ABSTRACT
The idea behind ambiguity-adaptive logics1 is that we have to make an inference to identify two occurrences of one non-logical constant (sentential, predicative or individual constant, henceforth NLC). If, for instance, we meet two times the word "chair", we can either say that both occurrences mean the same, or we can suspect them to have a different meaning. In general there are two extreme positions: (1)
we identify all occurrences of one NLC; (2) we refuse to identify any two occurrences with one another. The first position can be handled by applying Classical Logic (henceforth CL) to the original reading of a set of premises F. The second position can be handled by applying CL to a maximally ambiguous reading of the set of premises T1. This T1 is easily created by giving every occurrence of a NLC in F a different superscript. An ambiguity-adaptive logic starts from the maximally ambiguous reading, and reintroduces the original reading unless and until this would lead to the derivation of an inconsistency from the set of premises. The italic expression is typical for all adaptive logics, created by Diderik Batens, and the Ghent group.2 The ambiguity-adaptive logic ACL2 can be characterized by the theorems 1 and 2:3
THEOREM 1 F I-CL -L iff T1 hCL C[ ^ C{ V ... V C* ± Cln for some NLC Cm. & ^ Cj refers to either ~((7i = Cj), if C is a sentential letter, to ~C* = Cj if C is a constant, or to ~(Vxi)...(Vxn)(C'xi...xn = C^Xi...xn) if C is a predicate of rank n.
