Talk:Paraconsistent logic: Difference between revisions

Revision as of 02:33, 19 February 2017

Revision as of 00:56, 8 July 2017

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::Thanks. I cleaned up the remainder of the section since I don't have a conflict because it is not my work. Please make improvements.

::The correct reference for the applications section is the following:

:::Carl Hewitt. ''Formalizing common sense reasoning for scalable inconsistency-robust information coordination using Direct Logic Reasoning and the Actor Model.'' in Vol. 52 of Studies in Logic. College Publications. ISBN-10: {{ISBN |1848901593}}. 2015.

::[[User:Prof. Carl Hewitt|Carl]] ([[User talk:Prof. Carl Hewitt|talk]]) 17:14, 26 August 2016 (UTC)

:::Hi there. The changes in question seem to have been implemented, as per the comment above. Please note that, while citing yourself should be discussed on the talk page (as you have done), it is not necessary to place the edit request template, unless no other editors are working on the article. Regards, [[User:VB00|VB00]] ([[User talk:VB00|talk]]) 11:49, 1 January 2017 (UTC)

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Each of these principles has been challenged.

One approach is to reject disjunction introduction but keep disjunctive syllogism and transitivity. In this approach, rules of [[natural deduction]] hold, except for [[disjunction introduction]] and [[excluded middle]]; moreover, inference A⊢B does not mean necessarily mean entailment A⇒B. Also, the following usual Boolean properties hold: [[double negation]] as well as [[associativity]], [[commutativity]], [[distributivity]], [[De Morgan's laws|De Morgan]], and [[idempotence]] inferences (for conjunction and disjunction). Furthermore, inconsistency-robust proof by contradiction holds for entailment (A⇒(B∧¬B))⊢¬B. [[Carl Hewitt]] favours this approach, claiming that having the usual Boolean inferences, [[Natural deduction]], [[Double negation elimination]], [[Rule of weakening|Weakening for inference]] (If ⊢A, then B⊢A), and inconsistency robust [[Proof by Contradiction]] are huge advantages in [[software engineering]].<ref name="commonsense">"Carl Hewitt. ''Formalizing common sense reasoning for scalable inconsistency-robust information coordination using Direct Logic Reasoning and the Actor Model.''" in Vol. 52 of Studies in Logic. College Publications. ISBN-10: {{ISBN |1848901593}}. 2015.</ref>

Another approach is to reject disjunctive syllogism. From the perspective of [[dialetheism]], it makes perfect sense that disjunctive syllogism should fail. The idea behind this syllogism is that, if ''¬ A'', then ''A'' is excluded and ''B'' can be inferred from ''A ∨ B''. However, if ''A'' may hold as well as ''¬ A'', then the argument for the inference is weakened.