On February 9, 2012, at 3 p.m., Kohei Kishida (ILLC) will give a talk at the LIRa seminar. The title of the talk is Autonomy of Substructures and the Converse Barcan Formula. The abstract is below. The talk will take place in room D1.113, Science Park 904.
The notion of a substructure is found in many fields of mathematics, as well as in logic and semantics. One of the goals of this paper is to show that there is an interesting sense in which certain substructures can be called “autonomous” from superstructures. To the sense of autonomy I put forward, a formal expression can be given in terms of commutative diagrams, which I establish through analysis of examples and non-examples from both mathematics and logic. The topics covered in this analysis include: the problem of logical omniscience in epistemic logic and impossible possible worlds; universal accessibility relations and S5 ones; extensionality of sentential operators and quantifiers; and free logic and domains of individuals. The sense of autonomy and its formalization I introduce prove to be helpful in the study of these topics. In particular, it is the other goal of this paper to apply the formalization to quantified modal logic and to propose a modification over the widely accepted thesis that the converse Barcan formula characterizes increasing domains. It turns out that the formula is really about the autonomy of domains, characterizing a fundamental contrast between two views of the relationship between necessity and existence, one put forward by Kripke and the other essentially shared by David Lewis.