An Adaptive Logic Based on Jaśkowskiˈs Approach to Paraconsistency
نویسنده
چکیده
Discussive logics (also called discursive logics) were introduced in 1948 by Stanis law Jaśkowski and constitute the first family of formal paraconsistent logics. The basic mechanism behind discussive logics is as simple as ingenious. Where L is some modal logic and Γ♦ = {♦A | A ∈ Γ}, a discussive logic DL, associated with L, is obtained by specifying the language L of DL and by stipulating that, where A and the members of Γ are well-formed formulas of L, Γ `DL A iff Γ♦ `L ♦A. It is easily observed that, given an appropriate choice of L and of L, DL is paraconsistent. This is the case, for instance, if L is the language of Classical Logic (henceforth CL) and L is S5 (in view of ♦A, ♦∼A 0S5 ♦B). Where “∧” stands for the classical conjunction, discussive logics moreover do not allow to infer A ∧ ∼A from A and ∼A (in view of ♦A, ♦∼A 0L ♦(A ∧ ∼A)). Especially from the perspective of interpreting discussions, discussive logics seem highly attractive. If two participants in a discussion contradict each other, we tend to interpret their statements in a modal way: “Someone accepts A; someone accepts ∼A”. From this, neither “someone accepts B” nor “someone accepts both A and ∼A” follows. This is exactly what discussive logics allow for. There is, however, a drawback. If L comprises the classical connectives, the above mechanism leads to a system that is as rich as CL for single-premise inferences, but that invalidates all interesting multiple-premise inferences of CL (Adjunction, Modus Ponens, Modus Tollens, . . . ). This is why Jaśkowski dismissed the idea to formulate discussive logics in terms of the classical connectives (see [17, pp. 149–150]). Instead, he proposed
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ورودعنوان ژورنال:
- J. Philosophical Logic
دوره 35 شماره
صفحات -
تاریخ انتشار 2006