Kappa calculus and evidential strength: A note on Åqvist's logical theory of legal evidence

Lennart Åqvist (1992) proposed a logical theory of legal evidence, based on the Bolding-Ekelöf of degrees of evidential strength. This paper reformulates Åqvist's model in terms of the probabilistic version of the kappa calculus. Proving its acceptability in the legal context is beyond the present scope, but the epistemological debate about Bayesian Law isclearly relevant. While the present model is a possible link to that lineof inquiry, we offer some considerations about the broader picture of thepotential of AI & Law in the evidentiary context. Whereas probabilisticreasoning is well-researched in AI, calculations about the threshold ofpersuasion in litigation, whatever their value, are just the tip of theiceberg. The bulk of the modeling desiderata is arguably elsewhere, if one isto ideally make the most of AI's distinctive contribution as envisaged forlegal evidence research.

A class of generalized Lévy Laplacians in infinite dimensional calculus

A class of generalized Lévy Laplacians which contain as a special case the ordinary Lévy Laplacian are considered. Topics such as limit average of the second order functional derivative with respect to a certain equally dense (uniformly bounded) orthonormal base, the relations with Kuo’s Fourier transform and other infinite dimensional Laplacians are studied.

[Performance review] Carl Djerassi, Calculus

Review of a semi-staged performance of Calculus by Carl Djerassi at the Royal Institution, London on 30 September 2002.

A revised classification for direct tooth-colored restorative materials

Composite resins and glass-ionomer cements were introduced to dentistry in the 1960s and 1970s, respectively. Since then, there has been a series of modifications to both materials as well as the development other groups claiming intermediate characteristics between the two. The result is a confusion of materials leading to selection problems. While both materials are tooth-colored, there is a considerable difference in their properties, and it is important that each is used in the appropriate situation. Composite resin materials are esthetic and now show acceptable physical strength and wear resistance. However, they are hydrophobic, and therefore more difficult to handle in the oral environment, and cannot support ion migration. Also, the problems of gaining long-term adhesion to dentin have yet to be overcome. On the other hand, glass ionomers are water-based and therefore have the potential for ion migration, both inward and outward from the restoration, leading to a number of advantages. However, they lack the physical properties required for use in load-bearing areas. A logical classification designed to differentiate the materials was first published by McLean et al in 1994, but in the last 15 years, both types of material have undergone further research and modification. This paper is designed to bring the classification up to date so that the operator can make a suitable, evidence-based, choice when selecting a material for any given situation.

Does an incremental filling technique reduce polymerization shrinkage stresses

It is widely accepted that volumetric contraction and solidification during the polymerization process of restorative composites in combination with bonding to the hard tissue result in stress transfer and inward deformation of the cavity walls of the restored tooth. Deformation of the walls decreases the size of the cavity during the filling process. This fact has a profound influence on the assumption-raised and discussed in this paper-that an incremental filling technique reduces the stress effect of composite shrinkage on the tooth. Developing stress fields for different incremental filling techniques are simulated in a numerical analysis. The analysis shows that, in a restoration with a well-established bond to the tooth-as is generally desired-incremental filling techniques increase the deformation of the restored tooth. The increase is caused by the incremental deformation of the preparation, which effectively decreases the total amount of composite needed to fill the cavity. This leads to a higher-stressed tooth-composite structure. The study also shows that the assessment of intercuspal distance measurements as well as simplifications based on generalization of the shrinkage stress state cannot be sufficient to characterize the effect of polymerization shrinkage in a tooth-restoration complex. Incremental filling methods may need to be retained for reasons such as densification, adaptation, thoroughness of cure, and bond formation. However, it is very difficult to prove that incrementalization needs to be retained because of the abatement of shrinkage effects.

A multi-scale atomistic-continuum modelling of crack propagation in a two-dimensional macroscopic plate

A novel multi-scale seamless model of brittle-crack propagation is proposed and applied to the simulation of fracture growth in a two-dimensional Ag plate with macroscopic dimensions. The model represents the crack propagation at the macroscopic scale as the drift-diffusion motion of the crack tip alone. The diffusive motion is associated with the crack-tip coordinates in the position space, and reflects the oscillations observed in the crack velocity following its critical value. The model couples the crack dynamics at the macroscales and nanoscales via an intermediate mesoscale continuum. The finite-element method is employed to make the transition from the macroscale to the nanoscale by computing the continuum-based displacements of the atoms at the boundary of an atomic lattice embedded within the plate and surrounding the tip. Molecular dynamics (MD) simulation then drives the crack tip forward, producing the tip critical velocity and its diffusion constant. These are then used in the Ito stochastic calculus to make the reverse transition from the nanoscale back to the macroscale. The MD-level modelling is based on the use of a many-body potential. The model successfully reproduces the crack-velocity oscillations, roughening transitions of the crack surfaces, as well as the macroscopic crack trajectory. The implications for a 3-D modelling are discussed.

