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  1. William C. Purdy (2006). Inexpressiveness of First-Order Fragments. Australasian Journal of Logic 4:1-12.
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  2. William C. Purdy (2002). Complexity and Nicety of Fluted Logic. Studia Logica 71 (2):177 - 198.
    Fluted Logic is essentially first-order predicate logic deprived of variables. The lack of variables results in reduced expressiveness. Nevertheless, many logical problems that can be stated in natural language, such as the famous Schubert's Steamroller, can be rendered in fluted logic. Further evidence of the expressiveness of fluted logic is its close relation to description logics. Already it has been shown that fluted logic is decidable and has the finite-model property. This paper shows that fluted logic has the exponential-model property (...)
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  3. William C. Purdy (2002). Review: Fred Sommers, George Englebretsen, An Invitation to Formal Reasoning. The Logic of Terms. [REVIEW] Bulletin of Symbolic Logic 8 (1):97-100.
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  4. F. Sommers, G. Englebretsen & William C. Purdy (2002). REVIEWS-An Invitation to Formal Reasoning. Bulletin of Symbolic Logic 8 (1):97-99.
     
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  5. William C. Purdy (1999). Quine's 'Limits of Decision'. 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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  6. William C. Purdy (1996). Fluted Formulas and the Limits of Decidability. 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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  7. William C. Purdy (1996). Decidability of Fluted Logic with Identity. 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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  8. William C. Purdy (1992). A Variable-Free Logic for Mass Terms. Notre Dame Journal of Formal Logic 33 (3):348-358.
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  9. William C. Purdy (1992). On the Question ``Do We Need Identity?''. Notre Dame Journal of Formal Logic 33 (4):593-603.
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  10. William C. Purdy (1991). A Logic for Natural Language. Notre Dame Journal of Formal Logic 32 (3):409-425.
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  11. William C. Purdy (1991). Surface Reasoning. Notre Dame Journal of Formal Logic 33 (1):13-36.
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