Inferential erotetic logic and inquisitive semantics give accounts of questions and model various aspects of questioning. In this paper we concentrate upon connections between inquisitiveness, being the core concept of INQ, and question raising, characterized in IEL by means of the concepts of question evocation and erotetic implication. We consider the basic system InqB of INQ, remain at the propositional level and show, inter alia, that: a disjunction of all the direct answers to an evoked question (...) is always inquisitive; a formula is inquisitive if, and only if it evokes a yes–no question whose affirmative answer expresses a possibility for the formula; inquisitive formulas evoke questions whose direct answers express all the possibilities for the formulas, and each question erotetically implies a question whose direct answers express the possibilities for the direct answers to the implying question. (shrink)

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". (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)

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.

A fascinating recent turn in epistemology focuses on inquiring attitudes like wondering and being curious. Many have argued that these attitudes are governed by norms similar to those that govern our doxastic attitudes. Yet, to date, this work has only considered norms that might *prohibit* having certain inquiring attitudes (``norms of restriction''), while ignoring those that might *require* having them (``norms of expansion''). We aim to address that omission by offering a framework that generates norms of expansion for inquiring attitudes. (...) The framework draws on inferential erotetic logic, which we explain and augment with some theorems. We explore several of the norms that it yields - some sympathetically, others unsympathetically. (shrink)

A fascinating recent turn in epistemology focuses on inquiring attitudes like wondering and being curious. Many have argued that these attitudes are governed by norms similar to those that govern our doxastic attitudes. Yet, to date, this work has only considered norms that might prohibit having certain inquiring attitudes (“norms of restriction”), while ignoring those that might require having them (“norms of expansion”). We aim to address that omission by offering a framework that generates norms of expansion for inquiring attitudes. (...) The framework draws on inferential erotetic logic, which we explain and augment with some theorems. We explore several of the norms that it yields—some sympathetically, others unsympathetically. (shrink)

An erotetic calculus for a given logic constitutes a sequent-style proof-theoretical formalization of the logic grounded in Inferential Erotetic Logic ). In this paper, a new erotetic calculus for Classical Propositional Logic ), dual with respect to the existing ones, is given. We modify the calculus to obtain complete proof systems for the propositional part of paraconsistent logic CLuN and its extensions CLuNs and mbC. The method is based on dual resolution. (...) Moreover, the resolution rule is non-clausal. According to the authors knowledge, this is the first account of resolution for mbC. Last but not least, as the method is grounded in IEL, it constitutes an important tool for the so-called question-processing. (shrink)

Our aim is to model the behaviour of a cognitive agent trying to solve a complex problem by dividing it into sub-problems, but failing to solve some of these sub-problems. We use the powerful framework of erotetic search scenarios combined with Kleene’s strong three-valued logic. ESS, defined on the grounds of Inferential Erotetic Logic, has appeared to be a useful logical tool for modelling cognitive goal-directed processes. Using the logical tools of ESS and the three-valued (...) logic, we will show how an agent could solve the initial problem despite the fact that the sub-problems remain unsolved. Thus our model not only indicates missing information but also specifies the contexts in which the problem-solving process may end in success despite the lack of information. We will also show that this model of problem solving may find use in an analysis of natural language dialogues. (shrink)

The aim of this paper is to introduce erotetic search scenarios known from Inferential Erotetic Logic by using the framework of epistemic erotetic logic. The key notions used in this system are those of askability and epistemic erotetic implication. Scenarios are supposed to represent all rational strategies of an agent solving the problem posed by the initial question where the interaction with an external information source is seen as a series of updates of (...) the agent’s knowledge. (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 (...) class='Hi'>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)

The dependency relation between questions is discussed in terms of compliance (developed within inquisitive semantics – INQ) and erotetic implication (developed within Inferential Erotetic Logic – IEL). I show that INQ approach to questions’ dependency is more narrow and strict than the one offered by IEL.

