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  1.  21
    Full Lambek Calculus in Natural Deduction.Ernst Zimmermann - 2010 - Mathematical Logic Quarterly 56 (1):85-88.
    A formulation of Full Lambek Calculus in the framework of natural deduction is given.
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  2.  27
    Predicate Logical Extensions of Some Subintuitionistic Logics.Ernst Zimmermann - 2009 - Studia Logica 91 (1):131-138.
    The paper presents predicate logical extensions of some subintuitionistic logics. Subintuitionistic logics result if conditions of the accessibility relation in Kripke models for intuitionistic logic are dropped. The accessibility relation which interprets implication in models for the propositional base subintuitionistic logic considered here is neither persistent on atoms, nor reflexive, nor transitive. Strongly complete predicate logical extensions are modeled with a second accessibility relation, which is a partial order, for the interpretation of the universal quantifier.
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  3.  30
    A Predicate Logical Extension of a Subintuitionistic Propositional Logic.Ernst Zimmermann - 2002 - Studia Logica 72 (3):401-410.
    We develop a predicate logical extension of a subintuitionistic propositional logic. Therefore a Hilbert type calculus and a Kripke type model are given. The propositional logic is formulated to axiomatize the idea of strategic weakening of Kripke''s semantic for intuitionistic logic: dropping the semantical condition of heredity or persistence leads to a nonmonotonic model. On the syntactic side this leads to a certain restriction imposed on the deduction theorem. By means of a Henkin argument strong completeness is proved making use (...)
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  4.  29
    Elementary Definability and Completeness in General and Positive Modal Logic.Ernst Zimmermann - 2003 - Journal of Logic, Language and Information 12 (1):99-117.
    The paper generalises Goldblatt's completeness proof for Lemmon–Scott formulas to various modal propositional logics without classical negation and without ex falso, up to positive modal logic, where conjunction and disjunction, andwhere necessity and possibility are respectively independent.Further the paper proves definability theorems for Lemmon–Scottformulas, which hold even in modal propositional languages without negation and without falsum. Both, the completeness theorem and the definability theoremmake use only of special constructions of relations,like relation products. No second order logic, no general frames are (...)
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  5.  2
    Rationalitätsgrade in Schwachen Belief-Logiken.Ernst Zimmermann - 1997 - In Julian Nida-Rümelin & Georg Meggle (eds.), Analyomen 2, Volume I: Logic, Epistemology, Philosophy of Science. De Gruyter. pp. 183-194.
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