Mathematics and logic for digital devices.

Mode of access: Internet.

Fuzzy logic in web data mining for website assessment

This paper proposes a novel application of fuzzy logic to web data mining for two basic problems of a website: popularity and satisfaction. Popularity means that people will visit the website while satisfaction refers to the usefulness of the site. We will illustrate that the popularity of a website is a fuzzy logic problem. It is an important characteristic of a website in order to survive in Internet commerce. The satisfaction of a website is also a fuzzy logic problem that represents the degree of success in the application of information technology to the business. We propose a framework of fuzzy logic for the representation of these two problems based on web data mining techniques to fuzzify the attributes of a website.

The possessive logic of patriarchal white sovereignty: The High Court and the Yorta Yorta decision

Race is fundamental in shaping the development of Australian law just as it has played its part in other former colonies, such as the United States, where a body of critical race theory has been established on the basis of this premise. Drawing on this theory I argue that the possessive logic of patriarchal white sovereignty works ideologically to naturalise the nation as a white possession by informing and circulating a coherent set of meanings about white possession as part of common sense knowledge and socially produced conventions in the High Court's Yorta Yorta decision.

A First Order Predicate Logic Formulation of the 3D Reconstruction Problem and its Solution Space

This paper defines the 3D reconstruction problem as the process of reconstructing a 3D scene from numerous 2D visual images of that scene. It is well known that this problem is ill-posed, and numerous constraints and assumptions are used in 3D reconstruction algorithms in order to reduce the solution space. Unfortunately, most constraints only work in a certain range of situations and often constraints are built into the most fundamental methods (e.g. Area Based Matching assumes that all the pixels in the window belong to the same object). This paper presents a novel formulation of the 3D reconstruction problem, using a voxel framework and first order logic equations, which does not contain any additional constraints or assumptions. Solving this formulation for a set of input images gives all the possible solutions for that set, rather than picking a solution that is deemed most likely. Using this formulation, this paper studies the problem of uniqueness in 3D reconstruction and how the solution space changes for different configurations of input images. It is found that it is not possible to guarantee a unique solution, no matter how many images are taken of the scene, their orientation or even how much color variation is in the scene itself. Results of using the formulation to reconstruct a few small voxel spaces are also presented. They show that the number of solutions is extremely large for even very small voxel spaces (5 x 5 voxel space gives 10 to 10(7) solutions). This shows the need for constraints to reduce the solution space to a reasonable size. Finally, it is noted that because of the discrete nature of the formulation, the solution space size can be easily calculated, making the formulation a useful tool to numerically evaluate the usefulness of any constraints that are added.

Embedding defeasible logic into logic programming

Defeasible reasoning is a simple but efficient approach to nonmonotonic reasoning that has recently attracted considerable interest and that has found various applications. Defeasible logic and its variants are an important family of defeasible reasoning methods. So far no relationship has been established between defeasible logic and mainstream nonmonotonic reasoning approaches. In this paper we establish close links to known semantics of logic programs. In particular, we give a translation of a defeasible theory D into a meta-program P(D). We show that under a condition of decisiveness, the defeasible consequences of D correspond exactly to the sceptical conclusions of P(D) under the stable model semantics. Without decisiveness, the result holds only in one direction (all defeasible consequences of D are included in all stable models of P(D)). If we wish a complete embedding for the general case, we need to use the Kunen semantics of P(D), instead.

Extending the theory of Owicki and Gries with a logic of progress

This paper describes a logic of progress for concurrent programs. The logic is based on that of UNITY, molded to fit a sequential programming model. Integration of the two is achieved by using auxiliary variables in a systematic way that incorporates program counters into the program text. The rules for progress in UNITY are then modified to suit this new system. This modification is however subtle enough to allow the theory of Owicki and Gries to be used without change.

Logic of Violations: A gentzen systems for reasoning with contrary-to-duty obligations

In this paper we present a Gentzen system for reasoning with contrary-to-duty obligations. The intuition behind the system is that a contrary-to-duty is a special kind of normative exception. The logical machinery to formalise this idea is taken from substructural logics and it is based on the definition of a new non-classical connective capturing the notion of reparational obligation. Then the system is tested against well-known contrary-to-duty paradoxes.

Linear temporal logic and z refinement

Since Z, being a state-based language, describes a system in terms of its state and potential state changes, it is natural to want to describe properties of a specified system also in terms of its state. One means of doing this is to use Linear Temporal Logic (LTL) in which properties about the state of a system over time can be captured. This, however, raises the question of whether these properties are preserved under refinement. Refinement is observation preserving and the state of a specified system is regarded as internal and, hence, non-observable. In this paper, we investigate this issue by addressing the following questions. Given that a Z specification A is refined by a Z specification C, and that P is a temporal logic property which holds for A, what temporal logic property Q can we deduce holds for C? Furthermore, under what circumstances does the property Q preserve the intended meaning of the property P? The paper answers these questions for LTL, but the approach could also be applied to other temporal logics over states such as CTL and the mgr-calculus.

Interface adaptor logic: A new model for interfacing peripherals in IP based designs

The introduction of standard on-chip buses has eased integration and boosted the production of IP functional cores. However, once an IP is bus specific retargeting to a different bus is time-consuming and tedious, and this reduces the reusability of the bus-specific IP. As new bus standards are introduced and different interconnection methods are proposed, this problem increases. Many solutions have been proposed, however these solutions either limit the IP block performance or are restricted to a particular platform. A new concept is presented that can connect IP blocks to a wide variety of interface architectures with low overhead. This is achieved through the use a special interface adaptor logic layer.

Norm modifications in defeasible logic

This paper proposes a framework based on Defeasible Logic (DL) to reason about normative modifications. We show how to express them in DL and how the logic deals with conflicts between temporalised normative modifications. Some comments will be given with regard to the phenomenon of retroactivity.

A technique for modular logic program refinement

A refinement calculus provides a method for transforming specifications to executable code, maintaining the correctness of the code with respect to its specification. In this paper we introduce modules into a logic programming refinement calculus. Modules allow data types to be grouped together with sets of procedures that manipulate the data types. By placing restrictions on the way a program uses a module, we develop a technique for refining the module so that it uses a more efficient representation of the data type.