My aim in this paper is to use a formal approach to the Turing test. This approach is based on a tool developed within Inferential Erotetic Logic, so called erotetic search scenarios. First, I reconstruct the setting of the Turing test proposed by A.M. Turing. On this basis, I build a model of the test using erotetic search scenarios framework. I use the model to investigate one of the most interesting issues of the TT setting (...) – the interrogator’s perspective and role in the test. (shrink)

This book is a study in the logic of questions (sometimes called erotetic logic). The central topics in erotetic logic have been the structure of questions and the question-answer relationship. This book doesn't neglect these problems, but much of it is focussed on other issues. The main subject is the logical analysis of certain relations between questions and the contexts of their appearance. And our aim is to elaborate the conceptual apparatus of the inferential (...) approach to the logic of questions. Questions are asked for many reasons and for different purposes. Yet, before a question is asked or posed, a questioner must arrive at it. In many cases arriving at a question resembles coming to a conclusion: there are some premises involved and some inferential thought processes take place. If we agree that a conclusion need not be "conclusive", we may say that sometimes questions can play the role of conclusions. But questions can also perform the role of premises: we often pass from some "initial" question to another question. In other words, there are inferential thought processes - we shall call them erotetic inferences - in which questions play the roles of conclusions or conclusions and premises. The inferential approach to the logic of questions focusses its attention on the analysis of erotetic inferences. This book consists of eight chapters. (shrink)

In earlier publications of the first author it was shown that intentional explanation of actions, functional explanation of biological traits and causal explanation of abnormal events share a common structure. They are called explanation by specification (of a goal, a biological function, an abnormal causal factor, respectively) as opposed to explanation by subsumption under a law. Explanation by specification is guided by a schematic train of thought, of which the argumentative steps not concerning questions were already shown to be logically (...) valid (elementary) arguments.Independently, the second author developed a new, inferential approach to erotetic logic, the logic of questions. In this approach arguments resulting in questions, with declarative sentences and/or other questions as premises, are analyzed, and validity of such arguments is defined. (shrink)

The concept of cooperative question-responses as an extension of cooperative behaviours used by interfaces for databases and information systems is proposed. A procedure to generate question-responses based on question dependency and erotetic search scenarios is presented. The procedure is implemented in Prolog.

In this paper, we consider how an agent may manage a questioning agenda in a situation where multiple information sources are available. We work within the framework of formal dialogue systems with the underpinning of Inferential Erotetic Logic. Firstly, we present the formal dialogue system DL(IEL)mult for managing multi-agent information retrieval. Then, we extend the proposed system so that it is capable of representing group and individual levels for the question decomposition process. We also propose two measures (...) for evaluating information sources: their cooperativeness and success levels; next, we analyse how the choice of agents may influence the way in which a solution for a given problem is reached. (shrink)

Drawing inspiration from the notion of evocation employed in inferential erotetic logic, we defend an ‘evoked questions norm’ on inquiring attitudes. According to this norm, it is rational to have an inquiring attitude concerning a question only if that question is evoked by your background information. We offer two arguments for this norm. First, we develop an argument from convergence. Insights from several independent literatures (20th-century ordinary-language philosophy, inferential erotetic logic, inquisitive epistemic logic, (...) and contemporary zetetic epistemology) all converge on the evoked questions norm. Second, we show that suitably interpreted, the evoked questions norm correctly predicts several underappreciated kinds of bad questions. It does this, in part, by recovering versions of previously defended ignorance and knowledge norms. Some of those bad questions cannot be predicted by either norm singly, but only when corporately taken to reflect a common normative category. We identify this category as evocation. (shrink)

"The importance of questions is beyond doubt. But the degree of attention paid to them in logic and linguistics is still less than they deserve." What is a question? How to represent questions in formal languages? How to model reasoning in which questions are involved? Can we prove anything by means of pure questioning? How to model goal-directed problem solving? These are the main issues of Andrzej Wi niewski's "Questions, Inferences, and Scenarios." This book offers a state-of-the-art exposition of (...) Inferential Erotetic Logic, that is, an approach to the logic of questions focused on inferences which lead to questions as conclusions. Wi niewski characterizes semantic relations which determine validity of these inferences within the framework of Minimal Erotetic Semantics, applicable to a wide range of formal languages. He elaborates in detail the concept of erotetic search scenario, a tool for modelling problem solving. Moreover, the author presents some applications of Inferential Erotetic Logic in proof theory. Andrzej Wi niewski is one of the most prominent contemporary researchers in the logic of questions. Currently, he is a full professor at the Department of Logic and Cognitive Science, Institute of Psychology, Adam Mickiewicz University in Pozna, Poland. (shrink)

