title: Proving the existence of solutions in logical arithmetic

authors: Cleary, John G.

subjects: computer science

abstract: Logical arithmetic is a logically correct technique for real arithmetic in Prolog which uses constraints over interval representations for its implementation.  Four problems with the technique are considered: answers are conditional and uninformative; iterative computations may lead to unboundedly large constraint networks; it is difficult and ineffective to deal with negation; and computing extrema is often not effective.  A solution to these problems is proposed in the form of "existential intervals" which record the existence of a solution to a set of constraints within an interval.  It is shown how to operate on existential intervals and how they solve the four problems.

text: Proving the existence of solutions in logical arithmetic Logical arithmetic is a logically correct technique for real arithmetic in Prolog which uses constraints over interval representations for its implementation.  Four problems with the technique are considered: answers are conditional and uninformative; iterative computations may lead to unboundedly large constraint networks; it is difficult and ineffective to deal with negation; and computing extrema is often not effective.  A solution to these problems is proposed in the form of "existential intervals" which record the existence of a solution to a set of constraints within an interval.  It is shown how to operate on existential intervals and how they solve the four problems.

year: 1993-10

title: Teacher-researcher relationships and collaborations in research.

authors: Cowie, Bronwen

subjects: collaborative research

abstract: To understand the complexity of the classroom in ways that might inform teaching research in needed that explains both why and how something works. Teacher-researcher collaboration is essential if this is to happen. Collaborative work can ensure that research builds on from what teachers know and can do. Researchers working with teachers to address their current concerns are more likely to generate insights into what teachers might do and where they might go next. Collaboration can contribute a warrant for relevance for research findings. At the same teachers deepen and enhance their own practice through engaging in the research process. This paper describes and discusses some approaches to collaboration that have enables researchers and teachers to access a diversity of ideas and expertise to their mutual benefit.

text: Teacher-researcher relationships and collaborations in research. To understand the complexity of the classroom in ways that might inform teaching research in needed that explains both why and how something works. Teacher-researcher collaboration is essential if this is to happen. Collaborative work can ensure that research builds on from what teachers know and can do. Researchers working with teachers to address their current concerns are more likely to generate insights into what teachers might do and where they might go next. Collaboration can contribute a warrant for relevance for research findings. At the same teachers deepen and enhance their own practice through engaging in the research process. This paper describes and discusses some approaches to collaboration that have enables researchers and teachers to access a diversity of ideas and expertise to their mutual benefit.

year: 2010

title: Hostile shores: catastrophic events in prehistoric New Zealand and their impact on Maori coastal communities [Book Review]

authors: Lowe, David J.

abstract: This article reviews the book: “Hostile shores: catastrophic events in prehistoric New Zealand and their impact on Maori coastal communities”, by Bruct McFadgen.

text: Hostile shores: catastrophic events in prehistoric New Zealand and their impact on Maori coastal communities [Book Review] This article reviews the book: “Hostile shores: catastrophic events in prehistoric New Zealand and their impact on Maori coastal communities”, by Bruct McFadgen.

year: 2008