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Studia Logica

, Volume 107, Issue 1, pp 167–194 | Cite as

Inference as Doxastic Agency. Part I: The Basics of Justification Stit Logic

  • Grigory K. OlkhovikovEmail author
  • Heinrich Wansing
Article

Abstract

In this paper we consider logical inference as an activity that results in proofs and hence produces knowledge. We suggest to merge the semantical analysis of deliberatively seeing-to-it-that from stit theory (Belnap et al. in Facing the future: agents and choices in our indeterminist world, Oxford University Press, New York, 2001) and the semantics of the epistemic logic with justification from (Artemov and Nogina in Journal of Logic and Computation 15:1059–1073, 2005). The general idea is to understand proving that A as seeing to it that a proof of A is (publicly) available. We introduce a semantics of various notions of proving as an activity and present a number of valid principles that relate the various notions of proving to each other and to notions of justified knowledge, implicit knowledge, and possibility. We also point out and comment upon certain principles our semantics fails to validate.

Keywords

Proofs as acts Doxastic agency Epistemic logic Justification logic dstit logic 

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Notes

Acknowledgements

We would like to thank an anonymous reviewer for her/his useful comments and Claudia Smart for correcting the English. Also, we would like to acknowledge financial support from the Deutsche Forschungsgemeinschaft, DFG, project WA 936/11-1.

