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  1. Semisimples in Varieties of Commutative Integral Bounded Residuated Lattices.Antoni Torrens - 2016 - Studia Logica 104 (5):849-867.
    In any variety of bounded integral residuated lattice-ordered commutative monoids the class of its semisimple members is closed under isomorphic images, subalgebras and products, but it is not closed under homomorphic images, and so it is not a variety. In this paper we study varieties of bounded residuated lattices whose semisimple members form a variety, and we give an equational presentation for them. We also study locally representable varieties whose semisimple members form a variety. Finally, we analyze the relationship with (...)
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  • Inconsistency lemmas in algebraic logic.James G. Raftery - 2013 - Mathematical Logic Quarterly 59 (6):393-406.
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  • Structural Completeness in Substructural Logics.J. S. Olson, J. G. Raftery & C. J. Van Alten - 2008 - Logic Journal of the IGPL 16 (5):453-495.
    Hereditary structural completeness is established for a range of substructural logics, mainly without the weakening rule, including fragments of various relevant or many-valued logics. Also, structural completeness is disproved for a range of systems, settling some previously open questions.
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  • Lattice BCK logics with Modus Ponens as unique rule.Joan Gispert & Antoni Torrens - 2014 - Mathematical Logic Quarterly 60 (3):230-238.
    Lattice BCK logic is the expansion of the well known Meredith implicational logic BCK expanded with lattice conjunction and disjunction. Although its natural axiomatization has three rules named modus ponens, ∨‐rule and ∧‐rule, we show that we can give an equivalent presentation with just modus ponens and ∧‐rule, however it is impossible to obtain an equivalent presentation with modus ponens as unique rule. In this paper we study and characterize all axiomatic extensions of lattice BCK logic with modus ponens as (...)
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  • Free-decomposability in Varieties of Pseudocomplemented Residuated Lattices.D. Castaño, J. P. Díaz Varela & A. Torrens - 2011 - Studia Logica 98 (1-2):223-235.
    In this paper we prove that the free pseudocomplemented residuated lattices are decomposable if and only if they are Stone, i.e., if and only if they satisfy the identity ¬ x ∨ ¬¬ x = 1. Some applications are given.
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