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Reasoning Processes as Epistemic Dynamics

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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.

References

  • Adams E (1998) A primer of probability logic. CSLI, ISBN 978-1-57586-067-1

  • Aliseda A (2000) Abduction as epistemic change: a Peircean model in artificial intelligence. Abduction and Induction. Springer, Netherlands, pp 45–58

  • Aliseda A (2003) Mathematical reasoning vs. abductive reasoning: a structural approach. Synthese 134(1–2):25–44. doi:10.1023/A:1022127429205

    Article  Google Scholar 

  • Aliseda A (2006) Abductive reasoning. Logical investigations into discovery and explanation, volume 330 of Synthese library series. Springer, ISBN 978-1-4020-3907-2

  • Artëmov SN, Nogina E (2005) Introducing justification into epistemic logic. J Log Comput 15(6):1059–1073. doi:10.1093/logcom/exi053

    Article  Google Scholar 

  • Bacharach M, Gérard-Varet L-A, Mongin P, Shin HS (eds) (1997) Epistemic logic and the theory of games and decisions, volume 20 of Theory and decision library. Springer, ISBN 978-0-7923-4804-7. doi:10.1007/978-1-4613-1139-3

  • Balbiani P, Baltag A, van Ditmarsch H, Herzig A, Hoshi T, de Lima T (2009) ‘Knowable’ as ‘known after an announcement’. Rev Symb Log 1(3):305–334. doi:10.1017/S1755020308080210

    Article  Google Scholar 

  • Baltag A, Smets S (2008) A qualitative theory of dynamic interactive belief revision. In Bonanno G, van der Hoek W, Wooldridge M (eds) Logic and the foundations of game and decision theory (LOFT7), volume 3 of Texts in logic and games. Amsterdam University Press, Amsterdam pp 13–60, ISBN 978-90 8964 026 0

  • Baltag A, Smets S (2009) Learning by questions and answers: from belief-revision cycles to doxastic fixed points. In Ono H, Kanazawa M, de Queiroz RJGB (eds) WoLLIC, volume 5514 of Lecture notes in computer science. Springer, pp 124–139, ISBN 978-3-642-02260-9. doi:10.1007/978-3-642-02261-6_11

  • Beall JC, Restall G (2000) Logical pluralism. Aust J Philos 78(4):475–493. doi:10.1080/00048400012349751

    Article  Google Scholar 

  • Beall JC, Restall G (2006) Logical pluralism. Oxford University Press, Oxford, ISBN 978-0-19-928840-3

    Google Scholar 

  • Boutilier C (1994) Unifying default reasoning and belief revision in a modal framework. Artif Intell 68(1):33–85. doi:10.1016/0004-3702(94)90095-7

    Article  Google Scholar 

  • Chellas BF (1980) Modal logic: an introduction. Cambridge University Press, Cambridge, ISBN 0-521-295157

    Book  Google Scholar 

  • D’Agostino M, Floridi L (2009) The enduring scandal of deduction. Is propositional logic really uninformative? Synthese 167(2):271–315. doi:10.1007/s11229-008-9409-4

    Article  Google Scholar 

  • de Bruin B (2010) Explaining games: the epistemic programme in game theory, volume 346 of Synthese library series. Springer, Dordrecht, ISBN 978-1-4020-9905-2

  • Delgrande JP, Schaub T, Jackson WK (1994) Alternative approaches to default logic. Artificial Intelligence 70(1–2):167–237. doi:10.1016/0004-3702(94)90106-6

    Article  Google Scholar 

  • Fagin R, Halpern JY (1988) Belief, awareness, and limited reasoning. Artif Intell 34(1):39–76. doi:10.1016/0004-3702(87)90003-8

    Article  Google Scholar 

  • Fagin R, Halpern JY, Moses Y, Vardi MY (1995) Reasoning about knowledge. The MIT Press, Cambridge, ISBN 0-262-06162-7

    Google Scholar 

  • Fitch FB (1963) A logical analysis of some value concepts. J Symb Log 28(2):135–142. doi:10.2307/2271594

    Article  Google Scholar 

  • Flach PA, Kakas AC (eds) (2000) Abduction and Induction: essays on their relation and integration. Number 18 in applied logic series. Kluwer Academic, Dordrecht, ISBN 0-7923-6250-0

  • Gabbay DM, Woods J (2005) The reach of abduction: insight and trial, volume 2 of A practical logic of cognitive systems. Elsevier, ISBN 978-0-444-51791-3

  • Gärdenfors P (ed) (1992) Belief revision. Number 29 in Cambridge tracts in theoretical computer science. Cambridge University Press, ISBN 978-0-521-54564-8

