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Branching Time: The System Kb

  • Nicholas Rescher
  • Alasdair Urquhart
Part of the LEP Library of Exact Philosophy book series (LEP, volume 3)

Abstract

The concept of a “branching structure” includes the notion of a “tree”, of which it is a generalization. That is, dropping the conditions of discreteness and rootedness from the concept of a tree, we define a branching structure to be a set 7 over which a binary relation U (the accessibility relation of temporal posteriority) is defined, satisfying the conditions
$$(\forall x)(\forall y)(\forall z)[(Uxy\& Uyz) \supset Uxz][transitivity]$$
and
$$(\forall x)(\forall y)(\forall z)[(Uxz\& Uyz) \supset (Uxy \vee x = y \vee Uyx)][backwards{\kern 1pt} linearity]$$
Some examples of branching structures are Here the points (indicated in the finite case by nodal circles) are 7-elements and the connecting lines (indicated in the finite case by arrows and in the infinite case by relative placement from left to right) represent the U-relation.

Keywords

Search Tree Tense Structure Completeness Proof Open Future Counter Model 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag/Wien 1971

Authors and Affiliations

  • Nicholas Rescher
    • 1
  • Alasdair Urquhart
    • 1
  1. 1.PittsburghUSA

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