Abstract
In this paper syllogistic logic is extended first to full propositional logic, and then an interesting fragment of predicate logic that includes relations.
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References
van Benthem, J.: A linguistic turn: New directions in logic. In: Marcus, R., et al. (eds.) Logic, Methodology and Philosophy of Science, Salzburg, pp. 205–240 (1983)
van Benthem, J., et al.: Logic in Action, Amsterdam (to appear)
Burdidan, J.: Tractatus de Consequentiis. In: Hubien, H. (ed.) Johannis Buridani tractatus de consequentiis, critical edn. Publications universitaires, Louvain (1976)
Geach, P.: Reference and Generality. An Examination of Some Medieval and Modern Theories. Cornell University Press, Oxford (1962)
Geurts, B., van der Slik, F.: Monotonicity and processing load. Journal of Semantics 22, 97–117 (2005)
Goodstein, R.L.: Boolean Algebra. Pergamon Press, London (1963)
Leibniz, G.: A specimen of a demonstrated inference from the direct to the oblique. In: Parkinson (ed.) Leibniz. Logical Papers, pp. 88–89 (1966a)
Leibniz, G.: A paper on some logical difficulties. In: Parkinson (ed.) Leibniz. Logical Papers, pp. 115–121 (1966b)
Lukasiewicz, J.: Aristotle’s Sollogistic from the standpoint of Modern Formal Logic. Garland Publishers, New York (1957)
Lyndon, R.C.: Properties preserved under homomorphism. Pacific Journal of Mathematics 9, 142–154 (1959)
McIntosh, C.: Appendix F. In: Sommers, F. (ed.) The Logic of Natural Language, pp. 387–425. Clarendon Press, Oxford (1982)
Mortimer, M.: On language with two variables. Zeitschrift für Mathematische Logik und Grundlagen der Mathematik 21, 135–140 (1975)
Murphee, W.A.: The numerical syllogism and existential presupposition. Notre Dame Journal of Formal Logic 38, 49–64 (1997)
Pratt-Hartmann, I.: No syllogisms for the numerical syllogistic. In: Grumberg, O., et al. (eds.) Francez Festschrifft. LNCS, vol. 5553, pp. 192–203. Springer, Berlin (2009)
Pratt-Hartmann, I., Moss, L.: Logics for the Relational Syllogistics. Review of Symbolic Logic (to appear)
Purdy, W.: Fluted formulas and the limits of decidability. Journal of Symbolic Logic 61, 608–620 (1996)
Quine, W.V.O.: Algebraic logic and predicate functors, pp. 283–307 (1976)
Russell, B.: A critical exposition of the Philosophy of Leibniz. Cambridge University Press, Oxford (1900)
Sanchez, V.: Studies on Natural Logic and Categorial Grammar, PhD thesis, Universiteit van Amsterdam (1991)
Sherpherdson, J.: On the interpretation of Aristotelian syllogistic. Journal of Symbolic Logic 21, 131–147 (1956)
Sommers, F.: The Logic of Natural Language. Clarendon Press, Oxford (1982)
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van Rooij, R. (2010). Extending Syllogistic Reasoning. In: Aloni, M., Bastiaanse, H., de Jager, T., Schulz, K. (eds) Logic, Language and Meaning. Lecture Notes in Computer Science(), vol 6042. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14287-1_13
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DOI: https://doi.org/10.1007/978-3-642-14287-1_13
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