Strict General Setting for Building Decision Procedures into Theorem Provers

The efficient and flexible incorporating of decision procedures into theorem provers is very important for their successful use. There are several approaches for combining and augmenting of decision procedures; some of them support handling uninterpreted functions, congruence closure, lemma invoking etc. In this paper we present a variant of one general setting for building decision procedures into theorem provers (gs framework [18]). That setting is based on macro inference rules motivated by techniques used in different approaches. The general setting enables a simple describing of different combination/augmentation schemes. In this paper, we further develop and extend this setting by an imposed ordering on the macro inference rules. That ordering leads to a ”strict setting”. It makes implementing and using variants of well-known or new schemes within this framework a very easy task even for a non-expert user. Also, this setting enables easy comparison of different combination/augmentation schemes and combination of their ideas

The Direction of Technical Change in Capital-Resource Economies

We analyze a multi-sector growth model with directed technical change where man-made capital and exhaustible resources are essen- tial for production. The relative profitability of factor-specific inno- vations endogenously determines whether technical progress will be capital- or resource-augmenting. We show that convergence to bal- anced growth implies zero capital-augmenting innovations: in the long run, the economy exhibits purely resource-augmenting technical change. This result provides sound microfoundations for the broad class of models of exogenous/endogenous growth where resource-aug- menting progress is required to sustain consumption in the long run, contradicting the view that these models are conceptually biased in favor of sustainability.Endogenous Growth, Directed Technical Change, Exhaustible Resources, Sustainability

The Direction of Technical Change in Capital-Resource Economies

We analyze a multi-sector growth model with directed technical change where man-made capital and exhaustible resources are essential for production. The relative profitability of factor-specific innovations endogenously determines whether technical progress will be capital- or resource-augmenting. We show that convergence to balanced growth implies zero capital-augmenting innovations: in the long run, the economy exhibits purely resource-augmenting technical change. This result provides sound microfoundations for the broad class of models of exogenous/endogenous growth where resource-augmenting progress is required to sustain consumption in the long run, contradicting the view that these models are conceptually biased in favor of sustainability.Endogenous Growth; Directed Technical Change; Exhaustible Resources; Sustainability

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