Multiple Conclusion Rules in Logics with the Disjunction Property

2015/09/02 by Alex Citkin, Citkin, Alex
Mathematics · #03B55 #FOS: Mathematics #Logic (math.LO) #math.LO #msc:03B55

paper · pdf · doi:10.48550/arxiv.1509.00642

arxiv created 2015/09/02 · arxiv updated 2015/09/03

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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