On the relative proof complexity of deep inference via atomic flows
نویسنده
چکیده
Abstract. We consider the proof complexity of the minimal complete fragment, KS, of standard deep inference systems for propositional logic. To examine the size of proofs we employ atomic flows, diagrams that trace structural changes through a proof but ignore logical information. As results we obtain a polynomial simulation of versions of Resolution, along with some extensions. We also show that these systems, as well as bounded-depth Frege systems, cannot polynomially simulate KS, by giving polynomial-size proofs of certain variants of the propositional pigeonhole principle in KS.
منابع مشابه
On the relative proof complexity of deep inference via atomic flows
Abstract. We consider the proof complexity of the minimal complete fragment, KS, of standard deep inference systems for propositional logic. To examine the size of proofs we employ atomic flows, diagrams that trace structural changes through a proof but ignore logical information. As results we obtain a polynomial simulation of versions of Resolution, along with some extensions. We also show th...
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ورودعنوان ژورنال:
- Logical Methods in Computer Science
دوره 11 شماره
صفحات -
تاریخ انتشار 2015