George Metcalfe

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We present two embeddings of in nite-valued Lukasiewicz logic L into Meyer and Slaney’s abelian logic A, the logic of lattice-ordered abelian groups. We give new analytic proof systems for A and use the embeddings to derive corresponding systems for L. These include: hypersequent calculi for A and L and terminating versions of these calculi; labelled single(More)
We provide uniform and invertible logical rules in a framework of relational hypersequents for the three fundamental t-norm based fuzzy logics i.e., Łukasiewicz logic, Gödel logic, and Product logic. Relational hypersequents generalize both hypersequents and sequents-of-relations. Such a framework can be interpreted via a particular class of dialogue games(More)
In this work we present goal-directed calculi for the GödelDummett logic LC and its finite-valued counterparts, LCn (n ≥ 2). We introduce a terminating hypersequent calculus for the implicational fragment of LC with local rules and a single identity axiom. We also give a labelled goal-directed calculus with invertible rules and show that it is co-NP.(More)
Axiomatizations are presented for fuzzy logics characterized by uninorms continuous on the half-open real unit interval [0, 1), generalizing the continuous t-norm based approach of Hájek. Basic uninorm logic BUL is defined and completeness is established with respect to algebras with lattice reduct [0, 1] whose monoid operations are uninorms continuous on(More)
Extensions of monoidal t-norm logic MTL and related fuzzy logics with truth stresser modalities such as globalization and “very true” are presented here both algebraically in the framework of residuated lattices and proof-theoretically as hypersequent calculi. Completeness with respect to standard algebras based on t-norms, embeddings between logics,(More)
In this work we investigate bounded Lukasiewicz logics, characterised as the intersection of the k-valued Lukasiewicz logics for k = 2, . . . , n (n ≥ 2). These logics formalise a generalisation of Ulam’s game with applications in Information Theory. Here we provide an analytic proof calculus G LBn for each bounded Lukasiewicz logic, obtained by adding a(More)