Writings by Uwe Lück

Interval Orders, Time, and Comparisons

Interval orders are a means to model non-transitive indifference in comparison judgments as well as temporal relations between events. A chapter on history and (additional) applications is in Pirlot and Vincke (see references below); I also recommend Fishburn and Monjardet. The first-order theory of interval orders is just that of complete precedence among subsets in linear orders.

My work on a doctoral thesis (supervised by Godehard Link in Munich) deals with interval orders and their relations to linear orders, in particular with the orders of intervals of reals (also considering theory of measurement). In its course I wrote and submitted the following articles.

‘Continu’ous Time Goes by Russell’ I started with this, attempting to counter Thomason’s article on an alternative to Russell’s construction of instants from events. Both Thomason’s paper and mine characterize those interval orders that become a real order type through the respective construction. My contribution appeared in Notre Dame Journal of Formal Logic vol. 47, no. 3 (2006), pp. 397–434 — view abstract or more. Keywords: time, Russell, instants from events, continuum, interval order, axiom of choice.

‘Representing Interval Orders by Arbitrary Real Intervals’ This solves a representation problem once left open by Fishburn and deals with some related themes. ABSTRACT and DOWNLOAD Keywords: interval order, semiorder, linear order, representation; preferences/comparisons, economics/mathematical psychology/measurement.

References

• Fishburn, P.C., Interval Orders and Interval Graphs, New York, 1985.
• Fishburn, P.C., and B. Monjardet, ‘Norbert Wiener on the theory of measurement (1914, 1915, 1921)’, Journal of Mathematical Psychology 36 (1992), 165–184.
• Pirlot, M. and Ph. Vincke, Semiorders, Dordrecht, 1997.
• Thomason, S.K., ‘On constructing instants from events’, Journal of Philosophical Logic 13 (1984), 85–96.

Last revised 2015-12-03 © Uwe Lück

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