References
Barnes, R. F. and R. D. Gumb: 1979, ‘The Completeness of Presupposition Free Tense Logic’, Zeitschrift für Mathematische Logik und Grundlagen der Mathematik (hereafter ZMLGM) 25, 193–208.
Boolos, G.: 1979 The Unprovability of Consistency. Cambridge: Cambridge University Press.
Fine, K.: 1979 ‘Failures of the Interpolation Lemma in Quantified Modal Logic’, Journal of Symbolic Logic, 44 201–206.
Fine, K.: 1978, ‘Model Theory for Modal Logic, Part I-The De Re/De Dicto Distinction’, Journal of Philosophical Logic, 7 125–156.
Gabbay, D.: 1975 ‘Modal Theory for Tense Logics’, Annals of Mathematical Logic 8, 185–236.
Gumb, R. D., ‘Comments on Probabilistic Semantics’, [15]
Gumb, R. D. ‘The Craig-Lyndon Interpolation Lemma for (Free) Intuitionistic Logic with Equality’, [15]
Gumb, R. D.: 1979, Evolving Theories. New York: Haven, 1979.
Gumb, R. D.: 1984, ‘An Extended Joint Consistency Theorem for a Family of Free Modal Logics with Equality’, Journal of Symbolic Logic, 49.
Gumb, R. D.: 1972, Rule-Governed Linguistic Behavior, Mouton, The Hague.
Gumb, R. D. ‘A Translation of (Free) Intuitionistic Logic with Equality into Free S4 with Equality and Increasing Domains’, [15]
Harper, W. L.: ‘A Conditional Belief Semantics for Free Quantificational Logic with Identity’, in [15]
Leblanc, H.: 1976, Truth-Value Semantics North Holland, Amsterdam.
Leblanc, H. and Gumb, R. D.: ‘Completeness and Soundness Proofs for Three Brands of Intuitionistic Logic’, in [15]
Leblanc, H., Gumb, R. D., and Stern, R. (eds.): 1983, Essays in Semantics and Epistemology, Haven, New York.
Lemmon, E. J.: 1977, An Introduction to Modal Logic, Basil Blackwell, Oxford.
Makinson, D. C.: 1966, ‘On Some Completeness Theorems in Modal Logic’ ZMLGM 12 379–384.
Sahlqvist, H.: 1975, ‘Completeness and Correspondence in the First and Second Order Semantics for Modal Logic’ in S. Kanger (ed.), Proceedings of the Third Scandinavian Logic Symposium, Uppsala 1973, North Holland, Amsterdam.
Weaver, G. and R. D. Gumb' 1982, ‘First Order Properties of Relations with the Monotonic Closure Property’, ZMLGM, 28, 1–5.
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This paper summarizes work performed under a 1978–80 grant from the Foundation for the Advancement of Interdisciplinary Studies for research on evolving theories, intensional logics, probabilistic semantics, and applications of them to the semantics of natural languages. I have been interested in applications of logic to the semantics of natural languages for some time [10, p. 104]; needless to say, applications of the systems discussed in this paper stand in need for further articulation. I would like to express my appreciation to my friends Bob Barnes, Hugues Leblanc, and George Weaver for having worked with me over the past few years.
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Gumb, R.D. “Conservative” Kripke closures. Synthese 60, 39–49 (1984). https://doi.org/10.1007/BF00485617
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DOI: https://doi.org/10.1007/BF00485617