Erotetic Logic

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)

According to the traditional view in the philosophy of logic facts of logic bear normative authority regarding how one ought to reason. Usually this is to mean that the relation of logical consequence between statements has some special relevance for how one’s beliefs should cohere. However, as I will argue in this article, this is just one way in which logic is normative for reasoning. For one thing, belief is not the only kind of mental state involved in reasoning. Besides (...) adopting and revising beliefs, rational agents pose and resolve questions. For another thing, the consequence relation of classical logic can be conservatively extended such that it includes logical relations between questions as well. Therefore, there is an argument to be made that not only the inference of new beliefs from extant beliefs but also the process of raising additional questions falls under the normative authority of logic. Accordingly, a nuanced account of the normativity of logic presents itself, which convincingly deals with problems such as clutter-avoidance and the paradox of the preface. (shrink)

Inquisitive first-order logic, InqBQ, is a system which extends classical first-order logic with formulas expressing questions. From a mathematical point of view, formulas in this logic express properties of sets of relational structures. This paper makes two contributions to the study of this logic. First, we describe an Ehrenfeucht–Fraïssé game for InqBQ and show that it characterizes the distinguishing power of the logic. Second, we use the game to study cardinality quantifiers in the inquisitive setting. That is, we study what (...) statements and questions can be expressed in InqBQ about the number of individuals satisfying a given predicate. As special cases, we show that several variants of the question how many individuals satisfy α(x) are not expressible in InqBQ, both in the general case and in restriction to finite models. (shrink)

In this thesis, I develop and investigate various novel semantic frameworks for deontic logic. Deontic logic concerns the logical aspects of normative reasoning. In particular, it concerns reasoning about what is required, allowed and forbidden. I focus on two main issues: free-choice reasoning and the role of norms in deontic logic. -/- Free-choice reasoning concerns permissions and obligations that offer choices between different actions. Such permissions and obligations are typically expressed by a disjunctive clause in the scope of a deontic (...) operator. For instance, the sentence "Jane may take an apple or a pear" intuitively offers Jane a choice between two permitted courses of action: she may take an apple, and she may take a pear. In the first part of the thesis, I develop semantic frameworks for deontic logic that account for free-choice reasoning. I show that the resulting logics avoid problems that arise for other logical accounts of free-choice reasoning. The main technical contributions are completeness results for axiomatizations of the different logics. -/- Semantic frameworks for deontic logic typically only talk about norms implicitly. In the second part of the thesis, I clarify the role of norms in deontic logic. I develop a formal model of normative systems where norms are represented explicitly. The model takes into account both the hierarchical structure of normative systems, and the function of norms to regulate agent behavior. I show how the model can be used to clarify issues in the study of normative systems. I also develop a norm-based semantics for deontic action logic based on the model. (shrink)

Tomis Kapitan’s work on Peirce’s conception of abduction was instrumental for our coming to see how Peircean abduction both relates to and is importantly different from inference to the best explanation (IBE). However, he ultimately concluded that Peirce’s conception of abduction was a muddle. Despite the deeply problematic nature of Peirce’s theory of abduction in these respects, Kapitan’s work on Peircean abduction offers insight into the nature of abductive inquiry that is importantly relevant to the task of making sense of (...) explanatory inquiry in the sciences in general. The view developed here stems from his work and involves disambiguating three forms of inference involved in Peircean abduction in terms of Reichenbach’s and Laudan’s context models of inquiry. Importantly, this includes understanding that abduction involves the context of pursuit. (shrink)

Since Kripke, philosophers have distinguished a priori true statements from necessarily true ones. A statement is a priori true if its truth can be established before experience, and necessarily true if it could not have been false according to logical or metaphysical laws. This distinction can be captured formally using two-dimensional semantics. There is a natural way to extend the notions of apriority and necessity so they can also apply to questions. Questions either can or cannot be resolved before experience, (...) and either are or are not about necessary facts. Classical two-dimensionalism has no account of question meanings, so it has to be combined with a framework for question semantics in order to capture these observations. It is shown in [14] how two-dimensional semantics can be combined with inquisitive semantics, in which questions are analyzed in terms of information. The present paper investigates the logic of two-dimensional inquisitive semantics, and provides a complete proof system. (shrink)

The aim in this paper is to define an Abductive Question-Answer System for the minimal logic of formal inconsistency \. As a proof-theoretical basis we employ the Socratic proofs method. The system produces abductive hypotheses; these are answers to abductive questions concerning derivability of formulas from sets of formulas. We integrated the generation of and the evaluation of hypotheses via constraints of consistency and significance being imposed on the system rules.

