Abstract Learning Frameworks for Synthesis

We develop abstract learning frameworks (ALFs) for synthesis that embody the principles of CEGIS (counter-example based inductive synthesis) strategies that have become widely applicable in recent years. Our framework defines a general abstract framework of iterative learning, based on a hypothesis space that captures the synthesized objects, a sample space that forms the space on which induction is performed, and a concept space that abstractly defines the semantics of the learning process. We show that a variety of synthesis algorithms in current literature can be embedded in this general framework. While studying these embeddings, we also generalize some of the synthesis problems these instances are of, resulting in new ways of looking at synthesis problems using learning. We also investigate convergence issues for the general framework, and exhibit three recipes for convergence in finite time. The first two recipes generalize current techniques for convergence used by existing synthesis engines. The third technique is a more involved technique of which we know of no existing instantiation, and we instantiate it to concrete synthesis problems

The effect of multiple knowledge sources on learning and teaching

Current paradigms for machine-based learning and teaching tend to perform their task in isolation from a rich context of existing knowledge. In contrast, the research project presented here takes the view that bringing multiple sources of knowledge to bear is of central importance to learning in complex domains. As a consequence teaching must both take advantage of and beware of interactions between new and existing knowledge. The central process which connects learning to its context is reasoning by analogy, a primary concern of this research. In teaching, the connection is provided by the explicit use of a learning model to reason about the choice of teaching actions. In this learning paradigm, new concepts are incrementally refined and integrated into a body of expertise, rather than being evaluated against a static notion of correctness. The domain chosen for this experimentation is that of learning to solve "algebra story problems." A model of acquiring problem solving skills in this domain is described, including: representational structures for background knowledge, a problem solving architecture, learning mechanisms, and the role of analogies in applying existing problem solving abilities to novel problems. Examples of learning are given for representative instances of algebra story problems. After relating our views to the psychological literature, we outline the design of a teaching system. Finally, we insist on the interdependence of learning and teaching and on the synergistic effects of conducting both research efforts in parallel