Strengthened Conditionals

Raidl, Éric

doi:10.1007/978-981-15-7134-3_11

Cited by 6 publications

(18 citation statements)

References 11 publications

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“…For (ii), one has to consider Definition 6.2.8(b), according to which for every v such that Priest's notion of validity is easily seen to be equivalent to that for the S5-based logic of super strict implication (analogously to what happens in standard modal logics, an accessibility relation that is an equivalence relation is equivalent to a universal accessibility relation). Formally we have the following result: We find this result interesting since it entails that the logics of SSI are connexive logics having the same set of S5-validities of Priest's one, that are obtained without having to tamper with the Tarskian notion of consequence relation nor with the classical explosion model of negation [19]. Moreover, this entails that in Section 4 we have introduced a cut-free sequent calculus that characterizes validity in Priest's formal semantics.…”

Section: Soundnessmentioning

confidence: 85%

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Super-Strict Implications

Gherardi

Orlandelli

2021

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This paper introduces the logics of super-strict implications, where a super-strict implication is a strengthening of C.I. Lewis' strict implication that avoids not only the paradoxes of material implication but also those of strict implication. The semantics of super-strict implications is obtained by strengthening the (normal) relational semantics for strict implication. We consider all logics of super-strict implications that are based on relational frames for modal logics in the modal cube. it is shown that all logics of super-strict implications are connexive logics in that they validate Aristotle's Theses and (weak) Boethius's Theses. A proof-theoretic characterisation of logics of super-strict implications is given by means of G3-style labelled calculi, and it is proved that the structural rules of inference are admissible in these calculi. It is also shown that validity in the $$\mathsf{S5}$$-based logic of super-strict implications is equivalent to validity in G. Priest's negation-as-cancellation-based logic. Hence, we also give a cut-free calculus for Priest's logic.

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Section: Soundnessmentioning

confidence: 85%

“…Finally, another formal semantics for a connexive logic that is very similar to the one for SSI is the one adopted by G. Priest [16] to model the cancellation account of negation [19]. Section 7 will compare our proposal with Priest's one.…”

Section: Super-strict Implications and Related Workmentioning

confidence: 99%

Super-Strict Implications

Gherardi

Orlandelli

2021

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“…The remaining two axioms CT and CSS, instead, express principles that do not hold in VC. 10 CT expresses the intuition illustrated in Section 1 that a concessive conditional implies its consequent. This axiom replaces MI, but it is stronger than MI: if β holds, then α ⊃ β holds, but not the other way round.…”

Section: The System CCmentioning

confidence: 83%

“…WDW is derivable from RW, but the reverse is not true. 8 Similarly TI is a weak replacement of CS, in that it is derivable from CS, but for the converse we need CM. This is why CS is not derivable in CC.…”

Section: The System CCmentioning

confidence: 99%

An Axiomatic System for Concessive Conditionals

2023

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According to the analysis of concessive conditionals suggested by Crupi and Iacona, a concessive conditional $$p{{\,\mathrm{\hookrightarrow }\,}}q$$ p ↪ q is adequately formalized as a conjunction of conditionals. This paper presents a sound and complete axiomatic system for concessive conditionals so understood. The soundness and completeness proofs that will be provided rely on a method that has been employed by Raidl, Iacona, and Crupi to prove the soundness and completeness of an analogous system for evidential conditionals.

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“…If we want to stay within the language L ⊲ then labelled calculi for these logics can be given by a mixture of the calculi in [6] with those in [21]. A characterisation in terms of axiomatic systems can be given by exploiting the techniques used in [18]. We believe this latter problem to be of particular interest given the results of Lemma 6, but we leave it for future research.…”

Section: Discussionmentioning

confidence: 99%