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.

The neural representation of absolute direction during mental navigation in conceptual spaces

When humans mentally “navigate” bidimensional uniform conceptual spaces, they recruit the same grid-like and distance codes typically evoked when exploring the physical environment. Here, using fMRI, we show evidence that conceptual navigation also elicits another kind of spatial code: that of absolute direction. This code is mostly localized in the medial parietal cortex, where its strength predicts participants’ comparative semantic judgments. It may provide a complementary mechanism for conceptual navigation outside the hippocampal formation.

The New Common

This article describes a personal relationship to a common green space in a town in the United Kingdom during the lockdowns prompted by the Covid-19 pandemic in 2020–21. It considers the new meanings that are attaching to ‘commons’ as conceptual spaces and material places; and it links this consideration to the terms in which values and norms are being reassessed in the context of environmental crises.

Diagrams, Conceptual Space and Time, and Latent Geometry

The “origins” of (geometric) space is examined from the perspective of the so-called “conceptual space” or “semantic space”. Semantic space is characterized by its fundamental “locality” that generates an “implicit” mode of geometrizing. This view is examined from within three perspectives. First, the role that various diagrammatic entities play in the everyday life and pragmatic activities of selected ethnic groups is illustrated. Secondly, it is shown how conceptual spaces are fundamentally linked to the meaning effects of particular natural languages and these are very different from the global and universal aspects of Euclidean spaces. Thirdly, it is contended that these modes of creating body and culture-based spatial frameworks and related cosmogonies and cosmologies can be described as forms of “latent geometry” that initially appear unexplainable in any rational way. Nonetheless, and thanks to the deep mathematical reflections provided by René Thom, it is illustrated how the various ways of generating space can be further analyzed as distortions of mainstream spatialization furnished by Euclidean geometry that established the dominant universality of the ideas of space (and time).