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Relational semantics for logics with thin sets of connectives

Posted on January 21, 2015January 28, 2020 by Damir Dzhafarov

Katalin Bimbo

20 Feb, 2-3:30pm, LH 306

The use of a binary accessibility relation in the semantics for normal modal logics that was invented by Kripke in the late 1950s is well motivated not only philosophically, but also mathematically. A similar semantics for relevance logics that was introduced by Routley and Meyer in the early 1970s uses a ternary accessibility relation. Gaggle theory that was invented by Dunn in the early 1990s generalizes both Kripke’s as well as Routley and Meyer’s semantics. Gaggle theory predicts that a standard relational semantics for the major relevance logics such as T, E and R should have a ternary accessibility relation.

In this talk, I explore how the Routley-Meyer semantics for T and R fare, respectively, for the implicational fragments of these logics (or for slight extensions thereof).