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  1. The logic of natural language.Fred Sommers - 1982 - New York: Oxford University Press.
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  • What is a syllogism?Timothy J. Smiley - 1973 - Journal of Philosophical Logic 2 (1):136 - 154.
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  • Completeness of an ancient logic.John Corcoran - 1972 - Journal of Symbolic Logic 37 (4):696-702.
    In previous articles, it has been shown that the deductive system developed by Aristotle in his "second logic" is a natural deduction system and not an axiomatic system as previously had been thought. It was also stated that Aristotle's logic is self-sufficient in two senses: First, that it presupposed no other logical concepts, not even those of propositional logic; second, that it is (strongly) complete in the sense that every valid argument expressible in the language of the system is deducible (...)
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  • Formal Logic, or the Calculus of Inference, Necessary and Probable.Augustus de Morgan - 1847 - London, England: Taylor & Walton.
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  • Dynamic Logic.David Harel, Dexter Kozen & Jerzy Tiuryn - 2000 - MIT Press.
    This book provides the first comprehensive introduction to Dynamic Logic. Among the many approaches to formal reasoning about programs, Dynamic Logic enjoys the singular advantage of being strongly related to classical logic. Its variants constitute natural generalizations and extensions of classical formalisms. For example, Propositional Dynamic Logic (PDL) can be described as a blend of three complementary classical ingredients: propositional calculus, modal logic, and the algebra of regular events. In First-Order Dynamic Logic (DL), the propositional calculus is replaced by classical (...)
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  • On the decision problem for two-variable first-order logic.Erich Grädel, Phokion G. Kolaitis & Moshe Y. Vardi - 1997 - Bulletin of Symbolic Logic 3 (1):53-69.
    We identify the computational complexity of the satisfiability problem for FO 2 , the fragment of first-order logic consisting of all relational first-order sentences with at most two distinct variables. Although this fragment was shown to be decidable a long time ago, the computational complexity of its decision problem has not been pinpointed so far. In 1975 Mortimer proved that FO 2 has the finite-model property, which means that if an FO 2 -sentence is satisfiable, then it has a finite (...)
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  • Aristotle'S natural deduction reconsidered.John M. Martin - 1997 - History and Philosophy of Logic 18 (1):1-15.
    John Corcoran’s natural deduction system for Aristotle’s syllogistic is reconsidered.Though Corcoran is no doubt right in interpreting Aristotle as viewing syllogisms as arguments and in rejecting Lukasiewicz’s treatment in terms of conditional sentences, it is argued that Corcoran is wrong in thinking that the only alternative is to construe Barbara and Celarent as deduction rules in a natural deduction system.An alternative is presented that is technically more elegant and equally compatible with the texts.The abstract role assigned by tradition and Lukasiewicz (...)
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  • Three logicians: Aristotle, Leibniz, and Sommers and the syllogistic.George Englebretsen - 1981 - Assen, The Netherlands: Van Gorcum.
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  • Fragments of language.Ian Pratt-Hartmann - 2004 - Journal of Logic, Language and Information 13 (2):207-223.
    By a fragment of a natural language we mean a subset of thatlanguage equipped with semantics which translate its sentences intosome formal system such as first-order logic. The familiar conceptsof satisfiability and entailment can be defined for anysuch fragment in a natural way. The question therefore arises, for anygiven fragment of a natural language, as to the computational complexityof determining satisfiability and entailment within that fragment. Wepresent a series of fragments of English for which the satisfiabilityproblem is polynomial, NP-complete, EXPTIME-complete,NEXPTIME-complete (...)
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  • Augustus De Morgan and the Logic of Relations.Daniel D. Merrill - 1990 - Dordrecht, Netherland: Springer.
    The middle years of the nineteenth century saw two crucial develop ments in the history of modern logic: George Boole's algebraic treat ment of logic and Augustus De Morgan's formulation of the logic of relations. The former episode has been studied extensively; the latter, hardly at all. This is a pity, for the most central feature of modern logic may well be its ability to handle relational inferences. De Morgan was the first person to work out an extensive logic of (...)
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  • Aristotelian syllogisms and generalized quantifiers.Dag Westerståhl - 1989 - Studia Logica 48 (4):577-585.
    The paper elaborates two points: i) There is no principal opposition between predicate logic and adherence to subject-predicate form, ii) Aristotle's treatment of quantifiers fits well into a modern study of generalized quantifiers.
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  • Natural language syntax and first-order inference.David A. McAllester & Robert Givan - 1992 - Artificial Intelligence 56 (1):1-20.
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  • The Logic of Natural Language by Fred Sommers. [REVIEW]P. F. Strawson - 1982 - Journal of Philosophy 79 (12):786-790.
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