Thursday, April 30, 2009

Temporal Logic and Textuality

Over at Good Math, Bad Math Mark Chu-Carroll provides an excellent overview of temporal logic - logic built for reasoning about things that change over time.

Of course, I see text as being among the things that change over time. As we read, each statement builds a moment in time transitioning to another moment - in forward, backward, and parallel directions. So the connection between TL and text, possibly, is the matrix for breaking down texts in new and interesting ways.

MarkCC, as he is also known, talks mainly about Computational Tree Logic (CTL). read the following and marvel at its potential for thinking about texts:

The idea of the model CTL, as I said above, is based on Kripke semantics. Kripke semantics defines a changing system by using a collection of worlds. Each world consists of an assignment of truth values to each of the basic propositions, and a set of successor worlds. In Kripke semantics, you follow a path through the worlds - in each step, you move from a world to one of its successors. In CTL, a world represents a moment in time; the successors to a world represent the possible moments of time that immediately follow it.

The Kripke semantics of CTL effectively gives us a non-deterministic model of time. From a given moment, there can be more than one possible future - and we have no way of determining which possible future will come true until we reach it. So time becomes a tree of possibilities - from each moment, you could go to any of its successors, so each moment spawns a branch for each of its successors - and each path through the tree represents a timeline for a possible future.

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