry children, aged between 36 and 54 months were videotaped engaging in free play with each parent. The exhibit-ion of six distinct acts of pretend play and the expression of 16 mental sr:ate terms were coded during play. Each child was also administered a pantomime task and three standard false belief casks. Reliable associations were also found between false belief performance and the pretence categories of object substitution and role assignment, and the exhibition of imaginary object pantomimes. Moreover, the use of mental state terms was positively correlated with false belief and the pretence categories of object substitution, imaginary play and role assignment, and negatively correlated with the exhibition of body part object pantomimes. These findings indicate that the development of a mental state lexicon and some, bur not all, components of pretend play are dependent on the capacity for metarepresentational cognition.

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.

Drawing insight from pictures: The development of concepts of false drawing and false belief in children with deafness, normal hearing, and autism

Theory-of-mind concepts in children with deafness, autism, and normal development (N = 154) were examined in three experiments using a set of standard inferential false-belief tasks and matched sets of tasks involving false drawings. Results of all three experiments replicated previously published findings by showing that primary school children with deafness or autism, aged 6 to 13 years, scored significantly lower than normal-developing 4-year-old preschoolers on standard misleading-container and unseen-change tests of false-belief understanding. Furthermore, deaf and autistic children generally scored higher on drawing-based tests than on corresponding standard tests and, on the most challenging of the false-drawing tests in Experiment 2, they significantly outperformed the normal-developing preschoolers by clearly understanding their own false intentions and another person's false beliefs about an actively misleading drawing. In Experiment 3, preschoolers; outperformed older deaf and autistic children on standard tasks, but did less well on a task that required the drawing of a false belief. Methodological factors could not fully explain the findings, but early social and conversational experiences in the family were deemed likely contributors.

Corporate rumor activity, belief and accuracy

An integrated model relating workplace rumor activity, belief, and accuracy is proposed and tested. Senior VPs of Communications from a sample of Fortune-500 corporations and CEOs of established public relations firms were surveyed regarding rumor episodes that they had experienced. Results confirmed previous research on the role of uncertainty, anxiety, and belief in rumor activity. In addition, a reduced sense of control mediated the effects of uncertainty on anxiety, and anxiety mediated the effects of importance on rumor activity. Evidence was found for the roles of group bias in how strongly a rumor is believed. Rumor activity was also implicated in the formation of more accurate rumors. The significance of these results for rumor theory and for Public Relations practitioners is presented. (C) 2002 Elsevier Science Inc. All rights reserved.

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.

SHACC: a functional prototyper for a component calculus

Over the last decade component-based software development arose as a promising paradigm to deal with the ever increasing complexity in software design, evolution and reuse. SHACC is a prototyping tool for component-based systems in which components are modelled coinductively as generalized Mealy machines. The prototype is built as a HASKELL library endowed with a graphical user interface developed in Swing

Fractional calculus: a survey of useful formulas

This paper presents a survey of useful, established formulas in Fractional Calculus, systematically collected for reference purposes.

On development of fractional calculus during the last fifty years

Fractional calculus generalizes integer order derivatives and integrals. During the last half century a considerable progress took place in this scientific area. This paper addresses the evolution and establishes an assertive measure of the research development.