We describe Modular-E (ME), a specialized, model-theoretic logic for reasoning about actions.
For this idea to be applicable, we must suppose that agents at least sometimes do what they do in non-parametric settings because game-theoretic logic recommends certain actions as the 'rational' ones.
One example of interest is the computer-theoretic logic of Matthew Hennessy and Robin Milner, used for describing the behaviour of systems; here the arrows come in more than one colour, and moving along an arrow of a particular colour represents performing a particular 'action' to change the state.
A main source for the mathematics of model-theoretic logics is Barwise and Feferman (1985).
As already noted, the proof-theoretic side of logic is not pursued much in his work.
Another application to the graph-theoretic account of logic is the definition of an asymmetric combination technique called importing logics (cf. Rasga et al. 2011).
In addition to the usual set-theoretic operators, configuration logic is equipped with a coalescing operator + to express combination of configuration sets.
Again, we do not think this is the crucial ingredient for the creation of EG, but one key element which works well with his theory of signs and his model-theoretic view of logic.
Agreeing with both Hintikka's and Goldfarb's evaluation that Peirce belongs to Boole's tradition, Shin found a connection between the model-theoretic view of logic (where Boole and Peirce are placed) and EG's birth (see Shin 2002: 14 16, and Pietarinen 2006).
The latter has both a transformational and a model-theoretic characterization that reveals it as a relaxation of equilibrium logic, the logical reconstruction of answer set semantics, and is thus called the semi-equilibrium model semantics.
The argument for liveness (progress) is given in a set-theoretic version of temporal logic.
