Tolerant reasoning: nontransitive or nonmonotonic?

Cobreros, Pablo; Égré, Paul; Ripley, Dave; Rooij, Robert van

doi:10.1007/s11229-017-1584-8

Cited by 7 publications

(4 citation statements)

References 48 publications

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“…I believe that such semantic analysis would allow me to come up with another paper devoted to an adequate syntactic axiomatization of ≈. For this purpose, I employ Douven's analysis of a similar probabilistic entailment (Douven, 2014) as well as the shopper's guide by Hlobil to choosing your nonmonotonic logic (Hlobil, 2018) and Cobreros et al's entailments for tolerant reasoning (Cobreros & Egré & Ripley, 2021).…”

Section: Classifying ≈mentioning

confidence: 99%

A Supraclassical Probabilistic Entailment Relation

Shangin

2023

Философия-ВШЭ

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The paper presents an original supraclassical nontrivial plausible entailment relation $\vapprox$ that employs Kolmogorov's probability theory. Its crucial feature is the primitiveness of a conditional probability, which one calculates with the help of the method of truth tables for classical propositional logic. I study the properties of the entailment relation in question. In particular, I show that while being supraclassical, i.e., all classical entailments and valid formulas are $\vapprox$-valid, but not vice versa, it is not trivial and enjoys the same form of inconsistency as classical entailment ⊧ does. I specify the place of the proposed probability entailment relation in certain classifications of nonclassical entailment relations. In particular, I use Douven's analysis of some probabilistic entailment relations that contains dozens of properties that are crucial for any probabilistic entailment relation, as well as Hlobil's choosing your nonmonotonic logic: shopper’s guide, due to the fact that $\vapprox$ is not monotonic, and Cobreros, Egré, Ripley, van Rooij's entailment relations for tolerant reasoning. At last, I perform a comparative analysis of classical, the proposed, and some other entailment relations closely related to the latter: those introduced by Bocharov, Markin, Voishvillo, Degtyarev, Ivlev, where the last two entailment relations are based on the so-called principle of reverse deduction, which is an intuitively acceptable way to connect classical and probabilistic entailment relations.

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Section: Classifying ≈mentioning

confidence: 99%

A Supraclassical Probabilistic Entailment Relation

Shangin

2023

Философия-ВШЭ

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“…Again, this should not be interpreted as saying that there might be no approach, similar to Ripley's, which might reject Weakening on reasonable grounds. In fact, Ripley himself and his collaborators discussed alternatives of this sort in Cobreros et al (2017). However, such proposals do not motivate the rejection of Weakening in the plausibility of the addition of further assertions and denials taking an out of bounds positions, back into the bounds.…”

Section: Bilateralism and Classical Logicmentioning

confidence: 99%

Inferentialism and Relevance

Szmuc

2021

Anál. Filos.

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This paper provides an inferentialist motivation for a logic belonging in the connexive family, by borrowing elements from the bilateralist interpretation for Classical Logic without the Cut rule, proposed by David Ripley. The paper focuses on the relation between inferentialism and relevance, through the exploration of what we call relevant assertion and denial, showing that a connexive system emerges as a symptom of this interesting link. With the present attempt we hope to broaden the available interpretations for connexive logics, showing they can be rightfully motivated in terms of certain relevantist constraints imposed on assertion and denial.

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“…Independently of these results, philosophical work in logic has been produced arguing that long-standing paradoxes of vagueness and of truth can be solved by an appeal to substructural logics (see the recent special issue of Synthese on substructural approaches to paradox, [76]). Several authors have proposed that the key to solving semantic paradoxes (such as the Liar, or the Curry, or the sorites paradox), is by giving up some of the structural rules, including Transitivity [12,55,56,69,71,74], Reflexivity [25,44], Weakening [15,16,39], or Contraction [38,61,75]. Figure 1 gives an illustration of these various possible strategies by considering the following example, borrowed from [25], of a derivation of the Liar paradox in classical logic (the sentence λ is the Liar sentence, saying of itself that it is not true, ¬T λ ; the rules T -R and T -L express the intersubstitivity of φ with T φ ).…”

mentioning

confidence: 99%

Editorial Introduction: Substructural Logics and Metainferences

Barrio

Égré

2022

J Philos Logic

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The concept of substructural logic was originally introduced in relation to limitations of Gentzen's structural rules of Contraction, Weakening and Exchange. Recent years have witnessed the development of substructural logics also challenging the Tarskian properties of Reflexivity and Transitivity of logical consequence. In this introduction we explain this recent development and two aspects in which it leads to a reassessment of the bounds of classical logic. On the one hand, standard ways of defining the notion of logical consequence in classical logic naturally induce substructural logics when admitting more than two truth values; on the other hand, these substructural logics give rise to hierarchies of metainferences that can be used to approximate classical logic at different levels.

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Tolerant reasoning: nontransitive or nonmonotonic?

Cited by 7 publications

References 48 publications

A Supraclassical Probabilistic Entailment Relation

A Supraclassical Probabilistic Entailment Relation

Inferentialism and Relevance

Editorial Introduction: Substructural Logics and Metainferences

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