arXiv subjects

Robert Rothenberg

Publications and source records attributed to Robert Rothenberg.

3 recordsLinked to original sources

arXiv2013

Translating Labels to Hypersequents for Intermediate Logics with Geometric Kripke Semantics

We give a procedure for translating geometric Kripke frame axioms into structural hypersequent rules for the corresponding intermediate logics in Int^*/Geo that admit weakening, contraction and in some cases, cut. We give a procedure for translating labelled sequents in the corresponding logic to hypersequents that share the same linear models (which correspond to Gödel-Dummett logic). We prove that labelled proofs Int^*/Geo can be translated into hypersequent proofs that may use the linearity rule, which corresponds to the well-known communication rule for Gödel-Dummett logic.

math.LO↗

arXiv2011

Modality for Free: Notes on Adding the Tarskian Möglichkeit to Substructural Logics

We briefly examine the modal formulae that can be derived in Multiplicative Additive Linear Logic (MALL) and some extensions by using Tarksi's extensional modal operators. We also breifly compare this with a substructural form of the modal logic K.

math.LO↗

arXiv2011

Proof-Theoretic Soundness and Completeness

We give a calculus for reasoning about the first-order fragment of classical logic that is adequate for giving the truth conditions of intuitionistic Kripke frames, and outline a proof-theoretic soundness and completeness proof, which we believe is conducive to automation.

cs.LO↗