Quasi-deviant and Extended Logics
Haack also described what she calls a quasi-deviant logic. These logics are different from pure deviant logics in that:
- the set of well-formed formulas generated is a proper superset of the set of well-formed formulas generated by classical logic.
- the set of theorems generated is a proper superset of the set of theorems generated by classical logic, both in that the quasi-deviant logic generates novel theorems using well-formed formulas held in common with classical logic, as well as novel theorems using novel well-formed formulas.
Finally, Haack defined a class of merely extended logics. In these,
- the set of well-formed formulas generated is a proper superset of the set of well-formed formulas generated by classical logic.
- the set of theorems generated is a proper superset of the set of theorems generated by classical logic, but only in that the novel theorems generated by the extended logic are only a result of novel well-formed formulas.
Some systems of modal logic meet this definition. In such systems, any novel theorem would not parse in classical logic due to modal operators. While deviant and quasi-deviant logics are typically proposed as rivals to classical logic, the impetus behind extended logics is normally only to provide a supplement to it.
Read more about this topic: Deviant Logic
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