A Cut-Free Sequent Calculus for Defeasible Erotetic Inferences

Studia Logica (6):1-34 (2019)
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Abstract

In recent years, the e ffort 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 regular erotetic implication. While an attempt 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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Jared A. Millson
Rhodes College

Citations of this work

Inquiring Attitudes and Erotetic Logic: Norms of Restriction and Expansion.Dennis Whitcomb & Jared Millson - forthcoming - Journal of the American Philosophical Association:1-23.
A Defeasible Calculus for Zetetic Agents.Jared A. Millson - 2021 - Logic and Logical Philosophy 30 (1):3-37.
Calculizing classical inferential erotetic logic.Moritz Cordes - 2021 - Review of Symbolic Logic 14 (4):1066-1087.
A Logic for Best Explanations.Jared Millson & Christian Straßer - 2019 - Journal of Applied Non-Classical Logics 29 (2):184-231.
An Essay on Inferential Erotetic Logic.Andrzej Wiśniewski - 2021 - In Moritz Cordes (ed.), Asking and Answering: Rivalling Approaches to Interrogative Methods. Tübingen: Narr Francke Attempto. pp. 105–138.

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References found in this work

Syntax and semantics of questions.Lauri Karttunen - 1977 - Linguistics and Philosophy 1 (1):3--44.
Questions.C. L. Hamblin - 1958 - Australasian Journal of Philosophy 36 (3):159 – 168.

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