In this paper I discuss the role that question contents should play in an overall account of language, thought, and communication. Based on these considerations, I argue against the Fregean view that analyzes questions as distinguished only at the level of force. Questions, I argue, are associated with specific semantic objects, which play a distinctive role in thought and in compositional semantics, stand in logical relations to one another, and can act as contents of multiple speech acts. In the second (...) part of the paper, I present a recent approach to the semantics of questions – inquisitive semantics – and discuss how the notion of question content it provides can be fruitfully put to use in the different roles we identified. (shrink)

Inquisitive modal logic, InqML, is a generalisation of standard Kripke-style modal logic. In its epistemic incarnation, it extends standard epistemic logic to capture not just the information that agents have, but also the questions that they are interested in. Technically, InqML fits within the family of logics based on team semantics. From a model-theoretic perspective, it takes us a step in the direction of monadic second-order logic, as inquisitive modal operators involve quantification over sets of worlds. We introduce and investigate (...) the natural notion of bisimulation equivalence in the setting of InqML. We compare the expressiveness of InqML and first-order logic in the context of relational structures with two sorts, one for worlds and one for information states, and characterise inquisitive modal logic as the bisimulation invariant fragment of first-order logic over various natural classes of two-sorted structures. (shrink)

Questions are everywhere and the ubiquitous activities of asking and answering, as most human activities, are susceptible to failure – at least from time to time. This volume offers several current approaches to the systematic study of questions and the surrounding activities and works toward supporting and improving these activities. The contributors formulate general problems for a formal treatment of questions, investigate specific kinds of questions, compare different frameworks with regard to how they regulate the activities of asking and answering (...) of questions, and situate these activities in a wider framework of cognitive/epistemic discourse. From the perspectives of logic, linguistics, epistemology, and philosophy of language emerges a report on the state of the art of the theory of questions. (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)

The question of how to arrive at questions is ambiguous. I will concentrate on two readings: (i) How should one set up a formal syntax that accomodates questions? (ii) How does one, while working in a suitable formal language, arrive at a situation where one is allowed to or even must ask a certain question? In other words: How is the asking of questions regulated within a given formal language? I will propose an answer to question (i) and consider the (...) field of possibilities of answering (ii). (shrink)

The authors of 200 arguments for questions posed 19 types of questions, justified them in 62 different ways, offered a justification of the question for 50 different types of purposes, and posed the question for 49 different types of purposes. Further consolidation of the categories used in the analysis is desirable and possible. Of the six most commonly posed types of questions, only three (yes-no questions, select questions, and either-or questions) are at first glance capable of formal representation in an (...) erotetic language of the sort described by Wiśniewski (1995, 1996, 2013), but all six (including also requests to explain, identify and find a means) can be represented formally using the interrogative operators devised by Kubiński (1980). As for the types of justification, four passages argued against posing a question by denying one of its presuppositions, a strategy that implies that a question without a true answer is not worth posing. Only 20 passages, however, argued for a question by asserting a presupposition – typically in cases where their addressees might think that the premissed presupposition is false. Close analysis of five passages randomly selected from the 200 turned up four distinct conditions assumed to be necessary for a question to be worth posing: absence of a false presupposition, a way of working out a correct answer, an unbiased answerer, and a need to answer the question. The first three of these conditions can generally be presumed to be satisfied, and would need to be mentioned in justifying a question only if there was a suspicion that they were not. The fourth condition, a need to answer the question, typically does need to be established, and was the genus of the types of justification identified in half of the passages arguing for a non-rhetorical question. The dominant purpose for justifying a question, found in 111 of the passages, was to establish a need to answer the question; given that justifying a question typically amounts to establishing a need to answer it, this purpose is internal to the practice. The most common generic purposes for posing the question for which an author argued were to provoke thought, to introduce subsequent discussion of the question, to indirectly claim something (in the case of rhetorical questions), to issue a challenge, and to seek enlightenment. (shrink)

