# Contrary Inferences in Consistent Histories and a Set Selection Criterion

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## Abstract

The best developed formulation of closed system quantum theory that handles multiple-time statements, is the consistent (or decoherent) histories approach. The most important weaknesses of the approach is that it gives rise to many different consistent sets, and it has been argued that a complete interpretation should be accompanied with a natural mechanism leading to a (possibly) unique preferred consistent set. The existence of multiple consistent sets becomes more problematic because it allows the existence of contrary inferences [1]. We analyse the conceptual difficulties that arise from the existence of multiple consistent sets and provide a suggestion for a natural set selection criterion. This criterion does not lead to a unique physical consistent set, however it evades the existence of consistent sets with contrary inferences. The criterion is based on the concept of preclusion and the requirement that probability one propositions and their inferences should be non-contextual. The allowed consistent sets turn-out to be compatible with coevents which are the ontology of an alternative, histories based, formulation [2, 3, 4].

## Keywords

Consistent histories Decoherent histories Contrary inferences## Notes

### Acknowledgments

This work was supported by the UK Engineering and Physical Sciences Research Council (EPSRC) through Grant EP/K022717/1. Partial support from COST Action MP1006 is also gratefully acknowledged. The author is grateful to Robert Griffiths for his remarks concerning the conventional single-framework rule for consistent histories and to the anonymous reviewers for their constructive comments.

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