2020/07/14 by Fischer, Martin, Nicolai, Carlo, Fernandez, Pablo Dopico
#FOS: Computer and information sciences #FOS: Mathematics #Logic (math.LO) #Logic in Computer Science (cs.LO)
paper · doi:10.48550/arxiv.2007.07188
Questions concerning the proof-theoretic strength of classical versus non-classical theories of truth have received some attention recently. A particularly convenient case study concerns classical and nonclassical axiomatizations of fixed-point semantics. It is known that nonclassical axiomatizations in four- or three-valued logics are substantially weaker than their classical counterparts. In this paper we consider the addition of a suitable conditional to First-Degree Entailment -- a logic recently studied by Hannes Leitgeb under the label `HYPE'. We show in particular that, by formulating the theory PKF over HYPE one obtains a theory that is sound with respect to fixed-point models, while being proof-theoretically on a par with its classical counterpart KF. Moreover, we establish that also its schematic extension -- in the sense of Feferman -- is as strong as the schematic extension of KF, thus matching the strength of predicative analysis.