A comparative survey of integrated learning systems

This paper presents the duction framework for unifying the three basic forms of inference - deduction, abduction, and induction - by specifying the possible relationships and influences among them in the context of integrated learning. Special assumptive forms of inference are defined that extend the use of these inference methods, and the properties of these forms are explored. A comparison to a related inference-based learning frame work is made. Finally several existing integrated learning programs are examined in the perspective of the duction framework

Rerepresenting and Restructuring Domain Theories: A Constructive Induction Approach

Theory revision integrates inductive learning and background knowledge by combining training examples with a coarse domain theory to produce a more accurate theory. There are two challenges that theory revision and other theory-guided systems face. First, a representation language appropriate for the initial theory may be inappropriate for an improved theory. While the original representation may concisely express the initial theory, a more accurate theory forced to use that same representation may be bulky, cumbersome, and difficult to reach. Second, a theory structure suitable for a coarse domain theory may be insufficient for a fine-tuned theory. Systems that produce only small, local changes to a theory have limited value for accomplishing complex structural alterations that may be required. Consequently, advanced theory-guided learning systems require flexible representation and flexible structure. An analysis of various theory revision systems and theory-guided learning systems reveals specific strengths and weaknesses in terms of these two desired properties. Designed to capture the underlying qualities of each system, a new system uses theory-guided constructive induction. Experiments in three domains show improvement over previous theory-guided systems. This leads to a study of the behavior, limitations, and potential of theory-guided constructive induction.Comment: See http://www.jair.org/ for an online appendix and other files accompanying this articl

From coinductive proofs to exact real arithmetic: theory and applications

Based on a new coinductive characterization of continuous functions we extract certified programs for exact real number computation from constructive proofs. The extracted programs construct and combine exact real number algorithms with respect to the binary signed digit representation of real numbers. The data type corresponding to the coinductive definition of continuous functions consists of finitely branching non-wellfounded trees describing when the algorithm writes and reads digits. We discuss several examples including the extraction of programs for polynomials up to degree two and the definite integral of continuous maps

The principle of pointfree continuity

In the setting of constructive pointfree topology, we introduce a notion of continuous operation between pointfree topologies and the corresponding principle of pointfree continuity. An operation between points of pointfree topologies is continuous if it is induced by a relation between the bases of the topologies; this gives a rigorous condition for Brouwer's continuity principle to hold. The principle of pointfree continuity for pointfree topologies $\mathcal{S}$ and $\mathcal{T}$ says that any relation which induces a continuous operation between points is a morphism from $\mathcal{S}$ to $\mathcal{T}$. The principle holds under the assumption of bi-spatiality of $\mathcal{S}$. When $\mathcal{S}$ is the formal Baire space or the formal unit interval and $\mathcal{T}$ is the formal topology of natural numbers, the principle is equivalent to spatiality of the formal Baire space and formal unit interval, respectively. Some of the well-known connections between spatiality, bar induction, and compactness of the unit interval are recast in terms of our principle of continuity. We adopt the Minimalist Foundation as our constructive foundation, and positive topology as the notion of pointfree topology. This allows us to distinguish ideal objects from constructive ones, and in particular, to interpret choice sequences as points of the formal Baire space

Integrated and situated academic development for all categories of staff: lessons for constructive alignment from an HEA-accredited Continuing Professional Development scheme

Higher Education Academy (HEA) Fellowship and the UK Professional Standards Frameworks (UKPSF) are increasingly used within British higher education institutions to support the professional formation of university teachers. This paper evaluates the use of practitioner inquiry within an HEA-accredited scheme (OpenPAD) to support the professional development of part-time Associate Lecturers at a large distance-learning institution. OpenPAD was available between 2013 and 2016 to all academic and academic-related staff in the Open University, including the 5000+ part-time teaching-only staff who are the main focus of this evaluation. OpenPAD used situated learning through practitioner inquiry to generate evidence against the UKPSF. Participant experience is evaluated and lessons drawn, which may have implications for similar schemes in other institutions. Opportunities for the further integration of academic development opportunities for all categories of staff in a successor scheme are identified in a proposed alignment between academic development; career-related processes such as induction and appraisal; institutional teaching and learning policies; and scholarship agendas

Kripke Models for Classical Logic

We introduce a notion of Kripke model for classical logic for which we constructively prove soundness and cut-free completeness. We discuss the novelty of the notion and its potential applications