Models for relevant modal logics

✍ Scribed by André Fuhrmann

• Publisher: Springer Netherlands
• Year: 1990
• Tongue: English
• Weight: 789 KB
• Volume: 49
• Category: Article
• ISSN: 0039-3215
• DOI: 10.1007/bf00370161

✦ Synopsis

Semantics are given for modal extensions of relevant logics based on the kind of frames introduced in I-7]. By means of a simple recipe we may obtain from a class FRM (L) of unreduced frames characterising a (non-modal) logic L, frame-classes FRM m (L:M) eharacterising conjunctively regular modal extensions L.M of L. By displaying an incompleteness phenomenon, it is shown how the recipe fails when reduced frames are under consideration.

1 Richard Sylvan's (nee Routley) work on relevant modal logics has largely remained unpublished. Some of his results may overlap some of mine. As a supervisor of my doctoral thesis, Sylvan has generously advised me over an extended period of time. It is thus a pleasant duty to ascribe to him significant share in the work reported here. Final responsibility for the present article, however, lies solely with me.