References

  1. 1.
    Artemov, S., and E. Nogina, Introducing Justification into Epistemic Logic, Journal of Logic and Computation 15:1059–1073, 2005.CrossRefGoogle Scholar
  2. 2.
    Belnap, N.D., Before Refraining: Concepts for Agency, Erkenntnis 34:137–169, 1991.CrossRefGoogle Scholar
  3. 3.
    Belnap, N.D., M. Perloff, and M. Xu, Facing the Future: Agents and Choices in our Indeterminist World. Oxford UP, New York, 2001.Google Scholar
  4. 4.
    Broersen, J., A complete stit logic for knowledge and action, and some of its applications, in M. Baldoni et al. (eds.), Declarative Agent Languages and Technologies VI, 6th International Workshop, DALT 2008, LNCS vol. 5397, Springer, Berlin, 2009, pp. 47–59.Google Scholar
  5. 5.
    Davidson, D., The Logical Form of Action Sentences, in N. Rescher (ed.), The Logic of Decision and Action, University of Pittsburgh Press, Pittsburgh, 1967, pp. 81–120.Google Scholar
  6. 6.
    van Ditmarsch, H., W. van der Hoek, and B. Kooi, Dynamic Epistemic Logic, Springer, Berlin, 2007.CrossRefGoogle Scholar
  7. 7.
    Egré, P., Question-embedding and factivity, Grazer Philosophische Studien 77:85–125, 2008.CrossRefGoogle Scholar
  8. 8.
    Fagin, R., and Y. Halpern, Belief, Awareness, and Limited Reasoning, Artificial Intelligence 34:39–76, 1988.Google Scholar
  9. 9.
    Goldman, A., A Causal Theory of Knowing, The Journal of Philosophy 64:357–372, 1967.CrossRefGoogle Scholar
  10. 10.
    Harel, D., D. Kozen, and J. Tiuryn, Dynamic Logic, MIT Press, Cambridge, MA, 2000.CrossRefGoogle Scholar
  11. 11.
    Horty, J., An alternative stit operator, unpublished manuscript, Philosophy Department, University of Maryland.Google Scholar
  12. 12.
    Kleene, S.C., Introduction to Metamathematics, North-Holland, Amsterdam, 1952.Google Scholar
  13. 13.
    von Kutschera, F., Bewirken, Erkenntnis 24:253–281, 1986.CrossRefGoogle Scholar
  14. 14.
    Lehrer, K., and T. Paxson, Knowledge: Undefeated justified true belief, The Journal of Philosophy 66:1–22, 1969.CrossRefGoogle Scholar
  15. 15.
    López-Escobar, E.G.K., Refutability and Elementary Number Theory, Indigationes Mathematicae 34:362–374, 1972.CrossRefGoogle Scholar
  16. 16.
    Łos, J., Quelques Remarques, Théorèmes et Problèmes sur les Classes Définissables d’Algèbres, in Mathematical Interpretations of Formal Systems, North-Holland, Amsterdam, 1955, pp. 98–113.Google Scholar
  17. 17.
    Martin-Löf, P., On the Meanings of the Logical Constants and the Justifications of the Logical Laws, (The Siena Lectures) 1983, Nordic Journal of Philosophical Logic 1:11–60, 1996.Google Scholar
  18. 18.
    McCarthy, J., Situations, Actions, and Causal Laws, Technical Report Memo 2, Stanford University Artificial Intelligence Project, Stanford University, 1963; reprinted in M. Minsky (ed.), Semantic Information Processing, MIT Press, Cambridge, MA, 1968, pp. 410–417.Google Scholar
  19. 19.
    McHugh, C., Epistemic Responsibility abd Doxastic Agency, Philosophical Issues. A Supplement to Nous 23:132–157, 2013.CrossRefGoogle Scholar
  20. 20.
    Olkhovikov, G.K., and H. Wansing, An axiom system and a tableau calculus for STIT imagination logic, Journal of Philosophical Logic First Online: 28 January 2017,  https://doi.org/10.1007/s10992-017-9426-1.
  21. 21.
    Olkhovikov, G.K., and H. Wansing, Inference as doxastic agency. Part II: Ramifications and refinements, to appear in Australasian Journal of Logic.Google Scholar
  22. 22.
    Prawitz, D., On the idea of a general proof theory, Synthese 27:63–77, 1974.CrossRefGoogle Scholar
  23. 23.
    Prawitz, D., Explaining deductive inference, in H. Wansing (ed.), Dag Prawitz on Proofs and Meaning, Outstanding Contributions to Logic, Vol. 7, Springer, Dordrecht, 2015, pp. 65–100.Google Scholar
  24. 24.
    Reiter, R., The frame problem in the situation calculus: a simple solution (sometimes) and a completeness result for goal regression, in V. Lifshitz (ed.), Artificial Intelligence and Mathematical Theory of Computation: Papers in Honour of John McCarthy, Academic Press Professional, Inc., San Diego, CA 1991, pp. 359–380.Google Scholar
  25. 25.
    Segerberg, K., J.-J. Meyer, and M. Kracht, The Logic of Action, The Stanford Encyclopedia of Philosophy (Winter 2013 Edition), E.N. Zalta (ed.). http://plato.stanford.edu/archives/win2013/entries/logic-action/.
  26. 26.
    Semmling, C., and H. Wansing, From \(BDI\) and \(stit\) to \(bdi\)-\(stit\) logic, Logic and Logical Philosophy 17:185–207, 2008.CrossRefGoogle Scholar
  27. 27.
    Semmling, C., and H. Wansing, A sound and complete axiomatic system of \(bdi\)-\(stit\) logic, in M. Pelis (ed.), Logica Yearbook 2008, College Publications, London, 2009, pp. 193–210.Google Scholar
  28. 28.
    Semmling, C., and H. Wansing, Reasoning about Belief Revision, in. E.J. Olsson and S. Enqvist (eds.), Belief Revision meets Philosophy of Science, Springer, Dordrecht, 2011, pp. 303–328.Google Scholar
  29. 29.
    Shanahan, M.P., Solving the Frame Problem: A Mathematical Investigation of the Common Sense Law of Inertia, MIT Press, Cambridge, MA, 1997.Google Scholar
  30. 30.
    Smith, N., Frege’s judgement stroke and the conception of Logic as the study of inference not consequence, Philosophy Compass 4:639–665, 2009.CrossRefGoogle Scholar
  31. 31.
    Sundholm, G., “Inference versus consequence” revisited: inference, consequence, conditional, implication, Synthese 187:943–956, 2012.CrossRefGoogle Scholar
  32. 32.
    Thielscher, M., Reasoning Robots, The Art and Science of Programming Robotic Agents, Springer, Dordrecht, 2005.Google Scholar
  33. 33.
    Wansing, H., Doxastic Decisions, Epistemic Justification, and the Logic of Agency, Philosophical Studies 128:201–227, 2006.Google Scholar
  34. 34.
    Wansing, H., Proofs, disproofs, and their duals, in L. Beklemishev, V. Goranko and V. Shehtman (eds.), Advances in Modal Logic 2010, College Publications, London, 2010, pp. 483–505.Google Scholar
  35. 35.
    Wansing, H., Remarks on the logic of imagination. A step towards understanding doxastic control through imagination, Synthese 194:2843–2861, 2017, published online October 2015,  https://doi.org/10.1007/s11229-015-0945-4.
  36. 36.
    Wansing, H., Falsification, natural deduction, and bi-intuitionistic logic, Journal of Logic and Computation 26:425–450, 2016, published online July 2013,  https://doi.org/10.1093/logcom/ext035.
  37. 37.
    Xu, M., Axioms for deliberative STIT, Journal of Philosophical Logic 27:505–525, 1998.CrossRefGoogle Scholar

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Authors and Affiliations

  1. 1.Department of Philosophy IIRuhr University, BochumBochumGermany
  2. 2.Department of PhilosophyUral Federal UniversityEkaterinburgRussia

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