NEGATION: TWO POINTS OF VIEW
By Arnon Avron
In this paper we look at negation from two dierent points of view: a syntactical one and a semantical one. Accordingly, we identify two dierent types of negation. The same connective of a given logic might be of both types, but this might not always be the case.
The syntactical point of view is an abstract one. It characterizes connectives according to the internal role they have inside a logic, regardless of any meaning they are intended to have (if any). With regard to negation our main thesis is that the availabilityof what we call below an internal negation is what makes a logic essentially multiple-conclusion.
The semantic point of view, in contrast, is based on the intuitive meaning of a given connective. In the case of negation this is simply the intuition that the negation of a proposition A is true if A is not, and not true if A is true.
Like in most modern treatments of logics, our study of negation will be in the framework of Consequence Relations (CRs). See more
Posted by Tony Marmo at 03:52 GMT