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Non-deterministic Matrices for Semi-canonical Deduction Systems

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1 Author(s)
Lahav, O. ; Sch. of Comput. Sci., Tel Aviv Univ., Tel-Aviv, Israel

We use non-deterministic finite-valued matrices to provide uniform effective semantics for a large family of logics, emerging from "well-behaved" sequent systems in which the cut rule and/or the identity-axiom are not present. We exploit this semantics to obtain important proof-theoretic properties of systems of this kind, such as cut-admissibility. Non-determinism is shown to be essential for these purposes, since the studied logics cannot be characterized by ordinary finite-valued matrices. Our results shed light on the dual semantic roles of the cut rule and the identity-axiom, showing that they are crucial for having deterministic (truth-functional) finite-valued semantics.

Published in:

Multiple-Valued Logic (ISMVL), 2012 42nd IEEE International Symposium on

Date of Conference:

14-16 May 2012