A solution to the completeness problem for weakly aggregative modal logic
| Autor: | Peter Apostoli, Bryson Brown |
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| Rok vydání: | 1995 |
| Předmět: | |
| Zdroj: | Journal of Symbolic Logic. 60:832-842 |
| ISSN: | 1943-5886 0022-4812 |
| DOI: | 10.2307/2275759 |
| Popis: | We are accustomed to regardingKas the weakest modal logic admitting of a relational semantics in the style made popular by Kripke. However, in a series of papers which demonstrates a startling connection between modal logic and the theory of paraconsistent inference, Ray Jennings and Peter Schotch have developed a generalized relational frame theory which articulates an infinite hierarchy of sublogics ofK, each expressing a species of “weakly aggregative necessity”. Recall thatKis axiomatized, in the presence ofNandRM, by the schema of “binary aggregation”For eachn≥ 1, the weakly aggregative modal logicKnis axiomatized by replacingKwith the schema of “n-ary aggregation”which is ann-ary relaxation, or weakening, ofK. Note thatK1=K.In [3], the authors claim without proof thatKnis determined by the class of framesF= (W, R), whereWis a nonempty set andRis an (n+ 1)-ary relation onW, under the generalization of Kriple's truth condition according to which □αis true at a pointwinWif and only ifαis true at one ofx1,…,xnfor allx1,…,xninWsuch thatRw, x1,…,xn. |
| Databáze: | OpenAIRE |
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