×

The inapplicability of (selected) paraconsistent logics. (English) Zbl 1398.03139

Summary: In some cases one is provided with inconsistent information and has to reason about various consistent scenarios contained within that information. Our goal is to argue that filtered paraconsistent logics are not the right tool to handle such cases and that the problems generalise to a large class of paraconsistent logics. A wide class of paraconsistent (inconsistency-tolerant) logics is obtained by filtration: adding conditions to the classical consequence operation (for instance, \(\phi\) is a weak Rescher-Manor consequence of \(\Gamma\) just in case \(\phi\) follows classically from at least one maximally consistent subset of \(\Gamma\)). We start by surveying the most promising candidates and comparing their strengths. Then we discuss the mainstream views on how non-classical logics should be chosen for an application and argue that none of these allows us to choose any of the filtered logics for action-guiding reasoning with inconsistent information, because such reasoning has to start with the selection of possible scenarios – and such a process does not correspond to any of the mathematical models offered by filtered paraconsistent logics. Finally, we criticise the recent attempt to defend explorative hypothetical reasoning by means of weak Rescher-Manor consequence operation in [J. Meheus et al., J. Log. Comput. 26, No. 1, 361–380 (2016; Zbl 1444.03117)].

MSC:

03B53 Paraconsistent logics

Citations:

Zbl 1444.03117
Full Text: DOI

References:

[1] Beall, J., & Restall, G. (2006). Logical pluralism. Oxford: Oxford University Press. · Zbl 1374.03001
[2] Benferhat, S., Dubois, D., & Prade, H. (1997). Some syntactic approaches to the handling of inconsistent knowledge bases: A comparative study. Studia Logica,58, 17-45. · Zbl 0867.68100
[3] Cook, R. T. (2010). Let a thousand flowers bloom: A tour of logical pluralism. Philosophy Compass,5, 492-504.
[4] Meheus, J., Straßer, C., & Verdée, P. (2014). Which style of reasoning to choose in the face of conflicting information?Journal of Logic and Computation, doi:10.1093/logcom/ext030 · Zbl 1444.03117
[5] Payette, G., & Schotch, P. (2009). Preserving what? In P. Schotch, B. Brown, & R. Jennings (Eds.), On preserving: Essays on paraconsistent logic (pp. 81-99). Toronto: University of Toronto Press.
[6] Pollock, J. (1995). Cognitive carpentry. Cambridge, MA: MIT Press.
[7] Prakken, H. (2006). Combining sceptical epistemic reasoning with credulous practical reasoning. In P. Dunne & T. J. M. Bench-Capon (Eds.), Computational models of argument: Proceedings of COMMA 2006, September 11-12, 2006, Liverpool, UK (pp. 311-322). Amsterdam: IOS Press.
[8] Priest, G. (2013). Revising logic. [unpublished paper].
[9] Reggia, J. A., Nau, D. S., & Wang, P. Y. (1985). A formal model of diagnostic inference. I. Problem formulation and decomposition. Information Sciences,37, 227-256. · Zbl 0583.68046
[10] Rescher, N., & Manor, R. (1970). On inferences from inconsistent premises. Theory and Decision,1, 179-217. · Zbl 0212.31103
[11] Shapiro, S. (2006). Effectiveness. In J. van Benthem, G. Heinzmann, M. Rebuschi, & H. Visser (Eds.), The age of alternative logics: Assessing philosophy of logic and mathematics today (pp. 37-49). Berlin: Springer. · Zbl 1124.03002
[12] Simari, G. R., & Loui, R. P. (1992). A mathematical treatment of defeasible reasoning and its implementation. Artificial Intelligence,53, 125-157. · Zbl 1193.68238
[13] Urbaniak, R., & Batens, D. (in press). Induction. In S. O. Hansson & V. F. Hendricks (Eds.), Handbook of formal philosophy. Berlin: Springer.
[14] Wyatt, N. (2004). What Are Beall and Restall Pluralists About? What are Beall and Restall pluralists about?Australasian Journal of Philosophy,82, 409-420.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.