Inferential erotetic logic meets inquisitive semantics

Synthese, Jun 2015

Inferential erotetic logic (IEL) and inquisitive semantics (INQ) 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: (1) a disjunction of all the direct answers to an evoked question is always inquisitive; (2) a formula is inquisitive if, and only if it evokes a yes–no question whose affirmative answer expresses a possibility for the formula; (3) inquisitive formulas evoke questions whose direct answers express all the possibilities for the formulas, and (4) each question erotetically implies a question whose direct answers express the possibilities for the direct answers to the implying question.

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Inferential erotetic logic meets inquisitive semantics

Inferential erotetic logic meets inquisitive semantics Andrzej Wisniewski 0 Dorota Leszczy nska-Jasion 0 0 D. Leszczyn ska-Jasion Inferential erotetic logic (IEL) and inquisitive semantics (INQ) 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: (1) a disjunction of all the direct answers to an evoked question is always inquisitive; (2) a formula is inquisitive if, and only if it evokes a yes-no question whose affirmative answer expresses a possibility for the formula; (3) inquisitive formulas evoke questions whose direct answers express all the possibilities for the formulas, and (4) each question erotetically implies a question whose direct answers express the possibilities for the direct answers to the implying question. Logic of questions; Inferential erotetic logic; Inquisitive semantics - This paper focuses on interrelations between two notions: question raising and inquisitiveness. The former is in the centre of attention of inferential erotetic logic (IEL), while the latter is the core concept of inquisitive semantics (INQ). Work on this paper was supported by funds of the National Science Centre, Poland (DEC-2012/04/A/HS1/00715). 1.1 Inquisitive semantics Inquisitive semantics originated from an analysis of questions, but currently evolves toward a general theory of meaning. The beginnings of INQ date to the late 1990s. INQ, however, is currently a research programme rather than a completed theory: alternative accounts are still being proposed.1 The basic idea of INQ can be briefly expressed as follows: the meaning of a sentence comprises two components, informative content and inquisitive content. The former is the information provided by a sentence, the latter is the issue raised by the sentence. By and large, if the information provided is sufficient to settle the issue that is raised, the sentence is an assertion. If, however, the information provided is insufficient to settle the raised issue, the sentence is inquisitive. For example, the following: Mary is Peters mother. raises the issue whether Mary is Peters mother and provides information that Mary is Peters mother. The information provided settles the issue raised. Now let us consider: John is Peters father or George is Peter s father. Sentence (2) raises the issue who is Peters father, John or George, while the information provided amounts only to the claim that one of above possibilities holds. So (2) is inquisitive, while (1) is not. Observe that inquisitive sentences are akin to questions in being carriers of information to be completed. Both types of contents, as well as the concepts of possibility, assertion and inquisitiveness are modelled formally (see below). In what follows we concentrate upon the basic, most often used system of inquisitive semantics, labelled as InqB, and we remain at the propositional level only. 1.2 Inferential erotetic logic Generally speaking, IEL is a logic that analyses inferences in which questions play the role of conclusions and proposes criteria of validity for these inferences. The idea originates from the late 1980s.2 IEL starts with a simple observation that in many cases arriving at questions resembles coming to conclusions: there are premises involved and some inferential thought processes take place. In other words, there exist erotetic inferences, that is, thought processes in which questions occur as conclusions. These inferences are of (at least) 1 For various versions of INQ see, e.g., Groenendijk and Roelofsen (2009), Ciardelli and Roelof sen (2011), Groenendijk (2011), Ciardelli et al. (2013a, b), Ciardelli and Roelofsen (2014). For recent developments see: http://sites.google.com/site/inquisitivesemantics/. 2 The monograph Wisniewski (1995) summarizes results obtained until early nineties, while the book Wisniewski (2013) provides a state-of-the-art exposition of IEL. For a concise introduction see Wisniewski (2001) or Wisniewski (1996). two kinds, depending on the type of premises involved. In the case of an erotetic inference of the first kind the set of premises consists of declarative sentence(s) only, and an agent passes from it to a question. For example: (I) Mary is Peters mother. If Mary is Peters mother, then John is Peters father or George is Peters father. Who is Peters father: John or George? The premises of an erotetic inference of the second kind comprise a question and possibly some declarative sentence(s). For instance: (II) Where did Andrew leave for? If Andrew took his famous umbrella, then he left for London; otherwise he left for Paris or Moscow. Did Andrew take his famous umbrella? Erotetic inferences in wh (...truncated)


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Andrzej Wiśniewski, Dorota Leszczyńska-Jasion. Inferential erotetic logic meets inquisitive semantics, Synthese, 2015, pp. 1585-1608, Volume 192, Issue 6, DOI: 10.1007/s11229-013-0355-4