Analogies are considered a cognitive core mechanism, that is applied in many everday reasoning processes. Heuristic-driven theory projection (HDTP) is a logic-based framework that allows to model analogies with the aim of making analogical reasoning techniques available for artificial intelligence systems.
The formal properties of HDTP are investigated, refining and extending some of the original ideas. A special form of restricted higher-order anti-unification is proposed as a means for the generalization process, allowing to account for flexibility in the mapping while staying computationally tractable. Concerning the semantics, it is argued that a sensible interpretation can be given to the syntactic processes, based on an understanding of the involved mappings as a decent type of theory morphisms. The logical nature of HDTP also allows for a notion of re-representation that is discussed from a theoretical and algorithmic point of view. Moreover, the framework of HDTP is also analyzed from the abstract perspective of institution theory, suggesting that the main ideas can be spelled out in other logical formalisms as well.
To collect support for the practical utility of HDTP, it is applied to different fields in a series of studies. The domain of geometric analogy serves as an arena to demonstrate the operation of HDTP, including the treatment of ambiguous problems based on thoughts from Gestalt psychology. Another line of research explores how the idea of conceptual blending can be related to analogies and a formalization building on HDTP is presented, leading to the notion of theory blending. These ideas are applied to a classical problem of the field, the interpretation of noun-noun compounds, but they proof to be applicable in other areas as well, demonstrated by a framework for counterfactual reasoning. Furthermore, applications of analogical reasoning and theory blending in mathematics are discussed, including the formal modeling of an example from the history of mathematics and a framework to support mathematical discovery.
| Identifer | oai:union.ndltd.org:uni-osnabrueck.de/oai:repositorium.ub.uni-osnabrueck.de:urn:nbn:de:gbv:700-2016081114833 |
| Date | 11 August 2016 |
| Creators | Krumnack, Ulf |
| Contributors | Prof. Dr. Kai-Uwe Kühnberger, Prof. Dr. Ute Schmid, PD Dr. Helmar Gust |
| Source Sets | Universität Osnabrück |
| Language | English |
| Detected Language | English |
| Type | doc-type:doctoralThesis |
| Format | application/zip, application/pdf |
| Rights | Namensnennung 3.0 Unported, http://creativecommons.org/licenses/by/3.0/ |
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