On Combined Connectives

Logica Universalis 5 (2):205-224 (2011)

Combined connectives arise in combined logics. In fibrings, such combined connectives are known as shared connectives and inherit the logical properties of each component. A new way of combining connectives (and other language constructors of propositional nature) is proposed by inheriting only the common logical properties of the components. A sound and complete calculus is provided for reasoning about the latter. The calculus is shown to be a conservative extension of the original calculus. Examples are provided contributing to a better understanding of what are the common properties of any two constructors, say disjunction and conjunction
Keywords Combined connectives  common properties of connectives  combined logics
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DOI 10.1007/s11787-011-0032-7
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Fibring: Completeness Preservation.Alberto Zanardo, Amilcar Sernadas & Cristina Sernadas - 2001 - Journal of Symbolic Logic 66 (1):414-439.
Properties of Independently Axiomatizable Bimodal Logics.Marcus Kracht & Frank Wolter - 1991 - Journal of Symbolic Logic 56 (4):1469-1485.
Connectives Stranger Than Tonk.Heinrich Wansing - 2006 - Journal of Philosophical Logic 35 (6):653 - 660.

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