A formalization of logical imaging for information retrieval using quantum theory

In this paper we introduce a formalization of Logical Imaging applied to IR in terms of Quantum Theory through the use of an analogy between states of a quantum system and terms in text documents. Our formalization relies upon the Schrodinger Picture, creating an analogy between the dynamics of a physical system and the kinematics of probabilities generated by Logical Imaging. By using Quantum Theory, it is possible to model more precisely contextual information in a seamless and principled fashion within the Logical Imaging process. While further work is needed to empirically validate this, the foundations for doing so are provided.

Revisiting logical imaging for information retrieval

Retrieval with Logical Imaging is derived from belief revision and provides a novel mechanism for estimating the relevance of a document through logical implication (i.e. P(q -> d)). In this poster, we perform the first comprehensive evaluation of Logical Imaging (LI) in Information Retrieval (IR) across several TREC test Collections. When compared against standard baseline models, we show that LI fails to improve performance. This failure can be attributed to a nuance within the model that means non-relevant documents are promoted in the ranking, while relevant documents are demoted. This is an important contribution because it not only contextualizes the effectiveness of LI, but crucially ex- plains why it fails. By addressing this nuance, future LI models could be significantly improved.

The IKBALS project: multi-modal reasoning in legal knowledge based systems

In attempting to build intelligent litigation support tools, we have moved beyond first generation, production rule legal expert systems. Our work integrates rule based and case based reasoning with intelligent information retrieval. When using the case based reasoning methodology, or in our case the specialisation of case based retrieval, we need to be aware of how to retrieve relevant experience. Our research, in the legal domain, specifies an approach to the retrieval problem which relies heavily on an extended object oriented/rule based system architecture that is supplemented with causal background information. We use a distributed agent architecture to help support the reasoning process of lawyers. Our approach to integrating rule based reasoning, case based reasoning and case based retrieval is contrasted to the CABARET and PROLEXS architectures which rely on a centralised blackboard architecture. We discuss in detail how our various cooperating agents interact, and provide examples of the system at work. The IKBALS system uses a specialised induction algorithm to induce rules from cases. These rules are then used as indices during the case based retrieval process. Because we aim to build legal support tools which can be modified to suit various domains rather than single purpose legal expert systems, we focus on principles behind developing legal knowledge based systems. The original domain chosen was theAccident Compensation Act 1989 (Victoria, Australia), which relates to the provision of benefits for employees injured at work. For various reasons, which are indicated in the paper, we changed our domain to that ofCredit Act 1984 (Victoria, Australia). This Act regulates the provision of loans by financial institutions. The rule based part of our system which provides advice on the Credit Act has been commercially developed in conjunction with a legal firm. We indicate how this work has lead to the development of a methodology for constructing rule based legal knowledge based systems. We explain the process of integrating this existing commercial rule based system with the case base reasoning and retrieval architecture.

Reasoning paradigms in legal decision support systems

In this paper we discuss the strengths and weaknesses of a range of artificial intelligence approaches used in legal domains. Symbolic reasoning systems which rely on deductive, inductive and analogical reasoning are described and reviewed. The role of statistical reasoning in law is examined, and the use of neural networks analysed. There is discussion of architectures for, and examples of, systems which combine a number of these reasoning strategies. We conclude that to build intelligent legal decision support systems requires a range of reasoning strategies.

Beyond rule based reasoning - the meaning and use of cases

Commercial legal expert systems are invariably rule based. Such systems are poor at dealing with open texture and the argumentation inherent in law. To overcome these problems we suggest supplementing rule based legal expert systems with case based reasoning or neural networks. Both case based reasoners and neural networks use cases-but in very different ways. We discuss these differences at length. In particular we examine the role of explanation in existing expert systems methodologies. Because neural networks provide poor explanation facilities, we consider the use of Toulmin argument structures to support explanation (S. Toulmin, 1958). We illustrate our ideas with regard to a number of systems built by the authors

Deductive, inductive and analogical reasoning in legal decision support systems

In this paper we provide an overview of a number of fundamental reasoning formalisms in artificial intelligence which can and have been used in modelling legal reasoning. We describe deduction, induction and analogical reasoning formalisms, and show how they can be used separately to model legal reasoning. We argue that these formalisms can be used together to model legal reasoning more accurately, and describe a number of attempts to integrate the approaches.

