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Possibility pre-supposition free logics

Presupposition-free logics are usually taken to be free of existential presuppositions. Allowing individual constants (what we will call 'free variables' in this paper) not to designate is usually taken as allowing them not to designate some individual in a domain of existing individuals. One standard move that has been used in such a situation is then to have the non-existence designating free variables designate something else such as an individual in a domain disjoint from the domain of existing individuals. This move could be seen as a move to allowing non-existence designating free variables to designate imaginary, or fictional, or possible but non-existent individuals. The question can then arise as to whether or not an existential presupposition free logic has a possibility presupposition. It would certainly be so if the free variables must designate an individual either in the domain of existing individuals or in the domain of possible but nonexistent individuals. Since presupposition free logics were first designed to eliminate existential presupposition it would be interesting to see what are the results of designing possibility presupposition-free logics. One crucial feature of standard presupposition free logics is that the quantifiers range only over the domain of existing individuals, whereas free variables may designate any individual in either the existence domain or the domain of possible but non-existent individuals. In order to proceed towards a set of possibility presupposition-free logics, we could introduce quantifiers to range over a domain of possible individuals, which would include the set of existent individuals, and we could have the free variables designating any individual in either the domain of possible individuals or in a domain of impossible individuals (which would be disjoint from the possibility domain). As far as the truth of statements is concerned we could assume that all statements without free variables or with free variables designating possible individuals will come under the standard truth conditions. Statements containing free variables that designate impossible individuals could then be treated in a range of ways parallel to those set out by Leblanc and