Algorithmic information theory
Algorithmic information theory
Multilanguage hierarchical logics, or: how we can do without modal logics
Artificial Intelligence
IJCAI'93 Proceedings of the 13th international joint conference on Artifical intelligence - Volume 1
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Think of a context as expressed in a language which an agent, at some time, is learning to apply by some finite means to some aspect of the world. Think of that aspect as one amongst indefinitely many others. Think of the language as having a model or set of models whose domain consists of components of that aspect. Thus the language has a set of local models, see Giunchiglia and Ghidini[3]. The context may be defined in terms of that set of local models. Think of a possibility (as opposed to a possible world) as something that is partial, as argued by Humberstone [6]. In contrast, many philosophers discuss semantics as if (in principle) there is some complete language of fundamental (base) description for the world and its associated set of scientifically possible worlds. The complete language for describing the base might be identified with the language of a final theory of physics. This papers offers a critique of the view that there is even in principle a final theory of physics. The argument is based on a proof in algorithmic information theory by Chaitin [1,2]. The paper sketches a view, based on possibilities and local models semantics, of how to think of semantics in a world in which there is not, even in principle, a complete language of base description. It sketches an ontology for this world. If there is a supercontext, then it will not itself be a context. This is because it will not be completely describable using a finitely intelligible language. Each aspect of it will be describable in this way, but it itself will be ineffable.