Integrating Axiomatic and Analogical Reasoning
We present a computational model of a developing system with bounded rationality that is surrounded by an arbitrary number of symbolic domains. The system is fully automatic and makes continuous observations of facts emanating from those domains. The syst
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Department of Philosophy, Linguistics and Theory of Science, University of Gothenburg, Gothenburg, Sweden 2 Department of Applied Information Technology, Chalmers University of Technology, Gothenburg, Sweden [email protected] 3 Department of Applied Information Technology, University of Gothenburg, Gothenburg, Sweden [email protected] 4 Department of Mathematical Sciences, Chalmers University of Technology, Gothenburg, Sweden [email protected]
Abstract. We present a computational model of a developing system with bounded rationality that is surrounded by an arbitrary number of symbolic domains. The system is fully automatic and makes continuous observations of facts emanating from those domains. The system starts from scratch and gradually evolves a knowledge base consisting of three parts: (1) a set of beliefs for each domain, (2) a set of rules for each domain, and (3) an analogy for each pair of domains. The learning mechanism for updating the knowledge base uses rote learning, inductive learning, analogy discovery, and belief revision. The reasoning mechanism combines axiomatic reasoning for drawing conclusions inside the domains, with analogical reasoning for transferring knowledge from one domain to another. Thus the reasoning processes may use analogies to jump back and forth between domains. Keywords: Developing system · Bounded rationality domains · Axiomatic reasoning · Analogical reasoning
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Introduction
Analogies play a significant role in several cognitive processes, including decision making, perception, memory, problem solving, creativity, emotion, explanation, and communication [6]. In his lecture entitled Analogy as the Core of Cognition, Hofstadter stated that “analogy is the interstate freeway system of cognition” [9]. Analogies have been studied since antiquity, e.g. by Aristotle, who gave the famous example Palm:Hand :: Sole:Foot (Palm is to Hand as Sole is to Foot). A still older example might be the notion of proportionality, as in 3:6 :: 2:4 [5]. Aristotle set the stage for all later theories of analogical reasoning [1]. Gentner studied analogies in the context of logic and wrote [5]: c Springer International Publishing Switzerland 2016 B. Steunebrink et al. (Eds.): AGI 2016, LNAI 9782, pp. 181–191, 2016. DOI: 10.1007/978-3-319-41649-6 18
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When people hear an analogy such as “An electric battery is like a reservoir” how do they derive its meaning? We might suppose that they simply apply their knowledge about reservoirs to batteries, and that the greater the match, the better the analogy. What, then, is an analogy? In the aforementioned lecture, Hofstadter also stated [9]: It is tempting to think that the analogies are between things in the external world, but I really want to say that analogies happen inside your head (. . . ) They are connections between things inside your head (. . . ) Analogies are commonly modelled as follows [5,16]: (1) Define the notion of domain as a set of logical formulas; (2) Specify two domai
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