I consider two cognitive phenomena: inquiring and justifying, as complementary processes running in opposite directions. I explain on an example that the former process is driven by questions and the latter is a codification of the results of the first one. Traditionally, proof theory focuses on the latter process, and thus describes the former, at best, as an example of a backward proof search. I argue that this is not the best way to analyze cognitive processes driven by questions, and (...) that proof-theoretical analysis of questions can bring mutual benefits for both proof theory and erotetic logic. In the second part of my paper (sect. 6.3) I introduce the structural rules of weakening and contraction. Results concerning their admissibility are discussed. I also sketch an erotetic interpretation of the rule of weakening as reducing information noise, and that of contraction as securing information. (shrink)

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)

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)

In this paper we introduce a class of inquisitive Heyting algebras as algebraic structures that are isomorphic to algebras of finite antichains of bounded implicative meet semilattices. It is argued that these structures are suitable for algebraic semantics of inquisitive superintuitionistic logics, i.e. logics of questions based on intuitionistic logic and its extensions. We explain how questions are represented in these structures and provide several alternative characterizations of these algebras. For instance, it is shown that a Heyting algebra is inquisitive (...) if and only if its prime filters and filters generated by sets of prime elements coincide and prime elements are closed under relative pseudocomplement. We prove that the weakest inquisitive superintuitionistic logic is sound with respect to a Heyting algebra iff the algebra is what we call a homomorphic p-image of some inquisitive Heyting algebra. It is also shown that a logic is inquisitive iff its Lindenbaum–Tarski algebra is an inquisitive Heyting algebra. (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)

In recent years, the logic of questions and dependencies has been investigated in the closely related frameworks of inquisitive logic and dependence logic. These investigations have assumed classical logic as the background logic of statements, and added formulas expressing questions and dependencies to this classical core. In this paper, we broaden the scope of these investigations by studying questions and dependency in the context of intuitionistic logic. We propose an intuitionistic team semantics, where teams are embedded within intuitionistic Kripke models. (...) The associated logic is a conservative extension of intuitionistic logic with questions and dependence formulas. We establish a number of results about this logic, including a normal form result, a completeness result, and translations to classical inquisitive logic and modal dependence logic. (shrink)

This paper introduces the inquisitive extension of R, denoted as InqR, which is a relevant logic of questions based on the logic R as the background logic of declaratives. A semantics for InqR is developed, and it is shown that this semantics is, in a precisely defined sense, dual to Routley-Meyer semantics for R. Moreover, InqR is axiomatized and completeness of the axiomatic system is established. The philosophical interpretation of the duality between Routley-Meyer semantics and the semantics for InqR is (...) also discussed. (shrink)

Classical first-order logic \ is commonly used to study logical connections between statements, that is sentences that in every context have an associated truth-value. Inquisitive first-order logic \ is a conservative extension of \ which captures not only connections between statements, but also between questions. In this paper we prove the disjunction and existence properties for \ relative to inquisitive disjunction Open image in new window and inquisitive existential quantifier \. Moreover we extend these results to several families of theories, (...) among which the one in the language of \. To this end, we initiate a model-theoretic approach to the study of \. In particular, we develop a toolkit of basic constructions in order to transform and combine models of \. (shrink)

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 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)

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 sequents that are sound and complete for two species of erotetic inferences studied by Inferential Erotetic Logic : 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. (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 argues that questions have an important role to to play in logic, both semantically and proof-theoretically. Semantically, we show that by generalizing the classical notion of entailment to questions, we can capture not only the standard relation of logical consequence, which holds between pieces of information, but also the relation of logical dependency, which holds between information types. Proof-theoretically, we show that questions may be used in inferences as placeholders for arbitrary information of a given type; by manipulating (...) such placeholders, we may construct formal proofs of dependencies. Finally, we show that such proofs have a specific kind of constructive content: they do not just witness the existence of a certain dependency, but actually encode a method for transforming information of the types described by the assumptions into information of the type described by the conclusion. (shrink)

The book presents a new logical framework to capture the meaning of sentences in conversation. It is based on a richer notion of meaning than traditional approaches, and allows for an integrated treatment of statements and questions. The first part of the book presents the framework in detail, while the second demonstrates its many benefits.

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.

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.

