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Journal of Logic, Language and Information

Erschienen in:

25.09.2017

Equivalential Structures for Binary and Ternary Syllogistics

verfasst von: Selçuk Topal

Erschienen in: Journal of Logic, Language and Information | Ausgabe 1/2018

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Abstract

The aim of this paper is to provide a contribution to the natural logic program which explores logics in natural language. The paper offers two logics called \( \mathcal {R}(\forall ,\exists ) \) and \( \mathcal {G}(\forall ,\exists ) \) for dealing with inference involving simple sentences with transitive verbs and ditransitive verbs and quantified noun phrases in subject and object position. With this purpose, the relational logics (without Boolean connectives) are introduced and a model-theoretic proof of decidability for they are presented. In the present paper we develop algebraic semantics (bounded meet semi-lattice) of the logics using congruence theory.

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Black, M. (1945). A new method of presentation of the theory of the syllogism. The Journal of Philosophy, 42(17), 449–455.CrossRef

Bocharov, V. A. (1986). Boolean algebra and syllogism. Synthese, 66(1), 35–54.CrossRef

Corcoran, J. (1972). Completeness of an ancient logic. Journal of Symbolic Logic, 37, 696–702.CrossRef

D’Alfonso, D. (2012). The square of opposition and generalized quantifiers. In J. Y. Beziau & D. Jacquette (Eds.), Around and beyond the square of opposition. Springer.

De Morgan, A. (1847). Formal logic: Or, the calculus of inference, necessary and probable. London: Taylor and Walton.

Font, J. M., & Verdu, V. (1991). Algebraic logic for classical conjunction and disjunction. Studia Logica, 50(3–4), 391–419.CrossRef

Ivanov, N., & Vakarelov, D. (2012). A system of relational syllogistic incorporating full Boolean reasoning. Journal of Logic, Language and Information, 21(4), 433–459.CrossRef

Łukasiewicz, J. (1957). Aristotle’s syllogistic from the standpoint of modern formal logic (2nd ed., 222 p). Oxford University Press.

MacCaull, W., & Vakarelov, D. (2005). Lattice-based paraconsistent logic. In I. Düntsch & M. Winter (Eds.), Proceedings of RelMiCS 8, the 8th international seminar in relational methods in computer science (pp. 155–162).

Moss, L. S. (2008). Completeness theorems for syllogistic fragments. Logics for Linguistic Structures, 29, 143–173.

Moss, L. S. (2010). Syllogistic logics with verbs. Journal of Logic and Computation, 20(4), 947–967.CrossRef

Moss, L. (2011). Syllogistic logic with complements. In J. van Benthem, A. Gupta & E. Pacuit (Eds.), Games, norms and reasons. Synthese library (Studies in epistemology, logic, methodology, and philosophy of science) (Vol. 353). Dordrecht: Springer.

Orłowska, E., & VaKarelov, D. (2005). Lattice-based modal algebras and modal logics. In Logic, methodology and philosophy of science. Proceedings of the 12th international congress (pp. 147–170).

Peirce, C. S. (1880). On the algebra of logic. American Journal of Mathematics, 3(1), 15–57.CrossRef

Pratt-Hartmann, I., & Moss, L. S. (2009). Logics for the relational syllogistic. The Review of Symbolic Logic, 2(04), 647–683.CrossRef

Pratt-Hartmann, I., & Third, A. (2006). More fragments of language. Notre Dame Journal of Formal Logic, 47(2), 151–177.CrossRef

Schroeder, M. J. (2012). Search for syllogistic structure of semantic information. Journal of Applied Non-Classical Logics, 22(1–2), 83–103.CrossRef

Schumann, A. (2006). A lattice for the language of Aristotle’s syllogistic and a lattice for the language of Vasilév’s syllogistic. Logic and Logical Philosophy, 15(1), 17–37.CrossRef

Schumann, A. (2013). On two squares of opposition: The Lesniewskis style formalization of synthetic propositions. Acta Analytica, 28(1), 71–93.CrossRef

Schumann, A., & Akimova, L. (2015). Syllogistic system for the propagation of parasites. The case of Schistosomatidae (Trematoda: Digenea). Studies in Logic, Grammar and Rhetoric, 40(53), 303–319.

Sotirov, V. (1999). Arithmetizations of syllogistic a la Leibniz. Journal of Applied Non-Classical Logics, 9(2–3), 387–405.CrossRef

Vakarelov, D. (1977). Lattices related to Post algebras and their applications to some logical systems. Studia Logica, 36(1), 89–107.CrossRef

Van Benthem, J. (1984). Questions about quantifiers. Journal of Symbolic Logic, 49(2), 443–466.CrossRef

Van Benthem, J. F. (1985). Generalized quantifiers in natural language, no. 4. Berlin: Walter de Gruyter.

Van Eijck, J. (1985). Generalized quantifiers and traditional logic. In J. van Benthem & A. ter Meulen (Eds.), Generalized quantifiers, theory and applications. Dordrecht: Foris.

Van Eijck, J. (2005a). Natural logic for natural language. Logic, language, and computation (pp. 216–230). Berlin: Springer.

Van Eijck, J. (2005b). Syllogistics \(=\) monotonicity \( symmetry \) existential import. preprint May.

Westerståhl, D. (2005). On the Aristotelian square of opposition. Kapten Mnemos Kolumbarium, en festskrift med anledning av Helge Malmgrens 60-årsdag.

Titel: Equivalential Structures for Binary and Ternary Syllogistics
verfasst von: Selçuk Topal
Publikationsdatum: 25.09.2017
Verlag: Springer Netherlands
Erschienen in: Journal of Logic, Language and Information / Ausgabe 1/2018
Print ISSN: 0925-8531
Elektronische ISSN: 1572-9583
DOI: https://doi.org/10.1007/s10849-017-9260-4

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