Our aim is to express in exact terms the old idea of solving problems by pure questioning. We consider the problem of derivability: "Is A derivable from Δ by classical propositional logic?". We develop a calculus of questions E*; a proof (called a Socratic proof) is a sequence of questions ending with a question whose affirmative answer is, in a sense, evident. The calculus is sound and complete with respect to classical propositional logic. A Socratic proof in E* (...) can be transformed into a Gentzen-style proof in some sequent calculi. Next we develop a calculus of questions E**; Socratic proofs in E** can be transformed into analytic tableaux. We show that Socratic proofs can be grounded in Inferential Erotetic Logic. After a slight modification, the analyzed systems can also be viewed as hypersequent calculi. (shrink)

This paper develops a new proof method for two propositional paraconsistent logics: the propositional part of Batens' weak paraconsistent logic CLuN and Schütte's maximally paraconsistent logic Φv. Proofs are de.ned as certain sequences of questions. The method is grounded in Inferential Erotetic Logic.

People sometimes argue for questions, as can be verified by a Web search using as search terms phrases consisting of a conclusion indicator and an interrogative particle. These arguments provide a reason for asking the question and thus try to establish that it needs to be answered. Typically, they do so either in order to motivate interest in discovering the answer or in order to challenge addressees or a third party to explain their behaviour. The “inferential erotetic (...) class='Hi'>logic” of the Polish logician Andrzej Wiśniewski provides a basis for evaluating the inferences in such arguments. For an inference from one or more statements to a question to be valid, the statements and the context must entail that the question has a true answer without entailing that any particular answer is true. Further, there must be a point to asking the question, such as the addressees’ ignorance of the correct answer to it; this requirement may be a pragmatic rather than a semantic constraint. Wiśniewski’s logic also covers inferences from questions to questions, but humans rarely articulate such inferences; this part of his logic is applicable to problem solving and proof theory rather than to arguments for questions. (shrink)

It’s commonly thought that, in conversation, speakers accept and reject propositions that have been asserted by others. Do speakers accept and reject questions as well? Intuitively, it seems that they do. But what does it mean to accept or reject a question? What is the relationship between these acts and those of asking and answering questions? Are there clear and distinct classes of reasons that speakers have for acceptance and rejection of questions? This chapter seeks to address these issues. Beyond (...) their intrinsic interest to those working on the nature of questions, solutions to these problems may aid the extension of inferentialist approaches to logic and language. Inferentialists who think that inferences should be conceived in terms of the norms we are subject to in virtue of both the sentences we accept or assert as well as those we reject or deny are known as bilateralists. A coherent account of accepting and rejecting questions raises the prospects for a bilateralism that interprets question-involving or erotetic inferences according to these additional primitives. While a full-blown bilateralism for erotetic inferences and ultimately for question-forming operators themselves far exceeds this chapter’s scope, the work presented here does sketch the first steps in that direction. (shrink)

The concept of search scenario is explicated in terms of erotetic logic, i.e., the logic of questions. Different kinds of erotetic search scenarios are characterized. The basic logical properties of erotetic search scenarios are analyzed.

This paper argues for the idea that the logic of questions should focus its attention on the analysis of arguments in which questions play the role of conclusions. The relevant concepts of validity are discussed and the concept of the logic of questions of a semantically interpreted formalized language is introduced.

The concept of erotetic argument is introduced. Two relations between sets of declarative sentences and questions are analysed; and two classes of erotetic arguments are characterized.

happens, how it happens, and why it happens. Our assumption ought to be that this is as true in education as it is in atomic physics. But this leaves many other questions to answer. The crucial ones: What kind of science is proper or appropriate to education? How does it differ from physics? What is wrong with the prevai1~ ing, virtually unopposed research tradition in education? What could or should be done to replace it with a more adequate tradi tion? (...) What concepts are necessary to describe and explain what we find there? It is in this realm that we find ourselves. Where to start? One place - our place, needless to say - is with one limited but central concept in education, teaching. A long philosophical tradition concerned with the nature of teaching goes back (along with everything else) to Plato, divulging most recent ly in the work of such philosophers as B. O. Smith, Scheffler, Hirst, Komisar, Green, McClellan, Soltis, Kerr, Fenstermacher, et al. An empirical tradition runs parallelto the philosophers -it has its most notable modern proponents in Gage, the Soars, Berliner, Rosen shine, but its roots can be traced to the Sophists. These two tradi tions have been at loggerheads over the centuries. (shrink)

