The study of defeasible reasoning unites epistemologists with those working in AI, in part, because both are interested in epistemic rationality. While it is traditionally thought to govern the formation and (with)holding of beliefs, epistemic rationality may also apply to the interrogative attitudes associated with our core epistemic practice of inquiry, such as wondering, investigating, and curiosity. Since generally intelligent systems should be capable of rational inquiry, AI researchers have a natural interest in the norms that govern interrogative attitudes. Following (...) its recent coinage, we use the term ``zetetic'' to refer to the properties and norms associated with the capacity to inquire. In this paper, we argue that zetetic norms can be modeled via defeasible inferences to and from questions---a.k.a erotetic inferences---in a manner similar to the way norms of epistemic rationality are represented by defeasible inference rules. We offer a sequent calculus that accommodates the unique features of ``erotetic defeat" and that exhibits the computational properties needed to inform the design of zetetic agents. The calculus presented here is an improved version of the one presented in Millson (2019), extended to cover a new class of defeasible erotetic inferences. (shrink)

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. (shrink)

This paper answers the philosophical contentions defended in Horsten and Welch . It contains a description of the standard format of adaptive logics, analyses the notion of dynamic proof required by those logics, discusses the means to turn such proofs into demonstrations, and argues that, notwithstanding their formal complexity, adaptive logics are important because they explicate an abundance of reasoning forms that occur frequently, both in scientific contexts and in common sense contexts.

For Tarski logics, there are simple criteria that enable one to conclude that two premise sets are equivalent. We shall show that the very same criteria hold for adaptive logics, which is a major advantage in comparison to other approaches to defeasible reasoning forms. A related property of Tarski logics is that the extensions of equivalent premise sets with the same set of formulas are equivalent premise sets. This does not hold for adaptive logics. However a very similar criterion does. (...) We also shall show that every monotonic logic weaker than an adaptive logic is weaker than the lower limit logic of the adaptive logic or identical to it. This highlights the role of the lower limit for settling the adaptive equivalence of extensions of equivalent premise sets. (shrink)

By and large, Inferential Erotetic Logic (IEL, for short) is an approach to the logic of questions which puts in the centre of attention inferential aspects of questioning. IEL is not an enterprise of the last few years only. The idea originates from the late 1980s. It evolved through time. Initially, the stress was put on the phenomenon of question raising. This changed gradually, as some forms of reasoning that involve questions have appeared to be analyzable by means of the (...) conceptual apparatus developed. In this essay I present the basics of IEL and comment on them. Most, though not all, of the ideas discussed here have been scattered across my earlier publications. The invitation from the organizers of the Asking and Answering workshop (Greifswald, September 2020) resulted in an attempt of presenting the themes of IEL in a concise but, as I hope, also comprehensible way. (shrink)