The Emergence of Set-theoretical Semantics for Relevance Logics around 1970.

The early history of the relational (“possible world”) semantics for modal logics is well investigated. Successful applications of a relational semantics for relevance logics started to appear about a decade after the first set-theoretical semantics for normal modal logics were designed. This paper gives a brief out- line of the results from the late 1960s and the first years of the 1970s. We provide an exposition of three types of attempts (by five people) to provide set-theoretical semantics for relevance logics or some related logics—together with some historical details. The crucial technical features of the semantics can be characterized along the lines of the modeling of the implication connective, in particular, whether the modeling derives from a binary operation or from a ternary relation (which is not assumed to be an operation).

Authors

• Katalin Bimbó
• J. Michael Dunn

Keywords

• entailment
• relational semantics
• relevant implication
• relevance logic
• rigorous implication