Harry Deutsch

The completeness of S

The subsystem S of Parrys AI [10] (obtained by omitting modus ponens for the material conditional) is axiomatized and shown to be strongly complete for a class of three valued “Kripke style” models. It is proved that S is weakly complete for the class of consistent models, and therefore that Ackermanns rule γ is admissible in S. It also happens that S is decidable and contains the Lewis system S4 on translation — though these results are not presented here. S is arguably the most “relevant” relevant logic known at this time to be decidable.

A note on the decidability of a strong relevant logic

A modified filtrations argument is used to prove that the relevant logic S of [2] is decidable.

Semantic analysis of natural kind terms

This paper develops a model theoretic semantics for so called “natural kind terms” that reflects the viewpoint of (Kripke, 1980) and (Putnam, 1975). The semantics generates a formal counterpart of the “K-mechanism” investigated in (Salmon, 1981) and in unpublished work by Keith Donnellan.