An Axiomatic System for Concessive Conditionals

Raidl, Éric; Iacona, Andrea; Crupi, Vincenzo

doi:10.1007/s11225-022-10034-1

Cited by 3 publications

(8 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This connective has been investigated semantically [4] (termed strong super-strict implication) and axiomatically [27] (termed implicative conditional ). 25 There are some interesting similarities, as well as differences. Both connectives invalidate the paradoxes of strict implication-Antilogical Antecedent (AA) and Tautological Consequent (TC).…”

Section: Decidabilitymentioning

confidence: 99%

“…By Lemma 15, T* and MP. This Lemma was also used in [23][24][25] and can be obtained directly when LLE and RW are unrestricted in the logic. It is because these principles are restricted here, that we needed to pass through first proving that any formula is strictly equivalent to its twin.…”

Section: Thus By and And Rrw Again We Get ( (A ⊃ B) ∧ A ≡ (A ⊃ B) •• ...mentioning

confidence: 99%

“…In this paper we introduce an axiomatic system for the companion super-strict implication logic ST2 of all formulas in the language L that are valid in reflexive non-normal relational models (now used to interpret ). For the completeness results, we rely on the fact that , , and are expressible in terms of and vice-versa: this allows us to use the method of translation and backtranslation developed and used by one of the authors to axiomatise many different conditional logics [23][24][25]. That is, we prove the Soundness Theorem of S2 with respect to the class of reflexive non-normal relational models by simulating the system ST2 in the system S2.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Proof Systems for Super- Strict Implication

2023

View full text Add to dashboard Cite

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.

show abstract

Section: Decidabilitymentioning

confidence: 99%

Section: Thus By and And Rrw Again We Get ( (A ⊃ B) ∧ A ≡ (A ⊃ B) •• ...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Proof Systems for Super- Strict Implication

2023

View full text Add to dashboard Cite

show abstract

“…For example, Conjunctive Sufficiency fails. 6 Other strengthenings of the variably strict conditional have been suggested and investigated [11,35,55,57,67,68,71,72].…”

Section: Introductionmentioning

confidence: 99%

“…11 Sentences with even if that do not entail that the consequent is true should not be considered as concessive, in the sense defined above, but implicative, in spite of the presence of even [9,24]. For a recent axiomatization of concessive conditionals, see [61].…”

Section: Introductionmentioning

confidence: 99%

The Implicative Conditional

Raidl,

Gomes

2023

J Philos Logic

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Difference-Making Conditionals and Connexivity

Rott

2023

Stud Logica

View full text Add to dashboard Cite

Today there is a wealth of fascinating studies of connexive logical systems. But sometimes it looks as if connexive logic is still in search of a convincing interpretation that explains in intuitive terms why the connexive principles should be valid. In this paper I argue that difference-making conditionals as presented in Rott (Review of Symbolic Logic 15, 2022) offer one principled way of interpreting connexive principles. From a philosophical point of view, the idea of difference-making demands full, unrestricted connexivity, because neither logical truths nor contradictions or other absurdities can ever ‘make a difference’ (i.e., be relevantly connected) to anything. However, difference-making conditionals have so far been only partially connexive. I show how the existing analysis of difference-making conditionals can be reshaped to obtain full connexivity. The classical AGM belief revision model is replaced by a conceivability-limited revision model that serves as the semantic base for the analysis. The key point of the latter is that the agent should never accept any absurdities.

show abstract

An Axiomatic System for Concessive Conditionals

Cited by 3 publications

References 10 publications

Proof Systems for Super- Strict Implication

Proof Systems for Super- Strict Implication

The Implicative Conditional

Difference-Making Conditionals and Connexivity

Contact Info

Product

Resources

About