Logic, Language, and Information
The rapidly evolving interdisciplinary field of Logic, Language and Information (LLI) treats a variety of topics, ranging from knowledge representation to the syntax, semantics and pragmatics of natural language. Moreover, it does so from a variety of per
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Logic, Language, and Information Patrick Blackburn, Maarten de Rijke, Yde Venema!
The rapidly evolving interdisciplinary field of Logic, Language and Information (LLI) treats a variety of topics, ranging from knowledge representation to the syntax, semantics and pragmatics of natural language. Moreover, it does so from a variety of perspectives. However, one word more than any other gives the flavour of much contemporary work in LLI: dynamics. The purpose of this chapter is twofold. First, we give an impression of what L1I is and why dynamics plays such a fundamental role there. Second, we relate the study of dynamics to relation algebra. The essential point that will emerge is that many L1I approaches to dynamics can be naturally viewed as explorations of fragments of relation algebra via their set-theoretic representations. We proceed as follows. In Sect. 14.1 we sket.ch the developments that lead to the current focus on dynamics in LLI. The idea of logics of transitions emerges naturally from this discussion, and provides the bridge to the world of relation algebra. In Sect. 14.2 we discuss the syntax and semantics of a number of transitional logics in detail, emphasising the variety of options this essentially simple idea offers. In Sect. 14.3 we turn to more general technical themes. Issues discussed include the key model theoretic notion of a bisimulation, various metatheoretic properties of these logics and the idea of reiativisation, and recent work on dynamic modes of inference. We conclude with a discussion of newly emerging themes, and the limitations of the relational perspective.
14.1
Dynamics in logic, language and information
In broad terms, research in LLI aims to give abstract models of high-level information processing. It is reasonably simple to explain what is meant by "abstract": in principle it means any mathematical or computational model, though in practice it has tended to mean tools drawn from mathematical logic, theoretical computer science, or the logical and functional programming paradigms. Explaining what is meant by "high-level information processing" is less straightforward. There is a core intuition that many cognitive abilities such as language understanding, planning and spatial visualisation can be usefully thought of in terms of information 1The research of the third author has been made possible by a fellowship of the Royal Netherlands Academy of Arts and Sciences.
C. Brink et al. (eds.), Relational Methods in Computer Science © Springer-Verlag/Wien 1997
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Patrick Blackburn, Maarten de Rijke, Yde Venema
processing. Much research in LLI is concerned either with analysing such abilities (usually at a fairly high degree of abstraction) or with developing general models of information and information flow. Emphasis has tended to be placed on those aspects of high-level information processing that readily lend themselves to symbolic analysis, hence the ability of humans to work with beliefs and to cope with language have been the focus of attention. In summary: LLI borde
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