  • Gärdenfors P, Rott H (1994) Belief revision. In: Handbook of logic in artificial intelligence and logic programming, volume 4: epistemic and temporal logics. Oxford University Press, Oxford, pp 35–132, ISBN 0-19-853791-3

  • Gerbrandy J, Groeneveld W (1997) Reasoning about information change. J Log Lang Inf 6(2):147–196. doi:10.1023/A:1008222603071

    Article  Google Scholar 

  • Gierasimczuk N (2009) Bridging learning theory and dynamic epistemic logic. Synth Knowl Ration Action 169(2):371–384. doi:10.1007/s11229-009-9549-1

    Google Scholar 

  • Grossi D, Velázquez-Quesada FR (2009) Twelve angry men: a study on the fine-grain of announcements. In: He X, Horty JF, Pacuit E (eds) LORI-II, volume 5834 of Lecture notes in computer science. Springer, Berlin, pp 147–160, ISBN 978-3-642-04892-0. doi:10.1007/978-3-642-04893-7_12

  • Grossi D, Velázquez-Quesada FR (2010) Twelve angry men: a dynamic-epistemic study of awareness, implicit and explicit information. In: Grossi D, Kurzen L, Velázquez-Quesada FR (eds) Logic and interactive rationality. Seminar’s yearbook 2009. ILLC, The Netherlands, pp 42–68. http://www.illc.uva.nl/lgc/seminar/?page_id=727

  • Halpern JY (ed) (1986) Proceedings of the 1st conference on theoretical aspects of reasoning about knowledge. Monterey, CA, March 1986, San Francisco, CA, USA, Morgan Kaufmann, ISBN 0-934613-04-9

  • Harman G (1965) The inference to the best explanation. Philos Rev 74(1):88–95. doi:10.2307/2183532

    Article  Google Scholar 

  • Hendricks V, Symons J (2006) Where is the bridge? Epistemology and epistemic logic. Philos Stud 128(1):137–167. doi:10.1007/s11098-005-4060-0

    Article  Google Scholar 

  • Hendricks VF (2006) 8 bridges between formal and mainstream epistemology. Philos Stud 128(1):1–227

  • Hintikka J (1962) Knowledge and belief: an Introduction to the logic of the two notions. Cornell University Press, Ithaca, ISBN 1-904987-08-7

    Google Scholar 

  • Hintikka J (1970) Surface information and depth information. In: Hintikka J, Suppes P (eds) Information and inference, volume 28 of Synthese library. Springer, Dordrecht, pp 263–297, ISBN 978-94-010-3298-8. doi:10.1007/978-94-010-3296-4_8

  • Hintikka J (1973) Logic, language games and information. Kantian themes in the philosophy of logic. Clarendon Press, Oxford

    Google Scholar 

  • Hintikka J (1998) What is abduction? The fundamental problem of contemporary epistemology. Trans Charles S. Peirce Soc 34(3):503–533

    Google Scholar 

  • Hintikka J, Sandu G (2007) What is logic? In: Jacquette D (ed) Philosophy of logic, handbook of the philosophy of science. North-Holland, Amsterdam, pp 13–39, ISBN 978-0-444-51541-4

  • Hocutt MO (1972) Is epistemic logic possible? Notre Dame J Form Log 13(4):433–453. doi:10.1305/ndjfl/1093890705

    Article  Google Scholar 

  • Holliday WH, Icard TF (2010) Moorean phenomena in epistemic logic. In: Beklemishev L, Goranko V, Shehtman V (eds) Advances in modal logic. College Publications, pp. 178–199, ISBN 978-1-84890-013-4. http://www.aiml.net/volumes/volume8/Holliday-Icard

  • Kakas A, Kowalski R, Toni F (1992) Abductive logic programming. J Log Comput 2(6):719–770. doi:10.1093/logcom/2.6.719

    Article  Google Scholar 

  • Kelly KT (1996) The logic of reliable inquiry. Oxford University Press, ISBN 0-19-509195-7

  • Klarman S (2008) Abox abduction in description logic. Master’s thesis, ILLC, Amsterdam, The Netherlands, ILLC Master of Logic Series MoL-2008-03

  • Kleene SC (1938) On notation for ordinal numbers. J Symb Log 3(4):150–155. doi:10.2307/2267778

    Article  Google Scholar 

  • Klir GJ, Yuan B (1995) Fuzzy sets and fuzzy logic—theory and applications. Prentice Hall, ISBN 978-0-13-101171-7

  • Konolige K (1984) Belief and incompleteness. Technical report 319, SRI International

