Nonmonotonic Reasoning, Expectations Orderings, and Conceptual Spaces

In Gärdenfors and Makinson (Artif Intell 65(2):197–245, 1994) and Gärdenfors (Knowledge representation and reasoning under uncertainty, Springer-Verlag, 1992) it was shown that it is possible to model nonmonotonic inference using a classical consequence relation plus an expectation-based ordering of formulas. In this article, we argue that this framework can be significantly enriched by adopting a conceptual spaces-based analysis of the role of expectations in reasoning. In particular, we show that this can solve various epistemological issues that surround nonmonotonic and default logics. We propose some formal criteria for constructing and updating expectation orderings based on conceptual spaces, and we explain how to apply them to nonmonotonic reasoning about objects and properties.

Causal Inference via Constraint Satisfaction

In this chapter I introduce a number of ideas connected to causal inference that are inherently connected to info-metrics. In the context of this chapter, causal inference means the causality inferred from the available information. I begin by introducing and examining nonmonotonic and default logics, which were developed to deal with extremely high conditional probabilities. Other facets of info-metrics and causal inference are then discussed. I also show the direct effect of the complete set of input information on the inferred solution. I conclude the chapter with a detailed Markov example providing a more traditional approach to causal inference, developed within the info-metrics framework. The example builds on the notion of exogeneity and demonstrates that the info-metrics framework provides a simple way of incorporating additional exogenous information, thereby opening the way for empirical testing of causal inference. A short summary of the notion of “pure” causality is also provided.