Abstract: The theory of theory change due to Alchourrón, Gärdenfors, and Makinson ("AGM") has been widely known as being characterised by two packages of postulates. The basic package consists of six postulates and is very weak, the full package adds two further postulates and is very strong. Revisiting the three classic constructions of partial meet contraction, safe contraction and entrenchment-based construction and tracing the idea of limited discriminative powers in agents, I argue that four intermediate levels can be distinguished that play important roles within the AGM theory.
Abstract: Amsterdam-style logicians view modal logic as a fragment of classical logic, and description logicians view their own formalisms in much the same way. Moreover, first-order logic itself can be viewed as a modest fragment of the higher-order logics of Frege and Russell, a fragment with useful model-theoretic properties. All in all, the fine structure of logic is a key topic in contemporary research, as the intensive study of (say) the 2-variable and various guarded fragments attest.
In this talk I want to consider the role of logical fragments in applications. I will focus on applications in natural language, as this is an area rich in non-monotonic and defeasible inference. Moreover, as my perspective is that of computational (rather than theoretical) linguistics, I am interested in efficient solutions to computational tasks - that is, in fragments of computation. Drawing on a running example involving applications of description logic and classical planning to a dialogue system, I will discuss the role of computation to provide 'pragmatic glue' that lets us work with small well-explored logical fragments, while simultaneously providing the dynamics required to model various forms of non-monotonicity.
Abstract: We discuss postulates for inconsistency measures as proposed in the literature. We examine them both individually and as a collection. Although we criticize two of the main postulates, we mostly focus on the meaning of the postulates as a whole. Accordingly, we discuss a number of new postulates as substitutes and/or as alternative families.