  • Kraus S, Lehmann DJ, Magidor M (1990) Nonmonotonic reasoning, preferential models and cumulative logics. Artif Intell 44(1–2):167–207. doi:10.1016/0004-3702(90)90101-5

    Article  Google Scholar 

  • Lakemeyer G (1986) Steps towards a first-order logic of explicit and implicit belief. In: Halpern (1986), pp 325–340

  • Levesque HJ (1984) A logic of implicit and explicit belief. In Proceedings of AAAI-84, pp 198–202, Austin, TX

  • Lipton P (2004) Inference to the best explanation, 2nd edn. Routledge, New York, ISBN 0-415-24202-9. First edition: 1991

  • Lobo J, Uzcátegui C (1997) Abductive consequence relations. Artif Intell 89(1–2):149–171. doi:10.1016/S0004-3702(96)00032-X

    Article  Google Scholar 

  • Łukasiewicz J (1920) O logice trójwartościowej. Ruch Filozoficny 5:170–171, English translation: Łukasiewicz (1970)

  • Łukasiewicz J (1970) On three-valued logic. In: Borkowski L (ed) Selected works by Jan Łukasiewicz, pp 87–88. North-Holland Publishign Company, Amsterdam and London, ISBN 0-7204-2252-3

  • Magnani L (2001) Abduction, reason, and science: processes of discovery and explanation. Kluwer Academic, ISBN 0-306-46514-0

  • Mayer MC, Pirri F (1993) First order abduction via tableau and sequent calculi. Log J IGPL 1(1):99–117. doi:10.1093/jigpal/1.1.99

    Article  Google Scholar 

  • Mayer MC, Pirri F (1995) Propositional abduction in modal logic. Log J IGPL 3(6):907–919. doi:10.1093/jigpal/3.6.907

    Article  Google Scholar 

  • McCarthy J (1980) Circumscription—a form of non-monotonic reasoning. Artif Intell 13(1–2):27–39. doi:10.1016/0004-3702(80)90011-9

    Article  Google Scholar 

  • Meyer J-JC, van Der Hoek W (1995) Epistemic logic for AI and computer science. Cambridge University Press, New York, ISBN 0-521-46014-7

    Book  Google Scholar 

  • Montague R (1970) Universal grammar. Theoria 36(3):373–398. doi:10.1111/j.1755-2567.1970.tb00434.x

    Article  Google Scholar 

  • Nepomuceno-Fernández Á, Soler-Toscano F, Velázquez-Quesada FR (2013) An epistemic and dynamic approach to abductive reasoning: selecting the best explanation. Log J IGPL 21(6):943–961. doi:10.1093/jigpal/jzt013

    Article  Google Scholar 

  • Pacuit E (2007) Neighborhood semantics for modal logic. An introduction. Lecture notes for the ESSLLI course a course on neighborhood structures for modal logic. http://ai.stanford.edu/~epacuit/classes/esslli/nbhd_esslli.html.

  • Paul G (1993) Approaches to abductive reasoning: an overview. Artif Intell Rev 7(2):109–152. doi:10.1007/BF00849080

    Article  Google Scholar 

  • Perea A (2012) Epistemic game theory: reasoning and choice. Cambridge University Press, Cambridge, ISBN 978-1-107-40139-6

    Book  Google Scholar 

  • Plaza JA (1989) Logics of public communications. In: Emrich ML, Pfeifer MS, Hadzikadic M, Ras ZW (eds) Proceedings of the 4th international symposium on methodologies for intelligent systems, Tennessee, USA, Oak Ridge National Laboratory, ORNL/DSRD-24, pp 201–216

  • Quilici-Gonzalez ME, Haselager WFG (2005) Creativity: surprise and abductive reasoning. Semiotica 153(1–4):325–342. doi:10.1515/semi.2005.2005.153-1-4.325

    Google Scholar 

  • Reiter R (1980) A logic for default reasoning. Artif Intell 13(1–2):81–132. doi:10.1016/0004-3702(80)90014-4

    Article  Google Scholar 

  • Reyes-Cabello AL, Aliseda A, Nepomuceno-Fernández Á (2006) Towards abductive reasoning in first-order logic. Log J IGPL 14(2):287–304. doi:10.1093/jigpal/jzk019

    Article  Google Scholar 

  • Rott H (2001) Change, choice and inference: a study of belief revision and nonmonotonic reasoning. Number 42 in Oxford logic guides. Oxford Science Publications, ISBN 978-0-19-850306-4

  • Scott D (1970) Advice in modal logic. In: Lambert K (ed) Philosophical problems in logic. Reidel, Dordrecht, pp 143–173, ISBN 978-94-010-3272-8