Non-monotonic Reasoning and the Reversibility of Belief Change

Traditional approaches to nonmonotonic reasoning fail to satisfy a number of plausible axioms for belief revision and suffer from conceptual difficulties as well. Recent work on ranked preferential models (RPMs) promises to overcome some of these difficulties. Here we show that RPMs are not adequate to handle iterated belief change. Specifically, we show that RPMs do not always allow for the reversibility of belief change. This result indicates the need for numerical strengths of belief.

Qualitative spatial reasoning about directions in a corridor containing a single turn

An experiment was conducted to investigate the process of reasoning about directions in an egocentric space. Each participant walked through a corridor containing an angular turn ranging in size from 0° to 90°, in 15° increments. A direction was given to participants at the entrance of the corridor and they were asked to answer this direction at the end of this corridor. Considering the fact that participants had to reason the direction in the featureless corridor, two hypotheses were proposed: (i) reasoning about directions falls into qualitative reasoning by using a small number of coarse angular categories (four 90° categories or eight 45° categories: 90° categories consist of front, back, left, right; 45° categories consist of 90° categories and the four intermediates) that reference axes generate; (ii) reasoning about directions would be done by recalling the rotation angle from the traveling direction to the direction that participants tried to answer. In addition, the configuration of reference axes that participants employed was examined. Both hypotheses were supported, and the data designated that reference axes consisted of eight directions: a pair of orthogonal axes and diagonals.

The Number Crunch game : a simple vehicle for building algebraic reasoning skills

A newspaper numbers game based on simple arithmetic relationships is discussed. Its potential to give students of elementary algebra practice in semi-ad hoc reasoning and to build general arithmetic reasoning skills is explored.

Post-disaster reconstruction projects : a logical framework for community participation

In a post-disaster environment, housing reconstruction projects frequently face enormous difficulties due to the various, often apparently ill-considered, internal and external factors. Non-Governmental Organisations (NGOs) operating in post-disaster settings such as in Afghanistan continue to face blame over the failure of reconstruction projects, and worse, they are sometimes even viewed as being corrupt entities. While it is not always possible for NGOs to eliminate or reduce the impact of factors that are outside their control, they certainly can increase the chances of project success by placing considerable emphasis on working more effectively with the affected communities. To achieve maximum community participation in reconstruction projects , this research develops a specific logical framework to guide the process of community participation in post-disaster housing reconstruction in Afghanistan.

Numeracy and statistical reasoning on entering university

The relationship between mathematics and statistical reasoning frequently receives comment (Vere-Jones 1995, Moore 1997); however most of the research into the area tends to focus on mathematics anxiety. Gnaldi (2003) showed that in a statistics course for psychologists, the statistical understanding of students at the end of the course depended on students’ basic numeracy, rather than the number or level of previous mathematics courses the student had undertaken. As part of a study into the development of statistical thinking at the interface between secondary and tertiary education, students enrolled in an introductory data analysis subject were assessed regarding their statistical reasoning, basic numeracy skills, mathematics background and attitudes towards statistics. This work reports on some key relationships between these factors and in particular the importance of numeracy to statistical reasoning.

Numeracy counts in the statistical reasoning equation

The relationship between mathematics and statistical reasoning frequently receives comment (Vere-Jones 1995, Moore 1997); however most of the research into the area tends to focus on maths anxiety. Gnaldi (Gnaldi 2003) showed that in a statistics course for psychologists, the statistical understanding of students at the end of the course depended on students’ basic numeracy, rather than the number or level of previous mathematics courses the student had undertaken. As part of a study into the development of statistical thinking at the interface between secondary and tertiary education, students enrolled in an introductory data analysis subject were assessed regarding their statistical reasoning ability, basic numeracy skills and attitudes towards statistics. This work reports on the relationships between these factors and in particular the importance of numeracy to statistical reasoning.