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Finite H-Dimension Does not Imply Expressive Completeness

Ian Hodkinson
Journal of Philosophical Logic
Vol. 23, No. 5 (Oct., 1994), pp. 535-573
Published by: Springer
Stable URL: http://www.jstor.org/stable/30226533
Page Count: 39
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Finite H-Dimension Does not Imply Expressive Completeness
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Abstract

A conjecture of Gabbay (1981) states that any class of flows of time having the property known as finite H-dimension admits a finite set of expressively complete one-dimensional temporal connectives. Here we show that the class of 'circular' structures refutes the generalisation of this conjecture to Kripke frames. We then construct from this class, by a general method, a new class of irreflexive transitive flows of time that refutes the original conjecture. Our paper includes full descriptions of a method for establishing finite H-dimension for a class of structures and of the technique for extending finite H-dimension to other classes, and an introduction surveying the area of expressive completeness.

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