Four-Valued First-Order Semantics for RW

Shay Logan (North Carolina State University)

Shay Logan (North Carolina State) will present "Four-Valued First-Order Semantics for RW" at 11 in Arts West 211, West Wing via skype.

Quantified relevance logics are incomplete with respect to any obvious constant-domain semantics. So in order to give a semantics for which quantified relevance logics are complete, Fine resorted to a varying-domain (stratified) semantic theory. It has been argued that this raises three problems:

(1) Varying domains are inappropriate for many of the applications of logic,

(2) The complexity of the stratified semantics makes it an implausible choice for the semantics of logical inference, and

(3) The complexity of the stratified semantics makes it unusable in practice.

In this talk I will build a particularly simple example of the stratified semantics that is based on Restall’s four-valued semantics for propositional RW and use this to give (admittedly non-decisive) reasons to doubt the severity of each of these problems. In outline, the doubts I raise can be summarized as follows:

(1) It’s not clear stratified semantics should be thought of as a varying domain semantics. Even if it is, it’s not clear how inappropriate that is.

(2) Stratified semantics is not quite as complex as it seems from Fine’s presentation of it. Even if it were, it’s not clear how much of a problem that would be.

(3) Finally, I’ll give concrete ways to think about and visualize stratified models, making them much more accessible for practical uses.