Traditional approaches to the semantics of questions analyze questions indirectly, via the notion of an answer. In recent work on inquisitive semantics, a different perspective is taken: the meaning of a question is equated with its resolution conditions, just like the meaning of a statement is traditionally equated with its truth-conditions. In this paper I argue that this proposal improves on previous approaches, combining the formal elegance and explanatory power of Groenendijk and Stokhof’s partition theory with the greater generality afforded (...) by answer-set theories. (shrink)

Inquisitive dynamic epistemic logic extends standard public announcement logic incorporating ideas from inquisitive semantics. In IDEL, the standard public announcement action can be extended to a more general public utterance action, which may involve a statement or a question. While uttering a statement has the effect of a standard announcement, uttering a question typically leads to new issues being raised. In this paper, we investigate the logic of this general public utterance action. We find striking commonalities, and some differences, with (...) standard public announcement logic. We show that dynamic modalities admit a set of reduction axioms, which allow us to turn any formula of IDEL into an equivalent formula of static inquisitive epistemic logic. This leads us to establish several complete axiomatizations of IDEL, corresponding to known axiomatizations of public announcement logic. (shrink)

This paper presents a logic of questions developed as an extension of epistemic logic. We discuss many features that are important for erotetic logic. The aim is to introduce an erotetic system which corresponds well with epistemic terms and can form an appropriate background for dynamic approaches in epistemic logic.

FFormal dialogue system for tutorials DLT is introduced. The system allows for modelling certain behaviours related to questioning agendas observed in tutorial dialogues. Inferential Erotetic Logic is the underlying logic of questions used here. Tutorial dialogues retrieved from the Basic Electricity and Electronics Corpus are presented and analysed with the use of DLT.

The traditional use of the expression 'pseudoproblem' is analysed in order to clarify the talk of pseudoproblems and related phenomena. The goal is to produce a philosophically serviceable terminology that stays true to its historical roots. This explicative study is inspired by and makes use of the method of logical reconstruction. Since pseudoproblems are usually expressed by pseudoquestions a formal language of questions is presented as a possible reconstruction language for alleged pseudoproblems. The study yields an informal theory of pseudoproblems (...) whose presuppositions are critically investigated right away. At least one result remains: Claims of pseudoproblemship and their refutations must not be voiced casually - they are to be relativized and need substantial interpretive effort. (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)

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)

Information exchange can be seen as a dynamic process of raising and resolving issues. The goal of this paper is to provide a logical framework to model and reason about this process. We develop an inquisitive dynamic epistemic logic , which enriches the standard framework of dynamic epistemic logic , incorporating insights from recent work on inquisitive semantics. At a static level, IDEL does not only allow us to model the information available to a set of agents, like standard epistemic (...) logic, but also the issues that the agents entertain. At a dynamic level, IDEL does not only allow us to model the effects of communicative actions that provide new information, like standard DEL, but also the effects of actions that raise new issues. Thus, IDEL provides the fundamental tools needed to analyze information exchange as a dynamic process of raising and resolving issues. (shrink)

In many natural languages, there are clear syntactic and/or intonational differences between declarative sentences, which are primarily used to provide information, and interrogative sentences, which are primarily used to request information. Most logical frameworks restrict their attention to the former. Those that are concerned with both usually assume a logical language that makes a clear syntactic distinction between declaratives and interrogatives, and usually assign different types of semantic values to these two types of sentences. A different approach has been taken (...) in recent work on inquisitive semantics. This approach does not take the basic syntactic distinction between declaratives and interrogatives as its starting point, but rather a new notion of meaning that captures both informative and inquisitive content in an integrated way. The standard way to treat the logical connectives in this approach is to associate them with the basic algebraic operations on these new types of meanings. For instance, conjunction and disjunction are treated as meet and join operators, just as in classical logic. This gives rise to a hybrid system, where sentences can be both informative and inquisitive at the same time, and there is no clearcut division between declaratives and interrogatives. It may seem that these two general approaches in the existing literature are quite incompatible. The main aim of this paper is to show that this is not the case. We develop an inquisitive semantics for a logical language that has a clearcut division between declaratives and interrogatives. We show that this language coincides in expressive power with the hybrid language that is standardly assumed in inquisitive semantics, we establish a sound and complete axiomatization for the associated logic, and we consider a natural enrichment of the system with presuppositional interrogatives. (shrink)

