Thursday, March 25, 2010

Change Logic

As part of the reconstruction of the computability and intelligence concept in terms of propositional logic, I am currently working on an effective formalization of (causal) processes. I realized, that this is a goal which is very similar to certain branches of modal logic, but that the approach is very different. Although the work itself is still in a premature state, I thought it would be interesting to work out these differences and explain some core ideas. This resulted in a paper of five pages, that starts with the following preface:

Suppose, temporal logic is the subject that looks for a language and logic to reason about processes and things that change in time. Then it seems, that this implies a thorough study of time itself. But this is wrong. Time is a philosophical burden and dead weight in temporal logic. We shouldn't try to associate events to a time structure, we only need to realize change during the process. This paradigm shift is one starting point of a research project called change logic.

However, the elimination of time from temporal logic may not be so surprising as it tries to sound here. Actually, in the standard modal logical reconstruction, the relation to a time structure via a Kripke model is also only temporary. Once the formal system is motivated and its soundness and completeness is shown, time becomes superfluous here as well and disappears. In fact and in return, it is also possible to attach a linear time structure to what will be introduced as change logic.

So in the end, the real change with change logic does not so much come from a new philosophical semantics, but from the fact, that the whole thing was pulled off without adding new constructs to the syntax. In other words, change logic is temporal logic without modal operators.

The whole text is located here.