We outline a pragmatic-normative understanding of logic as a discipline that is completely anchored in the sphere of action, rules, means and ends: We characterize inferring as a speech act which is in need of regulation and we connect inferential rules with consequence relations. Furthermore, we present a scenario which illustrates how one actually assesses or can in principle assess the quality of logical rules with respect to justificatory questions. Finally, we speculate on the origin of logical rules (...) as a means of supporting our practice of inferring. (shrink)

Although there is a prima facie strong case for a close connection between the meaning and inferential role of certain expressions, this connection seems seriously threatened by the semantic and logical paradoxes which rely on these inferential roles. Some philosophers have drawn radical conclusions from the paradoxes for the theory of meaning in general, and for which sentences in our language are true. I criticize these overreactions, and instead propose to distinguish two conceptions of inferential role. This (...) distinction is closely tied to two conceptions of deductive logic, and it is the key, I argue, for understanding first the connection between meaning and inferential role, and second what the paradoxes show more generally. (shrink)

This book presents a unified theory of the human capacity for reasoning and decision-making. The erotetic theory accounts for a diverse range of empirically documented fallacies and framing effects and shows how the same mental processes that yield fallacies can yield what logicians call first-order validity and probabilistic coherence in reasoning, as well as rational decision-making as conceived by economists. The central idea is that our minds naturally aim at resolving issues, and if we are sufficiently inquisitive in the (...) process, we can avoid mistakes. The erotetic theory holds that both the successes and the failures of reason are due to this aim. Rationality is secured if we reach what will be called erotetic equilibrium. (shrink)

There are inferences from a sentence or a set of sentences to a question. The relation between the premises and conclusions of such inferences is sometimes called arising.

It is hard to imagine our life without questions. They facilitate orientation in our environment, enable interpersonal communication and make the acquisition of knowledge possible. Questions direct scientific research, are used as research tools and are an important medium of transferring knowledge in teaching. The book is intended as a par excellence philosophical monograph of the theory of questions, presenting the most important erotetic problems, their general background and selected practical applications. It is prepared in all fairness to results (...) acquired in the framework of the logical theories of questions but goes beyond this framework. (shrink)

Unconscious logical inference seems to rely on the syntactic structures of mental representations (Quilty-Dunn & Mandelbaum 2018). Other transitions, such as transitions using iconic representations and associative transitions, are harder to assimilate to syntax-based theories. Here we tackle these difficulties head on in the interest of a fuller taxonomy of mental transitions. Along the way we discuss how icons can be compositional without having constituent structure, and expand and defend the “symmetry condition” on Associationism (the idea that associative links and (...) transitions are perfectly symmetric). In the end, we show how a BIT (“bare inferential transition”) theory can cohabitate with these other non-inferential mental transitions. (shrink)

We seek a better understanding of why an inferential semantics devised by Tor Sandqvist yields full classical logic, by providing and analysing a direct proof via a suitable maximality construction.

ABSTRACT My aim in this paper is to present a pluralist thesis about the inferential role of logical constants, which embraces classical, relevant, linear and ordered logic. That is, I defend that a logical constant c has more than one correct inferential role. The thesis depends on a particular interpretation of substructural logics' vocabulary, according to which classical logic captures the literal meaning of logical constants and substructural logics encode a pragmatically enriched sense of those connectives. (...) The paper is divided into four parts: first, I introduce the motivation for the pluralist thesis of the paper; second I introduce the calculus for the different logics endorsed in the pluralist thesis; third, I motivate how the different behaviors of the logical vocabulary of these logics can be pragmatically interpreted, and fourth, I motivate how the different inferential roles that each substructural logic attribute to logical constants can coexist, and how we should reason with a logical constant c given this plurality. (shrink)

