Abstract
Considerable work has been undertaken on the neighbourhood semantics for S1 but little on S0.9. In this paper we use tableaux to represent the model-set / model-system neighbourhood semantics for both S1 and S0.9 and some other nearby systems. S0.9 is often seen as a more “natural” logic in the sequence: S0.5 to S0.9 to S2 to S3 than S1. This perception is discussed in terms of the interpretation of alternate worlds or model-sets.
Keywords
The semantics for S1 herein resulted from discussions with Graham Priest and Jerry Seligman in 2000.
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References
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Cresswell, Maxwell, J.: S1 is not so simple, Modality, Morality and Belief: Essays in Honour of Ruth Barcan Marcus, Sinnott-Armstrong, W., Raffman, D. Asher, N. (eds.) Cambridge University Press, Cambridge, pp. 29-40
Girle, Roderic, A.: S1 ≠ S0.9. Notre Dame. Journal of Formal Logic XVI (3), 339–344 (1975)
Girle, Roderic, A.: Logical Fiction: Real vs. Ideal, Pacific Rim International Conference on Artificial Intelligence, Hing-Yan, L. (ed.) Singapore, Nov 22-27 (1998)
Girle, Rod.: Modal Logics and Philosophy, Acumen, London (2000)
Hintikka, J.J.K.: Modality and Quantification. Theoria 27, 119–128 (1961)
Hintikka, J.J.K.: Knowledge and Belief. Cornell University Press, Ithaca (1962)
Lemmon, E.J.: Is there only one correct system of modal logic? Aristotelian Society Supplementary XXXIII, 23–40 (1959)
Scotch, Peter, K.: Remarks on the semantics of non-normal logics. Topoi 3, 85–90 (1984)
Sylvan, Richard.: Relational Semantics for all Lewis, Lemmon and Feys modal Logics, and most notably for systems between S0.3∘ and S1. The. Journal of Non.-classical Logic 6(99), 19–40 (1989)
Chellas, Brian F. and Segerberg, Krister, Modal Logics in the Vicinity of S1, Notre Dame Journal of Formal Logic, vol. 37(1) pp. 1–24 (1996)
Cresswell, Maxwell J.: S1 is not so simple, Modality, Morality and Belief: Essays in Honour of Ruth Barcan Marcus, Eds. Walter Sinnott-Armstrong, Diana Raffman, and Nicholas Asher, Cambridge University Press, Cambridge, pp. 29-40.
Girle, Roderic A., S1 S0.9, Notre Dame Journal of Formal Logic, Vol. XVI, Number 3, pp. 339–344 (July 1975)
Girle, Roderic, A.: Logical Fiction: Real vs. Ideal, Pacific Rim. In: International Conference on Artificial Intelligence, Ed. Lee Hing-Yan, Singapore, (November 22-27, 1998)
Girle, Rod.: Modal Logics and Philosophy, Acumen, London, (2000)
Hintikka, J.J.K.: Modality and Quantification, Theoria, Vol. 27, pp. 119–128 (1961)
Hintikka, J.J.K.: Knowledge and Belief, Cornell University Press, Ithaca (1962)
Lemmon, E.J. 1959. “Is there only one correct system of modal logic?” Aristotelian Society Supplementary vol. XXXIII, 23-40
Scotch, Peter K.: Remarks on the semantics of non-normal logics, Topoi, vol. 3, pp. 85–90 (1984)
Sylvan, Richard.: Relational Semantics for all Lewis, Lemmon and Feys modal Logics, and most notably for systems between S0.3 and S1, The Journal of Non-classical Logic, Vol. 6(99), pp. 19–40 (1989)
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Girle, R.A. (2007). The Neighbourhood of S0.9 and S1. In: Olivetti, N. (eds) Automated Reasoning with Analytic Tableaux and Related Methods. TABLEAUX 2007. Lecture Notes in Computer Science(), vol 4548. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73099-6_11
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DOI: https://doi.org/10.1007/978-3-540-73099-6_11
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