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  1. Decidability of Fluted Logic with Identity.William C. Purdy - 1996 - Notre Dame Journal of Formal Logic 37 (1):84-104.
    Fluted logic is the restriction of pure predicate logic to formulas in which variables play no essential role. Although fluted logic is significantly weaker than pure predicate logic, it is of interest because it seems closely to parallel natural logic, the logic that is conducted in natural language. It has been known since 1969 that if conjunction in fluted formulas is restricted to subformulas of equal arity, satisfiability is decidable. However, the decidability of sublogics lying between this restricted (homogeneous) fluted (...)
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  • Quine's 'limits of decision'.William C. Purdy - 1999 - Journal of Symbolic Logic 64 (4):1439-1466.
    In a 1969 paper, Quine coined the term 'limits of decision'. This term evidently refers to limits on the logical vocabulary of a logic, beyond which satisfiability is no longer decidable. In the same paper. Quine showed that not only monadic formulas, but homogeneous k-adic formulas for arbitrary k lie on the decidable side of the limits of decision. But the precise location of the limits of decision has remained an open question. The present paper answers that question. It addresses (...)
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  • Fluted formulas and the limits of decidability.William C. Purdy - 1996 - Journal of Symbolic Logic 61 (2):608-620.
    In the predicate calculus, variables provide a flexible indexing service which selects the actual arguments to a predicate letter from among possible arguments that precede the predicate letter (in the parse of the formula). In the process of selection, the possible arguments can be permuted, repeated (used more than once), and skipped. If this service is withheld, so that arguments must be the immediately preceding ones, taken in the order in which they occur, the formula is said to be fluted. (...)
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  • The fluted fragment with transitive relations.Ian Pratt-Hartmann & Lidia Tendera - 2022 - Annals of Pure and Applied Logic 173 (1):103042.
    The fluted fragment is a fragment of first-order logic (without equality) in which, roughly speaking, the order of quantification of variables coincides with the order in which those variables appear as arguments of predicates. It is known that this fragment has the finite model property. We consider extensions of the fluted fragment with various numbers of transitive relations, as well as the equality predicate. In the presence of one transitive relation (together with equality), the finite model property is lost; nevertheless, (...)
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  • Fred Sommers’ Contributions to Formal Logic.George Englebretsen - 2016 - History and Philosophy of Logic 37 (3):269-291.
    Fred Sommers passed away in October of 2014 in his 92nd year. Having begun his teaching at Columbia University, he eventually became the Harry A. Wolfson Chair in Philosophy at Brandeis University, where he taught from 1963 to 1993. During his long and productive career, Sommers authored or co-authored over 50 books, articles, reviews, etc., presenting his ideas on numerous occasions throughout North America and Europe. His work was characterized by a commitment to the preservation and application of historical insights (...)
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  • Traditional Logic and Computational Thinking.J. -Martín Castro-Manzano - 2021 - Philosophies 6 (1):12.
    In this contribution, we try to show that traditional Aristotelian logic can be useful (in a non-trivial way) for computational thinking. To achieve this objective, we argue in favor of two statements: (i) that traditional logic is not classical and (ii) that logic programming emanating from traditional logic is not classical logic programming.
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  • El pons scholastiscorum.J. Martín Castro Manzano & Jorge Medina-Delgadillo - 2020 - Dianoia 65 (85):55-72.
    Resumen En esta contribución ofrecemos una interpretación del pons asinorum que se basa en una lógica de términos contemporánea. Esto nos permite revitalizar la idea del pons asinorum para generar el -políticamente correcto- pons scholasticorum, una versión terminística del pons asinorum que conecta la inventio medii con el dictum de omni et nullo.In this contribution we offer an interpretation of the pons asinorum by using a contemporary term logic. This interpretation allows us to revitalize the concept of the pons asinorum (...)
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  • The completeness of a predicate-functor logic.John Bacon - 1985 - Journal of Symbolic Logic 50 (4):903-926.
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