A Cut-Free Sequent Calculus for Defeasible Erotetic Inferences

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

Authors
Jared A. Millson
California State University, Bakersfield
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.
Keywords Nonclassical Logics  Erotetic Logic  Defeasible Reasoning  Sequent Calculus  Inferentialism
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Reprint years 2018, 2019
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DOI 10.1007/s11225-018-9839-z
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References found in this work BETA

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.
Socratic Proofs.Andrzej Wiśniewski - 2004 - Journal of Philosophical Logic 33 (3):299-326.

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Citations of this work BETA

A Logic for Best Explanations.Jared Millson & Christian Straßer - 2019 - Journal of Applied Non-Classical Logics 29 (2):184-231.

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