Abstract
This paper describes how the effects of acts of asserting and conceding can be captured in a new logic \(\mathsf{DMPCL} \). \(\mathsf{DMPCL} \) is developed according to a strategy similar to the strategy that leads to the development of dynamic epistemic logics. Thus acts of asserting and conceding are modeled as updators of propositional commitments, and a complete set of reduction axioms is presented. This paper also describes an extension of \(\mathsf{DMPCL} \) called \(\mathsf{DMPCL}^{+}\), which deals with the effects of acts of withdrawing assertions and concessions together with the effects of acts of asserting and conceding. As may be expected, the effects of acts of withdrawing turn out to be very difficult to capture, and the completeness problem for \(\mathsf{DMPCL}^{+}\) is still open. Yet the possibility of withdrawal seems to be a distinguishing characteristic common to a wide range of acts whose effects are conventional or institutional, and so the logical dynamics of withdrawal seems to be of considerable significance to the study of social interactions among rational agents. We make a brief comparison with AGM approach to belief revision and briefly discuss an application of \(\mathsf{DMPCL}^{+}\) to scorekeeping for argumentation games.
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- 1.
A detailed, state-of-the-art textbook exposition of dynamic epistemic logic can be found in van Ditmarsch, van der Hoek and Kooi [14].
- 2.
This recipe was presented at the XXII World Congress of Philosophy, 30 July–5 August, 2008, Seoul, Korea.
- 3.
Strictly speaking, the necessitation rule for c-commitment is redundant since Mix Axiom enables us to derive it from the necessitation rule for a-commitment. We list it here in order to record the fact that \(\mathsf{MPCL} \) is normal.
- 4.
The restriction on φ is motivated by the fact that the truth of φ at w in M does not guarantee the truth of φ at w in \(M_{\mathrm{assert}_{i}\varphi}\) or the truth of φ at w in \(M_{\mathrm{concede}_{i}\varphi}\) if φ is not i-free. For more on this point, see [16, p. 9].
- 5.
An interesting discussion of the usefulness of explicit treatment of speech acts in such a system can be found in [10].
- 6.
The outline of the derivation is completely similar to that of the completeness of \(\ mathsf{ECL}\) given in [16].
- 7.
Strictly speaking, such acts of re-asserting and re-conceding do not always have the same effects as acts of withdrawals of withdrawals. The effect of the act of withdrawing the act of withdrawing of the form \(\circlearrowleft \mathrm{assert}_{i}\varphi\), for example, can be different from the effects of re-asserting φ. Consider a case where φ is asserted at stage s i , withdrawn at a later stage s j , and re-asserted at a still later stage s k by an agent. What would happen if, instead of re-asserting φ at s k , the agent withdrew at s k her earlier withdrawal of φ at s j? Her earlier assertion of φ at s i would become effective again. Now, the effects of re-asserting φ at s k can be different from the effects of asserting φ at s i as the former depend on the things said during the discourse between s i and s k . To be sure the things said during the discourse between s i and s k would also affect the states after her “resurrected” assertion of φ at S i . But there is no guarantee that they would “neutralize”, so to speak, the difference in such a way that the state after the withdrawal at s K of her earlier withdrawal would be exactly the same as the actual state after her re-asserting of φ at s K .
- 8.
Such a feature may require very careful treatment. For example, if an agent a in an argumentation game has withdrawn her earlier assertion or concession after many things have said by her opponent b as well as by her, some of the things said by b may be the kind of things which b would not have said if a had not made the very assertion or concession a has just withdrawn. Should we allow b to withdraw some of his own assertions or concessions for free? And how about a’s further withdrawals motivated by b’s withdrawals?
- 9.
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Acknowledgements
This work has been supported by JSPS Grant-in-Aid for Scientific Research (C) (KAKENHI 19520002). An earlier version of this paper was presented at LENLS (Logic and Engineering of Natural Language Semantics) 2008, 9–10 June, 2008, Asahikawa, Japan. As a fault was found in the truth definition for \( \mathsf{DMPCL}^{+} \) in this version shortly after LENLS 2008, it was revised immediately. Various parts of the more recent versions of the paper incorporating the revised truth definition were presented at the 11th Symposium: Contemporary Philosophical Issues, University of Rijeka, 30 May, 2009, Rijeka, Croatia, and at the 4th International Conference on Philosophy, 1–4 June 2009, Athens, Greece, as well as in lectures given at the University of Zagreb, Tsinghua University, and Hokkaido University in 2009. The truth definition for \( \mathsf{DMPCL}^{+} \) in the present version is not only revised but also generalized. I thank the participants of these events and the editors of the present volume for their interesting questions and helpful comments.
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Yamada, T. (2012). Dynamic Logic of Propositional Commitments. In: Trobok, M., Miščević, N., Žarnić, B. (eds) Between Logic and Reality. Logic, Epistemology, and the Unity of Science, vol 25. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-2390-0_10
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