Many‐Valued Logic

Malinowski, Grzegorz

doi:10.1002/9780470996751.ch35

Cited by 9 publications

(3 citation statements)

References 25 publications

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“…The commonly-accepted quantificational correlates to the threevalued weak Kleene matrices are described in Malinowski (2008) If we provide a bounds consequence reading to ⊨ ⋆ , we can continue to understand the validity of a position as the suggestion that it is outof-bounds to strictly assert each member of Γ while strictly denying each member of Δ. As a historical note, the strict-tolerant interpretation of the weak Kleene matrices is implicit in Fabrice Correia (2002), in which a consequence relation ⊪ C is considered.…”

Section: Content and Quantificationmentioning

confidence: 99%

Secrecy, Content, and Quantification

Ferguson

2021

Anál. Filos.

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While participating in a symposium on Dave Ripley’s forthcoming book Uncut, I had proposed that employing a strict-tolerant interpretation of the weak Kleene matrices provided a content-theoretical conception of the bounds of conversational norms that enjoyed advantages over Ripley’s use of the strong Kleene matrices. During discussion, I used the case of sentences that are taken to be out-of-bounds for being secrets as an example of a case in which the setting of conversational bounds in practice diverged from the account championed by Ripley. In this paper, I consider an objection that my treatment of quantifiers was mistaken insofar as the confidentiality of a sentence ϕ(t) may not lift to the sentence ∃xϕ(x) and draw from this objection that neither the strong nor the weak Kleene interpretation of quantifiers suﬃces, but that a novel interpretation may do so.

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Section: Content and Quantificationmentioning

confidence: 99%

Secrecy, Content, and Quantification

Ferguson

2021

Anál. Filos.

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“…Although not frequently encountered in the literature, Malinowski describes them in [10]. 2 One qualification is in order, namely, that the critique emphasizes the semantic interpretations.…”

Section: Tableau Calculus For Weak Kleene Logic With Restricted Quant...mentioning

confidence: 99%

Tableaux and Restricted Quantification for Systems Related to Weak Kleene Logic

Ferguson

2021

Lecture Notes in Computer Science

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“…This explains why scholars working on transparent theories of truth might be interested in transparent theories of truth built using functionally complete logics. Now, in order to get functionally complete extensions of the aforementioned four-valued infectious logics, we will follow Post's technique to obtain functionally complete n-valued logics, as presented by Malinowski in [47,[547][548]. 34 For the special case of four-valued logics counting with the values…”

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Theories of truth based on four-valued infectious logics

Ré

Pailós

Szmuc

2018

Logic Journal of the IGPL

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Infectious logics are systems which have a truth-value that is assigned to a compound formula whenever it is assigned to one of its components. This paper studies four-valued infectious logics as the basis of transparent theories of truth. This take is motivated (i) as a way to treat different pathological sentences (like the Liar and the Truth-Teller) differently, namely, by allowing some of them to be truth-value gluts and some others to be truthvalue gaps, and (ii) as a way to treat the semantic pathology suffered by at least some of these sentences as infectious. This leads us to consider four distinct four-valued logics: one where truth-value gaps are infectious, but gluts are not; one where truth-value gluts are infectious, but gaps are not; and two logics where both gluts and gaps are infectious, in some sense. Additionally, we focus on the proof-theory of these systems, by offering a discussion of two related topics. On the one hand, we prove some limitations regarding the possibility of providing standard Gentzen sequent calculi for these systems, by dualizing and extending some recent results for infectious logics. On the other hand, we provide sound and complete four-sided sequent calculi, arguing that the most important technical and philosophical features taken into account to usually prefer standard calculi are, indeed, enjoyed by the four-sided systems.

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Many‐Valued Logic

Cited by 9 publications

References 25 publications

Secrecy, Content, and Quantification

Secrecy, Content, and Quantification

Tableaux and Restricted Quantification for Systems Related to Weak Kleene Logic

Theories of truth based on four-valued infectious logics

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