Non-Normal Super-Strict Implications

Gherardi, Guido; Orlandelli, Eugenio

doi:10.4204/eptcs.358.1

Cited by 3 publications

(9 citation statements)

References 17 publications

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“…The logic of a conditional defined by this formula was also suggested by Priest [53, p. 145-6], and recently studied under the name of (weak) super-strict implication [15][16][17]. We could also call this conditional the possible-antecedent strict conditional.…”

Section: Introductionmentioning

confidence: 93%

“…In their discussions of conditionals, they often give examples that are overtly or covertly concessive. 16 It may be interesting to have a semantics that identifies what is common to all cases in which the linguistic structure If A, B is used (with or without the addition of words such as then, even, or still). Linguistic semanticists may go even further and try to indicate what is common in all uses of if, not only in 'If A, B' and related linguistic forms, but also in sentences containing to know if, to ask if, to wonder if, as if, etc.…”

Section: Introductionmentioning

confidence: 99%

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The Implicative Conditional

Raidl,

Gomes

2023

J Philos Logic

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This paper investigates the implicative conditional, a connective intended to describe the logical behavior of an empirically defined class of natural language conditionals, also named implicative conditionals, which excludes concessive and some other conditionals. The implicative conditional strengthens the strict conditional with the possibility of the antecedent and of the contradictory of the consequent. $${p\Rightarrow q}$$ p ⇒ q is thus defined as $${\lnot } \Diamond {(p \wedge \lnot q) \wedge } \Diamond {p \wedge } \Diamond {\lnot q}$$ ¬ ◊ ( p ∧ ¬ q ) ∧ ◊ p ∧ ◊ ¬ q . We explore the logical properties of this conditional in a reflexive normal Kripke semantics, provide an axiomatic system and prove it to be sound and complete for our semantics. The implicative conditional validates transitivity and contraposition, which we take to be integral parts of reasoning and communication. But it only validates restricted versions of strengthening the antecedent, right weakening, simplification, and rational monotonicity. Apparent counterexamples to some of these properties are explained as due to contextual factors. Finally, the implicative conditional avoids the paradoxes of material and strict implication, and validates some connexive principles such as Aristotle’s theses and weak Boethius’ thesis, as well as some highly entrenched principles of conditionals, such as conjunction of consequents, disjunction of antecedents, modus ponens, cautious monotonicity and cut.

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Section: Introductionmentioning

confidence: 93%

Section: Introductionmentioning

confidence: 99%

The Implicative Conditional

Raidl,

Gomes

2023

J Philos Logic

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“…Moreover, as shown in [4,5], both normal and non-normal logics for are Boethian logics: 3 is a non-symmetric implication validating both Aristotle's Thesis (AT) and weak Boethius' Thesis (wBT):…”

Section: Introductionmentioning

confidence: 95%

“…SSI is a refinement of C.I. Lewis' strict implication ( ) that has been studied in [4,5]. The idea behind SSI is to free strict implication from its paradoxes.…”

Section: Introductionmentioning

confidence: 99%

“…In previous work, logics for were studied mostly from a semantical perspective: [4] introduced relational semantics for normal logics of and [5] for some non-normal ones. The only proof systems introduced were labelled sequent calculi for normal logics of [4], but no proof system has been introduced yet for non-normal ones and no fully object-language axiomatisation of these logics, be it normal or non-normal has been provided.…”

Section: Introductionmentioning

confidence: 99%

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Proof Systems for Super- Strict Implication

2023

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This paper studies proof systems for the logics of super-strict implication $$\textsf{ST2}$$ ST 2 –$$\textsf{ST5}$$ ST 5 , which correspond to C.I. Lewis’ systems $$\textsf{S2}$$ S 2 –$$\textsf{S5}$$ S 5 freed of paradoxes of strict implication. First, Hilbert-style axiomatic systems are introduced and shown to be sound and complete by simulating $$\textsf{STn}$$ STn in $$\textsf{Sn}$$ Sn and backsimulating $$\textsf{Sn}$$ Sn in $$\textsf{STn}$$ STn , respectively (for $${\textsf{n}} =2, \ldots , 5$$ n = 2 , … , 5 ). Next, $$\textsf{G3}$$ G 3 -style labelled sequent calculi are investigated. It is shown that these calculi have the good structural properties that are distinctive of $$\textsf{G3}$$ G 3 -style calculi, that they are sound and complete, and it is shown that the proof search for $$\mathsf {G3.ST2}$$ G 3 . ST 2 is terminating and therefore the logic is decidable.

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Connexive Logic, Connexivity, and Connexivism: Remarks on Terminology

Wansing,

Omori

2023

Stud Logica

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Over the past ten years, the community researching connexive logics is rapidly growing and a number of papers have been published. However, when it comes to the terminology used in connexive logic, it seems to be not without problems. In this introduction, we aim at making a contribution towards both unifying and reducing the terminology. We hope that this can help making it easier to survey and access the field from outside the community of connexive logicians. Along the way, we will make clear the context to which the papers in this special issue on Frontiers of Connexive Logic belong and contribute.

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Non-Normal Super-Strict Implications

Cited by 3 publications

References 17 publications

The Implicative Conditional

The Implicative Conditional

Proof Systems for Super- Strict Implication

Connexive Logic, Connexivity, and Connexivism: Remarks on Terminology

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