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  1. Extension Properties and Subdirect Representation in Abstract Algebraic Logic.Tomáš Lávička & Carles Noguera - 2018 - Studia Logica 106 (6):1065-1095.
    This paper continues the investigation, started in Lávička and Noguera : 521–551, 2017), of infinitary propositional logics from the perspective of their algebraic completeness and filter extension properties in abstract algebraic logic. If follows from the Lindenbaum Lemma used in standard proofs of algebraic completeness that, in every finitary logic, intersection-prime theories form a basis of the closure system of all theories. In this article we consider the open problem of whether these properties can be transferred to lattices of filters (...)
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  • Implicational Logics II: Additional Connectives and Characterizations of Semilinearity.Petr Cintula & Carles Noguera - 2016 - Archive for Mathematical Logic 55 (3-4):353-372.
    This is the continuation of the paper :417–446, 2010). We continue the abstract study of non-classical logics based on the kind of generalized implication connectives they possess and we focus on semilinear logics, i.e. those that are complete with respect to the class of models where the implication defines a linear order. We obtain general characterizations of semilinearity in terms of the intersection-prime extension property, the syntactical semilinearity metarule and the class of finitely subdirectly irreducible models. Moreover, we consider extensions (...)
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  • Constructing Natural Extensions of Propositional Logics.Adam Přenosil - 2016 - Studia Logica 104 (6):1179-1190.
    The proofs of some results of abstract algebraic logic, in particular of the transfer principle of Czelakowski, assume the existence of so-called natural extensions of a logic by a set of new variables. Various constructions of natural extensions, claimed to be equivalent, may be found in the literature. In particular, these include a syntactic construction due to Shoesmith and Smiley and a related construction due to Łoś and Suszko. However, it was recently observed by Cintula and Noguera that both of (...)
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