Positive and negative Properties. A Logical Interpretation
Janusz Kaczmarek · Bulletin of the Section of Logic · 2003
In the paper we construct a simple sentential logic (LBK) based on the ontology presented in [3]. LBK has internal and external strata, which yield a double characterization of the connectives. This leads to the correspondence of LBK to Bochvar’s and Kleene’s logics. The connectives of the internal level correspond to the connectives of Bochvar’s internal logic and of Kleene’s weak logic, while the connectives of the external level correspond to those of Bochvar’s external logic and of Kleene’s strong logic. The ontological interpretation shows that the former represent the so-called connectives de re, the latter the connectives de dicto. 1. Inspirations We present a particular problem concerning properties of individuals. Given some representation of statements about individuals by the language of many-valued logic we show simple relations that connect objects and their properties. The problem is a piece of more general topic of formal representation of three categories of objects: universals (that are treated as incomplete objects), individuals (complete objects) and concepts (that are treated by philosophers as incomplete objects; we do not investigate them here). For our analysis we distinguished two types of objects: complete and incomplete. Complete objects can be identifled with individuals (like