Multiscale numerical modelling of crack propagation in two-dimensional metal plate

A novel multiscale model of brittle crack propagation in an Ag plate with macroscopic dimensions has been developed. The model represents crack propagation as stochastic drift-diffusion motion of the crack tip atom through the material, and couples the dynamics across three different length scales. It integrates the nanomechanics of bond rupture at the crack tip with the displacement and stress field equations of continuum based fracture theories. The finite element method is employed to obtain the continuum based displacement and stress fields over the macroscopic plate, and these are then used to drive the crack tip forward at the atomic level using the molecular dynamics simulation method based on many-body interatomic potentials. The linkage from the nanoscopic scale back to the macroscopic scale is established via the Ito stochastic calculus, the stochastic differential equation of which advances the tip to a new position on the macroscopic scale using the crack velocity and diffusion constant obtained on the nanoscale. Well known crack characteristics, such as the roughening transitions of the crack surfaces, crack velocity oscillations, as well as the macroscopic crack trajectories, are obtained.

Effects of structure on the comprehensibility of formal specifications

Use of structuring mechanisms (such as modularisation) is widely believed to be one of the key ways to improve software quality. Structuring is considered to be at least as important for specification documents as for source code, since it is assumed to improve comprehensibility. Yet, as with most widely held assumptions in software engineering, there is little empirical evidence to support this hypothesis. Also, even if structuring can be shown to he a good thing, we do not know how much structuring is somehow optimal. One of the more popular formal specification languages, Z, encourages structuring through its schema calculus. A controlled experiment is described in which two hypotheses about the effects of structure on the comprehensibility of Z specifications are tested. Evidence was found that structuring a specification into schemas of about 20 lines long significantly improved comprehensibility over a monolithic specification. However, there seems to be no perceived advantage in breaking down the schemas into much smaller components. The experiment can he fully replicated.

Reified temporal logics: an overview

There are three main approaches to the representation of temporal information in AI literature: the so-called method of temporal arguments that simply extends functions and predicates of first-order language to include time as the additional argument; modal temporal logics which are extensions ofthe propositional or predicate calculus with modal temporal operators; and reified temporal logics which reify standard propositions of some initial language (e.g., the classical first-order or modal logic) as objects denoting propositional terms. The objective of this paper is to provide an overview onthe temporal reified approach by looking closely atsome representative existing systems featuring reified propositions, including those of Allen, McDermott, Shoham, Reichgelt, Galton, and Ma and Knight. We shall demonstrate that, although reified logics might be more complicated in expressing assertions about some given objects with respect to different times, they accord a special status to time and therefore have several distinct advantages in talking about some important issues which would be difficult (if not impossible) to express in other approaches.

Using set operations to deal with the frame problem

This paper presents a simple approach to the so-called frame problem based on some ordinary set operations, which does not require non-monotonic reasoning. Following the notion of the situation calculus, we shall represent a state of the world as a set of fluents, where a fluent is simply a Boolean-valued property whose truth-value is dependent on the time. High-level causal laws are characterised in terms of relationships between actions and the involved world states. An effect completion axiom is imposed on each causal law, which guarantees that all the fluents that can be affected by the performance of the corresponding action are always totally governed. It is shown that, compared with other techniques, such a set operation based approach provides a simpler and more effective treatment to the frame problem.

Marginal adaptation and performance of bioactive dental restorative materials in deciduous and young permanent teeth

Objective: The aim of this study was to investigate the adaptation of different types of restorations towards deciduous and young permanent teeth. Materials and Methods: Class V cavities were prepared in deciduous and young permanent teeth and filled with different materials (a conventional glass-ionomer, a resin-modified glass-ionomer, a poly-acid-modified composite resin and a conventional composite resin). Specimens were aged in artificial saliva for 1, 6, 12 and 18 months, then examined by SEM. Results: The composite resin and the polyacid-modified composite had better marginal adaptation than the glass-ionomers,though microcracks developed in the enamel of the tooth. The glass-ionomers showed inferior marginal quality and durability, but no microcracking of the enamel. The margins of the resin-modified glass-ionomer were slightly superior to the conventional glass-ionomer. Conditioning improved the adaptation of the composite resin, but the type of tooth made little or no difference to the performance of the restorative material. All materials were associated with the formation of crystals in the gaps between the filling and the tooth; the quantity and shape of these crystals varied with the material. Conclusions: Resin-based materials are generally better at forming sound, durable margins in deciduous and young permanent teeth than cements, but are associated with microcracks in the enamel. All fluoride-releasing materials give rise to crystalline deposits.

Shear bond strengths of glass-ionomer cements to sound and to prepared carious dentine

The aim of this study was determine whether bonding of glass-ionomer cements to non-carious dentine differed from that to carious dentine. Five commercial cements were used, namely Fuji IX GP, Fuji IX capsulated, Fuji IX Fast capsulated (all GC, Japan), Ketac-Molar and Ketac-Molar Aplicap (both 3M-ESPE, Germany). Following conditioning of the substrate with 10% poly (acrylic acid) for 10 s, sets of 10 samples of the cements were bonded to prepared teeth that had been removed for orthodontic reasons. The teeth used had either sound dentine or sclerotic dentine. Shear bond strengths were determined following 24 h storage. For the auto-mixed cements, shear bond strength to sound dentine was found not to differ statistically from shear bond strength to sclerotic dentine whereas for hand-mixed cements, shear bond to sound dentine was found to be higher than to carious dentine (to at least p < 0.05). This shows that the chemical effects arising from interactions of glass-ionomer cements with the mineral phase of the tooth are the most important in developing strong bonds, at least in the shorter term.