An Axiomatic Account of Question Evocation: The Propositional Case

Wiśniewski, Andrzej

doi:10.3390/axioms5020014

Cited by 5 publications

(16 citation statements)

References 19 publications

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“…In this section all relevant definitions from IEL are summarized. As a general reference one may regard [24] or [25]. This and the next section do not include any substantial contributions on my part.…”

Section: Propositionalmentioning

confidence: 99%

“…2 In the latter part of the twentieth century more sophisticated approaches came to the fore. An incomplete list of the major approaches, excluding the more linguistically oriented ones, are: Kubi ński's system [13], whose original publication predates the better known categorical approach by Belnap and Steel [3], Wiśniewski's Inferential Erotetic Logic [24], Hintikka's Interrogative Model of Inquiry [11], and Ciardelli, Groenendijk, and Roelofsen's Inquisitive Semantics [6]. There is a lot to be said about each of these approaches and, indeed, about those that I omitted, too.…”

Section: §1 Introductionmentioning

confidence: 99%

“…However, Inferential Erotetic Logic (IEL) is of special interest when it comes to defining relations between questions and declarative expressions which can be considered to be inferential relations. 3 Large parts of the IEL program are outlined and developed in Andrzej Wiśniewski's 1995 book The Posing of Questions [24]. In this book the author provides a formalism to represent different kinds of questions.…”

Section: §1 Introductionmentioning

confidence: 99%

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Calculizing Classical Inferential Erotetic Logic

Cordes¹

2020

The Review of Symbolic Logic

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This paper contributes to the calculization of evocation and erotetic implication as defined by Inferential Erotetic Logic (IEL). There is a straightforward approach to calculizing (propositional) erotetic implication which cannot be applied to evocation. First-order evocation is proven to be uncalculizable, i.e. there is no proof system, say FOE, such that for all $X, Q$ : X evokes Q iff there is an FOE-proof for the evocation of Q by X. These results suggest a critique of the represented approaches to calculizing IEL. This critique is expanded into a programmatic reconsideration of the IEL-definitions of evocation and erotetic implication. From a different point of view these definitions should be seen as desiderata that may or may not play the role of a point of orientation when setting up “rules of asking.”

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Section: Propositionalmentioning

confidence: 99%

Section: §1 Introductionmentioning

confidence: 99%

Section: §1 Introductionmentioning

confidence: 99%

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Calculizing Classical Inferential Erotetic Logic

Cordes¹

2020

The Review of Symbolic Logic

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“…We also prove a cut-elimination theorem for the calculus (Section 4). We then demonstrate that the axioms and primitive rules that [25] provides for erotetic evocation are admissible in LK ? (Section 5).…”

Section: Erotetic Logic Proof Theory Sequent Calculus Defeasible Rmentioning

confidence: 99%

A Cut-Free Sequent Calculus for Defeasible Erotetic Inferences

Millson

2018

Stud Logica

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In recent years, the effort to formalize erotetic inferences-i.e., inferences to and from questions-has become a central concern for those working in erotetic logic. However, few have sought to formulate a proof theory for these inferences. To fill this lacuna, we construct a calculus for (classes of) sequents that are sound and complete for two species of erotetic inferences studied by Inferential Erotetic Logic (IEL): erotetic evocation and erotetic implication. While an effort has been made to axiomatize the former in a sequent system, there is currently no proof theory for the latter. Moreover, the extant axiomatization of erotetic evocation fails to capture its defeasible character and provides no rules for introducing or eliminating question-forming operators. In contrast, our calculus encodes defeasibility conditions on sequents and provides rules governing the introduction and elimination of erotetic formulas. We demonstrate that an elimination theorem holds for a version of the cut rule that applies to both declarative and erotetic formulas and that the rules for the axiomatic account of question evocation in IEL are admissible in our system.

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“…Recall that the role played in IEL by the concepts of question evocation and erotetic implication resembles that played by entailment in a logic of statements. Given the analogy, it seems worthwhile to build, at the proof-theoretic level, [16,21]), but there is no system for erotetic implication. The reduction theorems for erotetic implication presented above open a new perspective: in order to build a system for erotetic implication one may consider first-or even only-the conceptually (though not computationally) simpler case of pure e-implication.…”

Section: Summary and A Remarkmentioning

confidence: 99%

Deduction and Reduction Theorems for Inferential Erotetic Logic

Wiśniewski

2017

Stud Logica

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Abstract.The concepts of question evocation and erotetic implication play central role in Inferential Erotetic Logic. In this paper, deduction theorems for question evocation and erotetic implication are proven. Moreover, it is shown how question evocation by a finite non-empty set of declaratives can be reduced to question evocation by the empty set, and how erotetic implication based on a finite non-empty set of declaratives can be reduced to a relation between questions only.

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An Axiomatic Account of Question Evocation: The Propositional Case

Abstract: An axiomatic system for question evocation in Classical Propositional Logic is proposed. Soundness and completeness of the system are proven.

Cited by 5 publications

References 19 publications

Calculizing Classical Inferential Erotetic Logic

Calculizing Classical Inferential Erotetic Logic

A Cut-Free Sequent Calculus for Defeasible Erotetic Inferences

Deduction and Reduction Theorems for Inferential Erotetic Logic

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