Non-Eternalist Logic #2

From Non-Eternalist Logic and Symbol Binding.

A Dynamic Sentence Truth Value Logic

1. Begin with a standard Zero-Order Classical Logic.
2. Equip that logic with an additional Interpretation Function I** (we take I* and I to stand for the Complex and Propositional Truth Interpretation Functions, respectively).
3. Add the definition of a Sequence which specifies the temporal ordering of truth-evaluation operations on wff: S,Q,R such that I*(Q) is performed after I*(S).
4. We define I** as follows:

4a. A Chiastic Truth-Value such that given two Sequence S and S,Q such that:

4b. If I*(S) = T or I*(S) = F is obtained prior to the Truth-Value measurement on Q

4c. And I*(Q) = T is then obtained for sentence Q.

4d. Then, I**(S) = F.

4e. Also, we take it that for every Truth-Value of the last sentence Z of any Sequence the following holds: I*(Z) = I**(Z).

This represents the phenomena where a False (I*(Z) = F) statement Z following some preceding statement (of indeterminate Truth Value or otherwise) is used to essentially "falsify" the first - a language game trick I've seen some people use to encrypt public communication.