This article aims to contribute to the elucidation of the nature of inquiry. I start with some common desiderata for any theory of inquiry. I then categorize inquiry as a structured process. By focusing on its essential components, I advance a new characterization of inquiry as a combination of questioning attitudes guiding actions. Finally, I turn to the recent objection that questioning attitudes are not necessary for inquiry. I argue that inquiry is a structured process essentially constituted by questioning attitudes (...) having two precise functional roles, initiating and guiding the deployment of cognitive capacities towards an epistemic goal. (shrink)

How should we measure knowledge? According to the Counting Approach, we can measure knowledge by counting pieces of knowledge. Versions of the Counting Approach that try to measure knowledge by counting true beliefs with suitable support or by counting propositions known run into problems, stemming from infinite numbers of propositions and beliefs, difficulties in individuating propositions and beliefs, and cases in which knowing the same number of propositions contributes differently to knowledge. In this paper I develop a novel question-relative and (...) contextualist version of the counting approach, which measures an agent's knowledge by counting the number of complete answers of a contextually salient issue they can rule out. The question-relative and contextualist version of the Counting Approach avoids the issues for the proposition and belief-based systems, and offers a general, systematic, and explanatory system for measuring knowledge. (shrink)

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)

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)

Floridi’s chapter on relevant information bridges the analysis of “being informed” with the analysis of knowledge as “relevant information that is accounted for” by analysing subjective or epistemic relevance in terms of the questions that an agent might ask in certain circumstances. In this paper, I scrutinise this analysis, identify a number of problems with it, and finally propose an improvement. By way of epilogue, I offer some more general remarks on the relation between (bounded) rationality, the need to ask (...) the right questions, and the ability to ask the right questions. (shrink)

In this paper, we explore the conceptual problems arising when using network analysis in person- centered care (PCC) in psychiatry. Personalized network models are potentially helpful tools for PCC, but we argue that using them in psychiatric practice raises boundary problems, i.e., problems in demarcating what should and should not be included in the model, which may limit their ability to provide clinically-relevant knowledge. Models can have explanatory and representational boundaries, among others. We argue that we can make more explicit (...) what kind of questions personalized network models can address in PCC, given their representational and explanatory boundaries, using perspectival reasoning. (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)

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)

This book contains a selection of the papers presented at the Logic, Reasoning and Rationality 2010 conference in Ghent. The conference aimed at stimulating the use of formal frameworks to explicate concrete cases of human reasoning, and conversely, to challenge scholars in formal studies by presenting them with interesting new cases of actual reasoning. According to the members of the Wiener Kreis, there was a strong connection between logic, reasoning, and rationality and that human reasoning is rational in so far (...) as it is based on logic. Later, this belief came under attack and logic was deemed inadequate to explicate actual cases of human reasoning. Today, there is a growing interest in reconnecting logic, reasoning and rationality. A central motor for this change was the development of non-classical logics and non-classical formal frameworks. The book contains contributions in various non-classical formal frameworks, case studies that enhance our apprehension of concrete reasoning patterns, and studies of the philosophical implications for our understanding of the notions of rationality. (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)

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)

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.

I. Levi has advocated a decision-theoretic account of belief revision. We argue that the game-theoretic framework of Interrogative Inquiry Games, proposed by J. Hintikka, can extend and clarify this account. We show that some strategic use of the game rules generate Expansions, Contractions and Revisions, and we give representation results. We then extend the framework to represent explicitly sources of answers, and apply it to discuss the Recovery Postulate. We conclude with some remarks about the potential extensions of interrogative games, (...) with respect to some issues in the theory of belief change. (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)

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)

Pseudoproblems, pseudoquestions, pseudosentences (etc.) constitute an iridescent group of concepts which were prominently used by the Vienna Circle (including Wittgenstein). In the course of an explication this paper presents a compilation of the many different meanings that were given to these expressions. This includes the more prominent Viennese approaches as well as a more recent one by Roy Sorensen. A novel proposal concerning the use ofthe term is made, suggesting that nothing is just a pseudoproblem, but only relative to a (...) certain state of discourse. While the paper follows an explicative methodology, several uses of 'pseudoproblem', including the explicated one, relate pseudoproblemhood to other kinds of analysis. (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)

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)

Questions are triggers for explicit events of 'issue management'. We give a complete logic in dynamic-epistemic style for events of raising, refining, and resolving an issue, all in the presence of information flow through observation or communication. We explore extensions of the framework to multiagent scenarios and long-term temporal protocols. We sketch a comparison with some alternative accounts.

