Multiple Conclusion Rules in Logics with the Disjunction Property

Alex Citkin

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arXiv · 1509.00642

Multiple Conclusion Rules in Logics with the Disjunction Property

Alex Citkin

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Abstract

We prove that for the intermediate logics with the disjunction property any basis of admissible rules can be reduced to a basis of admissible m-rules (multiple-conclusion rules), and every basis of admissible m-rules can be reduced to a basis of admissible rules. These results can be generalized to a broad class of logics including positive logic and its extensions, Johansson logic, normal extensions of S4, n-transitive logics and intuitionistic modal logics.

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Alex Citkin. 2015-09-02. Multiple Conclusion Rules in Logics with the Disjunction Property. https://arxiv.org/abs/1509.00642

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