The Interrogative Model of Inquiry and Dynamic Epistemic Logics are two central paradigms in formal epistemology. This paper is motivated by the observation of a significant complementarity between them: on the one hand, the IMI provides a framework for investigating inquiry represented as an idealized game between an Inquirer and Nature, along with an account of the interaction between questions and inferences in information-seeking processes, but is lacking a formulation in the multi-agent case; on the other hand, DELs model various (...) operations of information change in multi-agent systems, but the field is lacking a proper integration of question and inference dynamics, along with an application to the investigation of inquiry processes. The goal of this paper is to integrate the two paradigms in such a way as to combine their respective insights. To this end, we develop a formal system called DEL $$_\mathrm{IMI }$$ IMI which aims to represent the interaction between question and inference dynamics in inquiry—as described by the IMI—in a multi-agent setting, and this in such a way as to enable an investigation of inquiry games with multi-agent dimensions. The DEL $$_\mathrm{IMI }$$ IMI system is designed to represent the possible moves of such inquiry games through three types of epistemic actions: agents addressing questions to Nature, agents addressing questions to other agents, agents drawing logical inferences. We then show how the resulting framework can be used to formally define multi-agent inquiry games. We conclude by evaluating the interest of the DEL $$_\mathrm{IMI }$$ IMI system for the IMI and DELs paradigms. (shrink)

Traditional logical theories are concerned with the characterization of valid reasoning. For such logical theories, the main object of investigation is the notion of entailment, a notion that is construed as a relation between two or more declarative statements, dictating when one of them can be legitimately inferred from the others. In the course of the previous century, however, and especially since the 1970s, the scope of logical theories has become much broader. In particular, logic is no longer only concerned (...) with declarative statements, but also with questions. Accordingly, the field is no longer focusing exclusively on the entailment relation that may hold between two or more statements, but also aims to characterize fundamental relations that may hold between questions, or between questions and statements. For instance, when does a statement resolve a given question? When does a statement evoke a certain question? And when does the resolution of one question depend on the resolu .. (shrink)

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)

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.

The method of Socratic proofs (SP-method) simulates the solving of logical problem by pure questioning. An outcome of an application of the SP-method is a sequence of questions, called a Socratic transformation. Our aim is to give a method of translation of Socratic transformations into trees. We address this issue both conceptually and by providing certain algorithms. We show that the trees which correspond to successful Socratic transformations—that is, to Socratic proofs—may be regarded, after a slight modification, as Gentzen-style proofs. (...) Thus proof-search for some Gentzen-style calculi can be performed by means of the SP-method. At the same time the method seems promising as a foundation for automated deduction. (shrink)

In classical logic, the proposition expressed by a sentence is construed as a set of possible worlds, capturing the informative content of the sentence. However, sentences in natural language are not only used to provide information, but also to request information. Thus, natural language semantics requires a logical framework whose notion of meaning does not only embody informative content, but also inquisitive content. This paper develops the algebraic foundations for such a framework. We argue that propositions, in order to embody (...) both informative and inquisitive content in a satisfactory way, should be defined as non-empty, downward closed sets of possibilities, where each possibility in turn is a set of possible worlds. We define a natural entailment order over such propositions, capturing when one proposition is at least as informative and inquisitive as another, and we show that this entailment order gives rise to a complete Heyting algebra, with meet, join, and relative pseudo-complement operators. Just as in classical logic, these semantic operators are then associated with the logical constants in a first-order language. We explore the logical properties of the resulting system and discuss its significance for natural language semantics. We show that the system essentially coincides with the simplest and most well-understood existing implementation of inquisitive semantics, and that its treatment of disjunction and existentials also concurs with recent work in alternative semantics. Thus, our algebraic considerations do not lead to a wholly new treatment of the logical constants, but rather provide more solid foundations for some of the existing proposals. (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)

We propose strategic games wherein the strategies consist of players asking each other questions and answering those questions. We study simplifications of such games wherein two players simultaneously ask each other a question that the opponent is then obliged to answer. The motivation for our research is to model conversation including the dynamics of questions and answers, to provide new links between game theory and dynamic logics of information, and to exploit the dynamic/strategic structure that, we think, lies implicitly inside (...) epistemic models for epistemic languages, and to make that structure an explicit subject of logical study. Our main contributions are: the notion of a two-person question-answer game with information goals, the existence and computation of equilibria for these games, the correspondence with Bayesian games and their equilibria, and a connection between logic and game theory namely the existence of equilibria for positive goal formulae. (shrink)

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)