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)

In this article, “Narrative Closure,” a theory of the nature of narrative closure is developed. Narrative closure is identified as the phenomenological feeling of finality that is generated when all the questions saliently posed by the narrative are answered. The article also includes a discussion of the intelligibility of attributing questions to narratives as well as a discussion of the mechanisms that achieve this. The article concludes by addressing certain recent criticisms of the view of narrative expounded by this article.

Douglas Walton’s multitudinous contributions to the study of argumentation seldom, if ever, directly engage with argumentation in mathematics. Nonetheless, several of the innovations with which he is most closely associated lend themselves to improving our understanding of mathematical arguments. I concentrate on two such innovations: dialogue types (§1) and argumentation schemes (§2). I argue that both devices are much more applicable to mathematical reasoning than may be commonly supposed.

The article presents the method of analytic description as applied in the theory of questions. This procedure, described by Tadeusz Czeżowski and broadly used in the Lvov-Warsaw School, is applied first of all at the pre-theoretic stage of research, namely to construct the conceptual scheme of a given discipline and to classify the objects of investigations. Ajdukiewicz’s theory of questions and its developments, in particular recent works of Adam Jonkisz, are presented as examples of the applications of this method. Analytic (...) description is contrasted with other procedures, which differ from it with respect to the empirical basis and theoretical perspective. On this background, differences between various currents in erotetic research as well as the sources of misunderstandings between the representatives of these currents are explained. (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.

This chapter explores perspectivism in the American Pragmatist tradition. On the one hand, the thematization of perspectivism in contemporary epistemology and philosophy of science can benefit from resources in the American Pragmatist philosophical tradition. On the other hand, the Pragmatists have interesting and innovative, pluralistic views that can be illuminated through the lens of perspectivism. I pursue this inquiry primarily through examining relevant sources from the Pragmatist tradition. I will illustrate productive engagements between pragmatism and perspectivism in three areas: in (...) the pragmatists’ fallibilistic theories of inquiry and truth, in their pluralistic metaphysics, and in their views on cultural pluralism. While there are some potential sticking points between pragmatism and perspectivism, particularly around the visual metaphor of perspective, these philosophical approaches nonetheless have much to learn from each other. Perspectivism is in danger of falling between the horns of pernicious relativism and a platitudinous view of the limits of human perception and cognition. The pragmatists accounts of truth and reality open the possibility of a more thoroughgoing perspectivism. I will follow this thread through Charles S. Peirce’s, William James’, and John Dewey’s theories of inquiry and truth, Peirce’s evolutionary metaphysics, James’ radical pluralism, Dewey’s cultural naturalism, Richard Rorty’s anti-essentialism, Jane Addams’ standpoint epistemology, W.E.B. Du Bois’ theory of race consciousness, Horace Kallen’s and Alain LeRoy Locke’s cultural pluralism, and Mary Parker Follett’s account of pluralistic integration. (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.

Popper emphasised both the problem-solving nature of human knowledge, and the need to criticise a scientific theory as strongly as possible. These aims seem to contradict each other, in that the former stresses the problems that motivate scientific theories while the one ignores the character of the problems that led to the formation of the theories against which the criticism is directed. A resolution is proposed in which problems as such are taken as prime in the search for knowledge, and (...) subject to discussion. This approach is then applied to the problem of induction. Popper set great stake to his solution of it, but others doubted its legitimacy, in ways that are clarified by changing the form of the induction problem itself. That change draws upon logic, which is the subject of another application: namely, in contrast to Popper’s adhesion to classical logic as the only welcome form (because of the maximal strength of criticism that it dispenses), can other logics be used without abandoning his philosophy of criticism? (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)

Prezentujemy dwa formalne narzędzia służące do modelowania rozumowań, za pomocą których rozwiązywane są szczególnego rodzaju problemy abdukcyjne. Pierwszy model, osadzony w formalizmie logiki pytań, bazuje na pojęciu słabej implikacji erotetycznej. Drugi model wykorzystuje relacje zawężania i odsiewania definiowane za po-mocą logiki pytań, semantyki sytuacyjnej i pojęcia relewancjiwątku. Na przykładzie analizy rozgrywek w grę Takie Życie pokazujemy, że oba modele adekwatnie charakteryzują dane empiryczne.

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.

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)

The issue of adequacy of the Turing Test (TT) is addressed. The concept of Turing Interrogative Game (TIG) is introduced. We show that if some conditions hold, then each machine, even a thinking one, loses a certain TIG and thus an instance of TT. If, however, the conditions do not hold, the success of a machine need not constitute a convincing argument for the claim that the machine thinks.

