Topic: PARACONSISTENCY
Another interesting introduction to Paraconsistent Logic:
PARACONSISTENT LOGICS INTRODUCTION
By Anthony Hunter
In practical reasoning, it is common to have “too much” information about some situation. In other words, it is common for there to be classically inconsistent information in a practical reasoning database [Besnard et al., 1995]. The diversity of logics proposed for aspects of practical reasoning indicates the complexity of this form of reasoning. However, central to practical reasoning seems to be the need to reason with inconsistent information without the logic being trivialized [Gabbay and Hunter, 1991; Finkelstein et al., 1994]. This is the need to derive reasonable inferences without deriving the trivial inferences that follow the ex falso quodlibet proof rule that holds in classical logic.[Ex falso quodlibet]
α ¬α
β
So for example, from a database {α, ¬α, α→β, δ} reasonable inferences might include α, ¬α, α→β, and δ by reflexivity, β by modus ponens, α^;β by introduction, ¬α→¬β and so on. In contrast, trivial inferences might include γ, γ^¬δ, etc, by ex falso quodlibet.
Solutions to the problem of inconsistent data include database revision and
paraconsistent logics. The first approach effectively removes data from the database to produce a new consistent database. In contrast, the second approach leaves the database inconsistent, but prohibits the logics from deriving trivial inferences. Unfortunately, the first approach means we may loose useful information— we may be forced to make a premature selection of our new database, or we may not even be able to make a selection. We consider here the advantages and disadvantages of the paraconsistent approach.
The primary objective of this chapter is to present a range of paraconsistent logics that give sensible inferences from inconsistent information.
Posted by Tony Marmo
at 09:36 BST
