Tolerant and Strict Truth
We present and briefy consider a logical approach to transparent truth. We describe eight logics, four including a fully transparent truth predicate, and describe some relations between them. The strongest logic we consider is a strengthening of classical logic: all classically valid inferences are valid in our logic, and more besides. The additions result from full transparency for our truth predicate. This is achieved by relaxing transitivity; the logic is not unrestrictedly transitive. The main paper presents a single model theory for all eight logics, and considers the application of this strongest logic to the liar paradox. An appendix gives a single proof theory for all eight logics.