Measure theory over boolean toposes

Metric Boolean algebras and constructive measure theory

A Boolean measure of similarity

We propose a way of measuring the similarity of a Boolean vector to a given set of Boolean vectors, motivated in part by certain data mining or machine learning problems. We relate the similarity measure to one based on Hamming distance and we develop from this some ways of quantifying the ‘quality’ of a dataset. Acknowledgements: Part of this work was carried out while Martin Anthony was visit...

Cocomplete toposes whose exact completions are toposes

Let E be a cocomplete topos. We show that if the exact completion of E is a topos then every indecomposable object in E is an atom. As a corollary we characterize the locally connected Grothendieck toposes whose exact completions are toposes. This result strengthens both the Lawvere–Schanuel characterization of Boolean presheaf toposes and Hofstra’s characterization of the locally connected Gro...

Minimization Over Boolean Graphs

This paper presents a systematic procedure for the design of gate-type combinational switchingcircuitswithoutdiredtedloops. Eachsuchcircuit(Boo1eangraph) is in correspondencewithasequence of decompositions of the Boolean function which it realizes. A general approach to functional decomposition i s given and, in terms of a convenient positional representation, efficient tests for the detection ...

Quantifying over boolean announcements

Various extensions of public announcement logic have been proposed with quantification over announcements. The best-known extension is called arbitrary public announcement logic, APAL. It contains a primitive language construct ✷φ intuitively expressing that “after every public announcement of a formula, formula φ is true.” The logic APAL is undecidable and it has an infinitary axiomatization. ...