Transitional Logic

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A transitional logic is a multi-value logic that is extended by extra values that directly represent values that change over time. The term was first introduced in a peer-reviewed publication here:

S. Thompson and A. Mycroft, Abstract Interpretation of Combinational Asynchronous Circuits, In Proc. 11th International Symposium on Static Analysis (SAS 2004), R. Giacobazzi, ed., LNCS 3148, Springer Verlag, August, 2004 [Proceedings][Preprint of Extended Journal Version]

though was first used informally (though unpublished) by Sarah Thompson in the early 1990s.

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Example

A number of transitional logics are known, and are classified within the SAS'04 paper. The simplest to understand is \mathbb{T}_5, a 5-valued extended logic with the following truth table:

Image:t5image.png

The values are defined as follows:

  • \ttt -- True (logic 1) for all time
  • \fff -- False (logic 0) for all time
  • \ft -- False, cleanly becoming True at some (undefined) point in time
  • \tf -- True, cleanly becoming False at some (undefined) point in time
  • \bigstar -- Any possible signal

Note that \bigstar is strictly a superset containing all possible waveforms (i.e. more formally \ttt \subseteq \bigstar, \fff \subseteq \bigstar, \ft \subseteq \bigstar and \tf \subseteq \bigstar).

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