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Abductive Question-Answer System (\(\mathsf {AQAS}\)) for Classical Propositional Logic

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Flexible Query Answering Systems (FQAS 2017)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 10333))

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Abstract

We propose a new approach to modelling abductive reasoning by means of an abductive question-answer system. We introduce the concept of an abductive question which is the starting point of abductive reasoning. The result of applying the question processing procedure is a question, which is simpler than the initial one. \(\mathsf {AQAS}\) generates abductive hypotheses that fulfil certain criteria in one step, i.e. processes of generation and evaluation of abductive hypotheses are integrated.

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Notes

  1. 1.

    Urbański and Wiśniewski [20] proposed a mechanism which enables to obtain abductive hypotheses in the form of law-like statements. The basis of the mechanism is similar as we use here. However, the two approaches differ when results of the abductive procedures are concerned. What is more, Urbański and Wiśniewski put it explicitly at the beginning of their article that they will not consider problem of the evaluation of abductive hypotheses.

  2. 2.

    However some remarks should be made at this point. In the well-known Abductive Logic Programming (\(\mathsf {ALP}\)) framework (on the propositional level) it is assumed that the set of abductive hypotheses (the set of abducibles) is known before abductive reasoning is triggered. Then, using integrity constraints and information from the knowledge base it can be figured out which hypotheses are good. Moreover, abductive hypotheses can be only of the form of atomic formulas. In \(\mathsf {AQAS}\) the set of abductive hypotheses is not known before the initial question is transformed and abductive hypotheses can be literals as well as formulas of the form of implication. We think that the novelty of our approach lays in the fact that the concept of abductive hypothesis is defined in a more general way.

  3. 3.

    \(\alpha , \beta \)-notation was introduced by Smullyan in [17] to simplify metalogical considerations.

  4. 4.

    A version of this calculus was introduced by Wiśniewski in [21]. In his approach only one formula can occur in the consequent of the sequent.

  5. 5.

    Similar constraints are also defined in [1, p. 74] (Aliseda describes those two criteria as constituting the consistent and the explanatory Abductive Explanatory Styles respectively) and as properties of the abduction for Abductive Logic Programming in [5].

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Acknowledgements

This work has been supported by the Polish National Science Center, grant no. 2012/04/A/HS1/00715 (first author) and DEC-2013/10/E/HS1/00172 (second author).

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Authors and Affiliations

  1. Department of Logic and Cognitive Science, Institute of Psychology, Adam Mickiewicz University in Poznań, Poznań, Poland

    Szymon Chlebowski & Andrzej Gajda

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  1. Szymon Chlebowski
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  2. Andrzej Gajda
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Correspondence to Szymon Chlebowski .

Editor information

Editors and Affiliations

  1. Roskilde University, Roskilde, Denmark

    Henning Christiansen

  2. ENSSAT-IRISA, Lannion Cedex, France

    Hélène Jaudoin

  3. University of Westminster, London, United Kingdom

    Panagiotis Chountas

  4. Roskilde University, Roskilde, Denmark

    Troels Andreasen

  5. Aalborg University, Esbjerg, Denmark

    Henrik Legind Larsen

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Chlebowski, S., Gajda, A. (2017). Abductive Question-Answer System (\(\mathsf {AQAS}\)) for Classical Propositional Logic. In: Christiansen, H., Jaudoin, H., Chountas, P., Andreasen, T., Legind Larsen, H. (eds) Flexible Query Answering Systems. FQAS 2017. Lecture Notes in Computer Science(), vol 10333. Springer, Cham. https://doi.org/10.1007/978-3-319-59692-1_1

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  • DOI: https://doi.org/10.1007/978-3-319-59692-1_1

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