Three semantic relations are analyzed: the relation of implication of a question by a question and a set of declarative sentences, the relation of implication of a question by a question, and the relation of strong implication of a question by a question and a set of declarative sentences. The connections between these concepts and the concepts of relative soundness, partial answerhood and presupposition are examined. The principal results are theorems about, to speak generally, epistemic reducibility of well-posed questions to (...) sequences of implied yes-no questions. (shrink)

Deflationists about truth hold that the function of the truth predicate is to enable us to make certain assertions we could not otherwise make. Pragmatists claim that the utility of negation lies in its role in registering incompatibility. The pragmatist insight about negation has been successfully incorporated into bilateral theories of content, which take the meaning of negation to be inferentially explained in terms of the speech act of rejection. We implement the deflationist insight in a bilateral theory by taking (...) the meaning of the truth predicate to be explained by its inferential relation to assertion. We combine this account of the meaning of the truth predicate with a new diagnosis of the Liar Paradox: its derivation requires the truth rules to preserve evidence, but these rules only preserve commitment. The result is a novel inferential deflationist theory of truth, which solves the Liar Paradox in a principled manner. We end by showing that our theory and simple extensions thereof have the resources to axiomatize the internal logic of several supervaluational hierarchies, including Cantini’s. This solves open problems of Halbach (2011) and Horsten (2011). (shrink)

We develop a novel solution to the negation version of the Frege-Geach problem by taking up recent insights from the bilateral programme in logic. Bilateralists derive the meaning of negation from a primitive *B-type* inconsistency involving the attitudes of assent and dissent. Some may demand an explanation of this inconsistency in simpler terms, but we argue that bilateralism’s assumptions are no less explanatory than those of *A-type* semantics that only require a single primitive attitude, but must stipulate inconsistency elsewhere. (...) Based on these insights, we develop a version of B-type expressivism called *inferential expressivism*. This is a novel semantic framework that characterises meanings by inferential roles that define which *attitudes* one can *infer* from the use of terms. We apply this framework to normative vocabulary, thereby solving the Frege-Geach problem generally and comprehensively. Our account moreover includes a semantics for epistemic modals, thereby also explaining normative terms under epistemic modals. (shrink)

Many conditionals seem to convey the existence of a link between their antecedent and consequent. We draw on a recently proposed typology of conditionals to argue for an old philosophical idea according to which the link is inferential in nature. We show that the proposal has explanatory force by presenting empirical results on the evidential meaning of certain English and Dutch modal expressions.

Starting from the notions of q-entailment and p-entailment, a two-dimensional notion of entailment is developed with respect to certain generalized q-matrices referred to as B-matrices. After showing that every purely monotonic singleconclusion consequence relation is characterized by a class of B-matrices with respect to q-entailment as well as with respect to p-entailment, it is observed that, as a result, every such consequence relation has an inferentially four-valued characterization. Next, the canonical form of B-entailment, a two-dimensional multiple-conclusion notion of entailment based (...) on B-matrices, is introduced, providing a uniform framework for studying several different notions of entailment based on designation, antidesignation, and their complements. Moreover, the two-dimensional concept of a B-consequence relation is defined, and an abstract characterization of such relations by classes of B-matrices is obtained. Finally, a contribution to the study of inferential many-valuedness is made by generalizing Suszko’s Thesis and the corresponding reduction to show that any B-consequence relation is, in general, inferentially four-valued. (shrink)

Inferential communities are communities using specific substantial argumentative schemes. The religious or scientific communities are examples. I discuss the status of the mathematical community as it appears through the position held by the French mathematician Henri Poincaré during his famous ar-guments with Russell, Hilbert, Peano and Cantor. The paper focuses on the status of complete induction and how logic and psychology shape the community of mathematicians and the teaching of mathematics.

Michael Dummett has proposed an influential analysis of the meaning of ethnic and racial slurs based on inferential rules. Timothy Williamson, however, finds the analysis problematic. It does not seem to explain how slurs are actually used. Williamson’s challenge for the inferentialist account of slurs has not gone unnoticed. In this article, I first discuss the debate between the inferentialists and Williamson. I argue that the inferentialist responses concentrate on the wrong issue and the real issue in Williamson’s challenge (...) is left untouched. I go on to specify his challenge and offer a solution to the challenge. The solution rests on the idea that the inferential rules for slurs involve a generic component. (shrink)