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Reasoning Processes as Epistemic Dynamics

Abstract

This work proposes an understanding of deductive, default and abductive reasoning as different instances of the same phenomenon: epistemic dynamics. It discusses the main intuitions behind each one of these reasoning processes, and suggest how they can be understood as different epistemic actions that modify an agent’s knowledge and/or beliefs in a different way, making formal the discussion with the use of the dynamic epistemic logic framework. The ideas in this paper put the studied processes under the same umbrella, thus highlighting their relationship and allowing a better understanding of how they interact together.

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Notes

  1. For example, after presenting a proposal for representing deduction under possible worlds models, it is briefly discussed (p. 6) how the obtained properties change when an agent’s knowledge is represented with neighbourhood models instead.

  2. Since \(\varphi\) can be any formula, the language can express the agent’s knowledge not only about propositional facts but also about her own (and eventually other agents’) knowledge.

  3. When \(R\) is reflexive, \({K}{\varphi } \rightarrow \varphi\) is valid: if an agent knows \(\varphi\), then \(\varphi\) is indeed the case.

  4. See the discussion on this so-called logical omniscience problem below.

  5. Fagin and Halpern (1988) define \({K_{\mathrm{Ex }}}{\varphi } := {K}{\varphi } \wedge {\mathrm{A} }{\varphi }\), but they actually interpret \({\mathsf{A}}(w)\) not as what the agent has recognised as true but rather as what she is aware of.

  6. This is in fact an instance of the so called ‘Moorean phenomena’, which lies at the root of Fitch’s famous “paradox of knowability” (Fitch 1963; Benthem 2004; Balbiani et al. 2009) and occurs when an epistemic action ‘invalidates’ itself. In its best known incarnation it appears as formulas that, after being publicly announced, are not known (Ditmarsch and Kooi 2006; Holliday and Icard 2010); in this neighbourhood model framework it appears as situations in which a logical consequence of what is explicitly known at some stage is not explicitly known after a closure-under-logical-consequence operation.

  7. Other authors (e.g., Hendricks and Symons 2006) have suggested that epistemic axioms can be seen instead as principles describing certain form of strong rationality.

  8. The plausibility relation is asked to be a locally connected and conversely well-founded preorder.

  9. The concept of abduction has been discussed in various fields, and this has led to different ideas of what abduction should consist of (see, e.g., Flach and Kakas 2000). This section focuses on the simple understanding of the abductive process stated in the opening sentence.

  10. While most work on strategies for finding abductive solutions focuses on formulae that are already part of the system (the aforementioned references), some others take a broader view, allowing not only changes in the underlying logical consequence relation (Soler-Toscano et al. 2010) but also the creation and/or modification of concepts (Quilici-Gonzalez and Haselager 2005). The present section is restricted (again) to the first case, but similar dynamic epistemic approaches can be made in the others (e.g., introducing/removing concepts can be represented via dynamics of awareness; van Benthem and Velázquez-Quesada 2010).

  11. In particular, the reader might miss the process of selecting the best explanation (Harman 1965; Lipton 2004; Hintikka 1998), which many authors consider to be the heart of abductive reasoning. Such action deserves a full discussion on its own and it will be not treated here; for discussions and proposals, we refer to the already mentioned Kakas et al. (1992), Mayer and Pirri (1993), Mayer and Pirri (1995), Reyes-Cabello et al. (2006), Klarman (2008) within classical approaches, and to Nepomuceno-Fernández et al. (2013), Soler-Toscano and Velázquez-Quesada (2014) within epistemic approaches.

  12. The classification can be even refined by considering finer epistemic attitudes, as safe beliefs (Baltag and Smets 2008) or strong beliefs (Baltag and Smets 2009).

  13. Interestingly, under this definition, ‘trivial’ solutions as the observation itself or contradictions (to the agent’s knowledge, or logical contradictions) are not explanatory: accepting them will not change the agent’s information.

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Velázquez-Quesada, F.R. Reasoning Processes as Epistemic Dynamics. Axiomathes 25, 41–60 (2015). https://doi.org/10.1007/s10516-014-9255-6

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Keywords

  • Deductive reasoning
  • Default reasoning
  • Abductive reasoning
  • Philosophy of science
  • Epistemic logic
  • Dynamic epistemic logic
  • Knowledge
  • Beliefs