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  1. Wendy MacCaull & Ewa Orłlowska (2002). Correspondence Results for Relational Proof Systems with Application to the Lambek Calculus. Studia Logica 71 (3):389-414.
    We present a general framework for proof systems for relational theories. We discuss principles of the construction of deduction rules and correspondences reflecting relationships between semantics of relational logics and the rules of the respective proof systems. We illustrate the methods developed in the paper with examples relevant for the Lambek calculus and some of its extensions.
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  2. Gerard Allwein & Wendy MacCaull (2001). A Kripke Semantics for the Logic of Gelfand Quantales. Studia Logica 68 (2):173-228.
    Gelfand quantales are complete unital quantales with an involution, *, satisfying the property that for any element a, if a b a for all b, then a a* a = a. A Hilbert-style axiom system is given for a propositional logic, called Gelfand Logic, which is sound and complete with respect to Gelfand quantales. A Kripke semantics is presented for which the soundness and completeness of Gelfand logic is shown. The completeness theorem relies on a Stone style representation theorem for (...)
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  3. Petr Hájek, Arithmetical Hierarchy Iii, Gerard Allwein & Wendy MacCaull (2001). Special Issue: Methods for Investigating Self-Referential Truth Edited by Volker Halbach Volker Halbach/Editorial Introduction 3. Studia Logica 68:421-422.
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  4. Wendy MacCaull (1998). Relational Semantics and a Relational Proof System for Full Lambek Calculus. Journal of Symbolic Logic 63 (2):623-637.
    In this paper we give relational semantics and an accompanying relational proof theory for full Lambek calculus (a sequent calculus which we denote by FL). We start with the Kripke semantics for FL as discussed in [11] and develop a second Kripke-style semantics, RelKripke semantics, as a bridge to relational semantics. The RelKripke semantics consists of a set with two distinguished elements, two ternary relations and a list of conditions on the relations. It is accompanied by a Kripke-style valuation system (...)
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  5. Wendy MacCaull (1996). Kripke Semantics for Logics with BCK Implication. Bulletin of the Section of Logic 25:41-51.
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