  • Segerberg K (1999) Default logic as dynamic doxastic logic. Erkenntnis 50(2–3):333–352. doi:10.1023/A:1005546526502

    Article  Google Scholar 

  • Sequoiah-Grayson S (2008) The scandal of deduction. J Philos Log 37(1):67–94. doi:10.1007/s10992-007-9060-4

    Article  Google Scholar 

  • Soler-Toscano F, Velázquez-Quesada FR (2014) Generation and selection of abductive explanations for non-omniscient agents. J Log Lang Inf 23(2):141–168. doi:10.1007/s10849-014-9192-1

    Article  Google Scholar 

  • Soler-Toscano F, Fernández-Duque D, Nepomuceno-Fernández Á (2010) A modal framework for modeling abductive reasoning. Log J IGPL. doi:10.1093/jigpal/jzq059

    Google Scholar 

  • Stalnaker R (1991) The problem of logical omniscience. I. Synthese 89(3):425–440. doi:10.1007/BF00413506

    Article  Google Scholar 

  • Troelstra A, Schwichtenberg H (2000) Basic proof theory, 2nd edn. Cambridge University Press, Cambridge, ISBN 0521779111

  • van Benthem J (1996) Exploring logical dynamics. CSLI Publications & FoLLI, Stanford, ISBN 1-57586-059-7

    Google Scholar 

  • van Benthem J (2004) What one may come to know. Analysis 64(2):95–105. doi:10.1093/analys/64.2.95

    Article  Google Scholar 

  • van Benthem J (2007) Dynamic logic for belief revision. J Appl Non-Class Log 17(2):129–155. doi:10.3166/jancl.17.129-155

    Article  Google Scholar 

  • van Benthem J (2008) Logical dynamics meets logical pluralism? Aust J Log 6:182–209

    Google Scholar 

  • van Benthem J (2011) Logical dynamics of information and interaction. Cambridge University Press, ISBN 978-0-521-76579-4

  • van Benthem J, Pacuit E (2011) Dynamic logics of evidence-based beliefs. Studia Log 99(1):61–92. doi:10.1007/s11225-011-9347-x

    Article  Google Scholar 

  • van Benthem J, Velázquez-Quesada FR (2010) The dynamics of awareness. Synthese 177 (Supplement 1):5–27. doi:10.1007/s11229-010-9764-9

  • van Ditmarsch H, Kooi B (2006) The secret of my success. Synthese 151(2):201–232. doi:10.1007/s11229-005-3384-9

    Article  Google Scholar 

  • van Ditmarsch H, van der Hoek W, Kooi B (2007) Dynamic epistemic logic. Springer,   ISBN 978-1-4020-5838-7

    Book  Google Scholar 

  • Vardi MY (1986) On epistemic logic and logical omniscience. In: Halpern (1986), pp 293–305

  • Velázquez-Quesada FR (2013) Explicit and implicit knowledge in neighbourhood models. In: Grossi D, Roy O, Huang H (eds) LORI, volume 8196 of Lecture notes in computer science. Springer, Berlin, pp 239–252, ISBN 978-3-642-40947-9.doi:10.1007/978-3-642-40948-6_19

  • Velázquez-Quesada FR (2014) Dynamic epistemic logic for implicit and explicit beliefs. J Log Lang Inf 23(2):107–140. doi:10.1007/s10849-014-9193-0

    Article  Google Scholar 

  • Velázquez-Quesada FR, Soler-Toscano F, Nepomuceno-Fernández Á (2013) An epistemic and dynamic approach to abductive reasoning: abductive problem and abductive solution. J Appl Log 11(4):505–522. doi:10.1016/j.jal.2013.07.002

    Article  Google Scholar 

  • Walliser B, Zwirn D, Zwirn H (2004) Abductive logics in a belief revision framework. J Log Lang Inf 14(1):87–117. doi:10.1007/s10849-004-2319-z

    Article  Google Scholar 

  • Wheeler GR, Pereira LM (2004) Epistemology and artificial intelligence. J Appl Log 2(4):469–493. doi:10.1016/j.jal.2004.07.007

    Article  Google Scholar 

  • Williams M-A., Rott H (eds) (2001) Frontiers in belief revision. Kluwer Academic Publishers, ISBN 978-0-7923-7021-5

  • Woods J (2012) Cognitive economics and the logic of abduction. Rev Symb Log 5(1):148–161. doi:10.1017/S175502031100027X

    Article  Google Scholar 

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  1. Grupo de Lógica, Lenguaje e Información, Facultad de Filosofía, Universidad de Sevilla, C/ Camilo José Cela S/N, 41018, Seville, Spain

    Fernando R. Velázquez-Quesada

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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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