Skip to main content
SpringerLink
Log in

A Proof-theoretic View of Necessity

  • Published:
Synthese Aims and scope Submit manuscript

Abstract

We give a reading of binary necessity statements of the form “ϕ is necessary for ψ” in terms of proofs. This reading is based on the idea of interpreting such statements as “Every proof of ψ uses ϕ”.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Anderson, A. and N. Belnap: 1975, Entailment, Volume I. Princeton University Press.

  • Anderson, A., N. Belnap, and M. Dunn: 1992, Entailment, Volume II. Princeton University Press.

  • Anderson, C. A.: 1995, ‘Proposition, State of Affairs’, in J. Kim and E. Sosa (eds.), A Companion to Metaphysics, Blackwell, pp. 419–421.

  • J. Alferes J. Leite L.M. Pereira H. Przymusinska T. Przymusinski (2000) ArticleTitle‘Dynamic Updates of Non-monotonic Knowledge Bases’ Journal of Logic Programming. 45 IssueID1–3 43–70 Occurrence Handle10.1016/S0743-1066(99)00065-5

    Article  Google Scholar 

  • Bull, R. and K. Segerberg: 1984, ‘Basic Modal Logic’, in D. Gabbay and F. Guenthner (eds.), Handbook of Philosophical Logic, Volume II, Kluwer, pp. 1–88.

  • Chellas, B.: 1980, Modal Logic: An Introduction, Cambridge University Press.

  • B.J. Copeland (2002) ArticleTitle‘The Genesis of Possible Worlds Semantics’ Journal of Philosophical Logic. 31 IssueID2 99–137 Occurrence Handle10.1023/A:1015273407895

    Article  Google Scholar 

  • J. Kleer Particlede (1986) ArticleTitle‘An Assumption-based TMS’ Artificial Intelligence. 28 127–162 Occurrence Handle10.1016/0004-3702(86)90080-9

    Article  Google Scholar 

  • J. Doyle (1979) ArticleTitle‘A Truth Maintenance System’ Artificial Intelligence. 12 231–272 Occurrence Handle10.1016/0004-3702(79)90008-0

    Article  Google Scholar 

  • Facchinetti, R., M. Krug, and F. Palmer (eds.): 2003, Modality in Contemporary English, de Gruyter.

  • Fagin, R., J. Halpern, Y. Moses, and M. Vardi: 1995, Reasoning about Knowledge, MIT Press.

  • Forster, Th.: 200x, ‘The Modal Aether’, in R. Kahle (ed.), Intensionality, A K Peters.

  • Frege, G.: 1892, ‘Über Sinn und Bedeutung’, Zeitschrift für Philosophie und philosophische Kritik (NF 100), 25–50.

  • Frege, G.: 1952, ‘Sense and Meaning’, in P. Geach and M. Black (eds.), Translations from the Philosophical Writings of Gottlob Frege. Basil Blackwell, 1952. English translation of (Frege, 1892).

  • A. Fuhrmann (1991) ArticleTitle‘Theory Contraction Through Base Contraction’ Journal of Philosophical Logic. 20 175–203 Occurrence Handle10.1007/BF00284974

    Article  Google Scholar 

  • Hansson, S.O.: 1998, ‘Revision of Belief Sets and Belief Bases’, in D. Dubois and H. Prade (eds.), Handbook of Defeasible Reasoning and Uncertainty Management Systems, Volume 3: Belief Change, Kluwer pp. 16–75.

  • G. Hughes M. Cresswell (1968) An Introduction to Modal Logic Methuen London

    Google Scholar 

  • Kahle, R.: 2002, ‘Structured Belief Bases’, Logical and Logical Philosophy 10, 45–58. Special issue of the Workshop LLP held spring 2001 at the TU Dresden.

  • Kracht, M.: 1999, Tools and Techniques in Modal Logic, Volume 142 of Studies in Logic and the Foundations of Mathematics, Elsevier.

  • S. Kripke (1963) ArticleTitle‘Semantical Analysis of Modal Logic I, Normal Propositional Calculi’ Zeitschrift für mathematische Logik und Grundlagen der Mathematik. 9 67–96

    Google Scholar 

  • C. Lewis C. Langford (1932) Symbolic logic The Century Co. New York

    Google Scholar 

  • Moschovakis, Y.: 1994, ‘Sense and Denotation as Algorithm and Value’, in J. Oikkonen and J. Väänänen (eds), Logic Colloquium ’90, Volume 2 of Lecture Notes in Logic, Springer, pp. 210–249.

  • A. Nayak (1994) ArticleTitle‘Foundational Belief Change’ Journal of Philosophical Logic. 23 495–533 Occurrence Handle10.1007/BF01049408

    Article  Google Scholar 

  • Nebel, B.: 1992, ‘Syntax-based Approaches to Belief Revision’, in P. Gärdenfors (ed.), Belief Revision, Cambridge University Press, pp. 52–88.

  • Russell, S. and P. Norvig: 1995, Artificial Intelligence – A Modern Approach, Prentice Hall.

  • Stalnaker, R.: 1995, ‘Modalities and Possible Worlds’, in J. Kim and E. Sosa (eds.), A Companion to Metaphysics, Blackwell, pp. 333–337.

  • Wehmeier, K.: 200x, ‘Descriptions in the Mood’, to appear in R. Kahle (ed.), Intensionality, AK Peters.

Download references

Author information

Authors and Affiliations

  1. CENTRIA, Universidade Nova de Lisboa, Portugal

    Reinhard Kahle

Authors
  1. Reinhard Kahle
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Reinhard Kahle.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kahle, R. A Proof-theoretic View of Necessity. Synthese 148, 659–673 (2006). https://doi.org/10.1007/s11229-004-6293-4

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11229-004-6293-4

Search

Navigation