Modal Logic in 4 Dimensions

This site reflects my current interest which is to construct a general decision procedure and semantic model that combines propositional, modal and deontic logics. However you may also find it worth a read if you have an interest in multi valued logics, four valued approaches to modal logic, matrices, multi valued lattices, modal geometry, squares of opposition or looking to find a use for the 2-bit (dibit) code 00, 01, 10 and 11. You may also have an interest in two-dimensional languages and paraconsistent logics. 

Given the following interpretation dibit code is here dubbed 4VBC for four valued bit code (note: not four valued logic). The four evaluations are:

00 = Not Excluded Middle (not well formed picture)

01 = Exists (picture represents existing state of affairs)

10 = Non Existent (picture does not represent existing state of affairs)

11 = Excluded Middle (well formed picture)

The four values are picture values. A picture is anything that represents some state of affairs. 

Let's be very clear: 4VBC is not a four valued logic. It only has two elementary semantic values. 4VBC is a two valued logic. The interpreted code 01 and 10 are its two semantic values whilst 00 and 11 are complex values built up from the two elementary values  i.e. 01 + 10 = 11,     01 x 10 = 00. 4VBC provides a means to reformulate how we present standard two valued logic.

Introducing a two dimensional language means the code is organized into pairs e.g. <00 01>.  Now there are 16 permutations of code. The right side dibit is the value of the target picture, the left side is the value of any alternative picture which disagrees with the target picture. Working through that idea results in a Propositional Modal and Deontic logic. This logic can be neatly rendered as the PMDL Tesseract.