On the Logical Philosophy of Assertive Graphs

摘要

The logic of assertive graphs (AGs) is a modification of Peirce's logic of existential graphs (EGs), which is intuitionistic and which takes assertions as its explicit object of study. In this paper we extend AGs into a classical graphical logic of assertions (C1AG) whose internal logic is classical. The characteristic feature is that both AGs and C1AG retain deep-inference rules of transformation. Unlike classical EGs, both AGs and C1AG can do so without explicitly introducing polarities of areas in their language. We then compare advantages of these two graphical approaches to the logic of assertions with a reference to a number of topics in philosophy of logic and to their deep-inferential nature of proofs.