Abstract
We give a simple sequent calculus presentation of R.B. Angell’s logic of analytic containment, recently championed by Kit Fine as a plausible logic of partial content.
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Anderson, A. R., and N. D. Belnap, Entailment: The Logic of Relevance and Neccessity, Vol. I. Princeton University Press, 1975.
Angell, R., Three Systems of First Degree Entailment, Journal of Symbolic Logic 47: 147, 1977.
Angell, R., Analytic truth-tables, Journal of Symbolic Logic 46(3): 677, 1981.
Angell, R., Deducibility, Entailment and Analytic Containment. In J. Norman and R. Sylvan (Eds.), Directions in Relevant Logic, Chapter 8, Dordrecht: Kluwer, 1989, pp. 119–144.
Belnap, N. D., Rescher’s Hypothetical Reasoning: An Amendment. In E. Sosa (Ed.), The Philosophy of Nicholas Rescher: Discussion and Replies, D. Reidel, 1979, pp. 19–28.
Brady, R. T., Universal Logic. Number 109 in csli Lecture Notes. Stanford: csli Publications, 2006.
Correia, F., Semantics for Analytic Containment, Studia Logica 77: 87–104, 2004.
Correia, F., Grounding and Truth-Functions, Logique Et Analyse 211: 251–279, 2010.
Correia, F., On the Logic of Factual Equivalence, The Review of Symbolic Logic 9(1): 103–122, 2016.
Daniels, C., A Story Semantics for Implication, Notre Dame Journal of Formal Logic 27: 221–246, 1986.
Deutsch, H., Paraconsistent Analytic Implication, Journal of Philosophical Logic 13: 1–11, 1984.
Dragalin, A., Mathematical Intuitionism. Introduction to Proof Theory. Providence: American Mathematical Society, 1988.
Ferguson, T. M., Cut-down operations on bilattices, In Proceedings of the 45th International Symposium on Multiple-Valued Logic (IEEE 2015), Los Alamitos, CA, IEEE Computer Society Press, 2015, pp. 163–172.
Ferguson, T. M., Faulty Belnap computers and subsystems of FDE, Journal of Logic and Computation 26(5): 1617–1636, 2016.
Fine, K., Analytic Implication, Notre Dame Journal of Formal Logic 27(2): 169–179, 1986.
Fine, K., Guide to ground. In F. Correia and B. Schnieder (Eds.), Metaphysical Grounding, pp. 37–80. Cambridge University Press, 2012 pp. 37–80.
Fine, K., A Note on Partial Content, Analysis 73(3): 413–419, 2013.
Fine, K., Truth-Maker Semantics for Intuitionistic Logic, Journal of Philosophical Logic 43: 549–577, 2014.
Fine, K., Angellic Content, Journal of Philosophical Logic 45(2): 199–226, 2016.
van Fraassen, B., Facts and Tautological Entailments, The Journal of Philosophy 66: 477–487, 1969.
Humberstone, L., False Though Partly True – An Experiment in Logic, Journal of Philosophical Logic 32: 613–665, 2003.
Negri, S., and J. von Plato, Structural Proof Theory, Cambridge University Press, Cambridge, 2001.
Paoli, F., Substructural Logics: A Primer, Kluwer Academic Publishers, 2002.
Parry, W., Ein Axiomensystem für eine neue Art von Implikation (analytische Implikation), Ergebnisse eines mathematischen Kolloquiums 4: 5–6, 1933.
Parry, W., Comparison of Entailment Theories, Journal of Symbolic Logic 37(2): 441–442, 1972.
Pynko, A. P., Characterizing Belnap’s Logic via De Morgan’s Laws, Mathematical Logic Quarterly 41: 442–454, 1995.
Troelstra, A., and H. Schwichtenberg, Basic Proof Theory. Cambridge: Cambridge University Press, 2000.
Yablo, S., Aboutness. Princeton: Princeton University Press, 2014.
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French, R. A Simple Sequent Calculus for Angell’s Logic of Analytic Containment. Stud Logica 105, 971–994 (2017). https://doi.org/10.1007/s11225-017-9719-y
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DOI: https://doi.org/10.1007/s11225-017-9719-y