Logics and Falsifications

Kapsner, Andreas

doi:10.1007/978-3-319-05206-9

Cited by 33 publications

(11 citation statements)

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“…Similarly, in intuitionistic logic A → ¬A is provable when ¬A is provable. The same goes for Nelson logics N 3 and N 4, as well as all the variations I introduced in [4].…”

Section: Is Humble Connexivity Boring?mentioning

confidence: 69%

“…Furthermore, the editors have pointed out to me that [15] also expresses ideas that go in a similar direction as the notion of humble connexivity does. 4 Again, remember that variations like ¬A → A are omitted in all clauses that follow and are to be understood implicitly.…”

Section: Background: Connexivity Weak and Strongmentioning

confidence: 99%

“…in [4]. I did not consider this logic there, but it might be seen as a simple alternative to the logics I proposed.…”

Section: What (Humble) Connexivity Is Aboutmentioning

confidence: 99%

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Humble Connexivity

Kapsner

2019

LLP

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In this paper, I review the motivation of connexive and strongly connexive logics, and I investigate the question why it is so hard to achieve those properties in a logic with a well motivated semantic theory. My answer is that strong connexivity, and even just weak connexivity, is too stringent a requirement. I introduce the notion of humble connexivity, which in essence is the idea to restrict the connexive requirements to possible antecedents. I show that this restriction can be well motivated, while it still leaves us with a set of requirements that are far from trivial. In fact, formalizing the idea of humble connexivity is not as straightforward as one might expect, and I offer three different proposals. I examine some well known logics to determine whether they are humbly connexive or not, and I end with a more wide-focused view on the logical landscape seen through the lens of humble connexivity.1 Not only is he, by giving me this challenge, responsible for the existence of this paper, he also gave a number of suggestions that were of tremendous help to me in writing this paper; section 6 in particular owes its inclusion and form to these suggestions. Two others have had an equally great impact on this paper, and they happen to be the editors of this volume. The idea of humble connexivity originates in my joint work with Hitoshi Omori. Even if what I'll have to say is probably more opinionated than he would have put it, I would not have been able to form

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“…Similarly, in intuitionistic logic A → ¬A is provable when ¬A is provable. The same goes for Nelson logics N 3 and N 4, as well as all the variations I introduced in [4].…”

Section: Is Humble Connexivity Boring?mentioning

confidence: 69%

Section: Background: Connexivity Weak and Strongmentioning

confidence: 99%

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Humble Connexivity

Kapsner

2019

LLP

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“…On the other hand, if ϕ is not provable, then there exists no proof of ϕ available that one can convert into a refutation of ϕ. Although this case counts as a satisfying instance of the BHK interpretation of the conditional, this state of affairs satisfies the BHK condition only vacuously by allowing what [5] calls an "empty promise conversion." If one is troubled by the vacuous satisfaction of conditionals  and this seems to be the type of thing that ought to trouble a constructivist  then one might then wish to reject all instances of the sentence ϕ → ∼ ϕ.…”

Section: Discussionmentioning

confidence: 99%

Inconsistent Models (and Infinite Models) for Arithmetics with Constructible Falsity

Ferguson

2018

LLP

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Abstract. An earlier paper on formulating arithmetic in a connexive logic ended with a conjecture concerning C ♯ , the closure of the Peano axioms in Wansing's connexive logic C. Namely, the paper conjectured that C ♯ is Post consistent relative to Heyting arithmetic, i.e., is nontrivial if Heyting arithmetic is nontrivial. The present paper borrows techniques from relevant logic to demonstrate that C ♯ is Post consistent simpliciter, rendering the earlier conjecture redundant. Given the close relationship between C and Nelson's paraconsistent N4, this also supplements Nelson's own proof of the Post consistency of N4 ♯ . Insofar as the present technique allows infinite models, this resolves Nelson's concern that N4 ♯ is of interest only to those accepting that there are finitely many natural numbers.

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“…N4 is FDE plus a semi-intuitionistic implication: Peirce's law does not hold, but the equivalence between ¬(A → B) and A ∧ ¬B holds. A Kripke semantics for N4 can be found in [13], p. 164, and it is essentially the local conditions for ¬, ∨, ∧ that mimic the conditions of FDE, the local conditions for ¬(A → B) and the intuitionistic global clause for →.…”

Section: The Logic Let Jmentioning

confidence: 99%

Kripke-Style Models for Logics of Evidence and Truth

Antunes

Carnielli

Kapsner³

et al. 2020

Axioms

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In this paper, we propose Kripke-style models for the logics of evidence and truth LETJ and LETF. These logics extend, respectively, Nelson’s logic N4 and the logic of first-degree entailment (FDE) with a classicality operator ∘ that recovers classical logic for formulas in its scope. According to the intended interpretation here proposed, these models represent a database that receives information as time passes, and such information can be positive, negative, non-reliable, or reliable, and a formula ∘A means that the information about A, either positive or negative, is reliable. This proposal is in line with the interpretation of N4 and FDE as information-based logics, but adds to the four scenarios expressed by them two new scenarios: reliable (or conclusive) information (i) for the truth and (ii) for the falsity of a given proposition.

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Logics and Falsifications

Cited by 33 publications

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Humble Connexivity

Humble Connexivity

Inconsistent Models (and Infinite Models) for Arithmetics with Constructible Falsity

Kripke-Style Models for Logics of Evidence and Truth

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