The aims of this paper are to provide a detailed taxonomy of noncanonical uses of interrogative sentences, i.e. when they are used not to ask a question but to convey some information, or to ask a question albeit not that expressed by the interrogative sentence exploited in the act, to identify properties of circumstances where an interrogative sentence is being used in this way, and to propose some maxims that govern the rational use of questions. Four main categories of such (...) cases are presented, and a few further subclasses are differentiated. I show how these types are interrelated, and what logical features differentiate them. I also propose a hypothesis for when an interrogative sentence is not being used in its primary mode. Studies on circumstances in which questions are used in other ways can shed light on maxims that govern asking and questioning in a rational conversation; therefore, some possible maxims of this kind are proposed. (shrink)

Questions are triggers for explicit events of ‘issue management’. We give a complete logic in dynamic-epistemic style for events of raising, refining, and resolving an issue, all in the presence of information flow through observation or communication. We explore extensions of the framework to multi-agent scenarios and long-term temporal protocols. We sketch a comparison with some alternative accounts.

The paper contains a survey of (mainly unpublished) adaptive logics of inductive generalization. These defeasible logics are precise formulations of certain methods. Some attention is also paid to ways of handling background knowledge, introducing mere conjectures, and the research guiding capabilities of the logics.

Taking the lead from orthodox quantum theory, I will introduce a handy generalization of the Boolean approach to propositions and questions: the orthoalgebraic framework. I will demonstrate that this formalism relates to a formal theory of questions (or ‘observables’ in the physicist’s jargon). This theory allows formulating attitude questions, which normally are non-commuting, i.e., the ordering of the questions affects the answer behavior of attitude questions. Further, it allows the expression of conditional questions such as “If Mary reads the book, (...) will she recommend it to Peter?”, and thus gives the framework the semantic power of raising issues and being informative at the same time. In the case of commuting observables, there are close similarities between the orthoalgebraic approach to questions and the Jäger/Hulstijn approach to question semantics. However, there are also differences between the two approaches even in case of commuting observables. The main difference is that the Jäger/Hulstijn approach relates to a partition theory of questions whereas the orthoalgebraic approach relates to a ‘decorated’ partition theory (i.e. the elements of the partition are decorated by certain semantic values). Surprisingly, the orthoalgebraic approach is able to overcome most of the difficulties of the Jäger/Hulstijn approach. Furthermore, the general approach is suitable to describe the different types of (non-commutative) attitude questions as investigated in modern survey research. Concluding, I will suggest that an active dialogue between the traditional model-theoretic approaches to semantics and the orthoalgebraic paradigm is mandatory. (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.

Philosophical intuition has become one of the most debated problems in recent years, largely due to the rise of the movement called experimental philosophy which challenged the conviction that philosophers have some special insight into abstract ideas such as being, knowledge, good and evil, intentional action, etc. In response to the challenge, some authors claim that there is a special cognitive faculty called philosophical intuition which delivers justification to philosophical theses, while some others deny it based on experimental results. A (...) relatively smaller group of researchers aim at clarifying what the alleged intuition is. I follow the latter path. In this paper I argue that philosophical intuition is in the first place the capacity enabling one to what I refer to as the recognition of one’s epistemic position. The latter means becoming aware of the seemingly trivial “fact” that the way in which the world manifests itself depends on the cognitive apparatus one has, thereby propelling one to draw a distinction between appearances and reality. The recognition at stake is a very specific capacity to approach the world solely as it is experienced. This capacity, I argue, is the core and the defining feature of philosophical intuition. As part of my argumentation I also distinguish between the intuition in question and its different manifestations; and then introduce a novel notion of erotetic intuition. My argument is called “old-fashion” to emphasize the fact that I draw mostly on four figures who were pivotal in the twentieth- century philosophy and whose influence on the current debate concerning philosophical intuition should be, I believe, stronger than it is; I mean Russell, Carnap, Wittgenstein, and Husserl. (shrink)

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)

The aim of this paper is to present a loop-free decision procedure for modal propositional logics K4, S4 and S5. We prove that the procedure terminates and that it is sound and complete. The procedure is based on the method of Socratic proofs for modal logics, which is grounded in the logic of questions IEL.

The aim of this paper is to present the method of Socratic proofs for seven modal propositional logics: K5, S4.2, S4.3, S4M, S4F, S4R and G. This work is an extension of [10] where the method was presented for the most common modal propositional logics: K, D, T, KB, K4, S4 and S5.