Two plans in the semantics of relevant logic

Takuro Onishi (Kyoto University)

Takuro Onishi (Kyoto) will present "Two plans in the semantics of relevant logic" at 11 on 16 March in Old Quad G10.

Abstract: In his paper "The American plan completed," Routley examined how to extend the four-valued semantics for FDE (so called American plan) to accommodate full relevant implication. The resultant four-valued frame semantics was hopelessly complicated, and he concluded that "[t]he American plan is ... little more than a very circuitous and cumbersome way of avoiding the much more intuitive Australian plan", which is a simple frame semantics with one ternary relation and one "star" function. In this talk, I will try to make clearer the relationship between the two plans by reorganizing Routley's semantics. In my model, the four-valued American approach serves as an explanatory basis to introduce "star-like" relations avoiding De and Omori's criticism about circularity, and the two-valued Australian frame semantics is considered as a developed form of the American plan.