Switch to: References

Add citations

You must login to add citations.
  1. Nested sequents for intermediate logics: the case of Gödel-Dummett logics.Tim S. Lyon - 2023 - Journal of Applied Non-Classical Logics 33 (2):121-164.
    We present nested sequent systems for propositional Gödel-Dummett logic and its first-order extensions with non-constant and constant domains, built atop nested calculi for intuitionistic logics. To obtain nested systems for these Gödel-Dummett logics, we introduce a new structural rule, called the linearity rule, which (bottom-up) operates by linearising branching structure in a given nested sequent. In addition, an interesting feature of our calculi is the inclusion of reachability rules, which are special logical rules that operate by propagating data and/or checking (...)
    Download  
     
    Export citation  
     
    Bookmark  
  • Display to Labeled Proofs and Back Again for Tense Logics.Agata Ciabattoni, Tim Lyon, Revantha Ramanayake & Alwen Tiu - 2021 - ACM Transactions on Computational Logic 22 (3):1-31.
    We introduce translations between display calculus proofs and labeled calculus proofs in the context of tense logics. First, we show that every derivation in the display calculus for the minimal tense logic Kt extended with general path axioms can be effectively transformed into a derivation in the corresponding labeled calculus. Concerning the converse translation, we show that for Kt extended with path axioms, every derivation in the corresponding labeled calculus can be put into a special form that is translatable to (...)
    Download  
     
    Export citation  
     
    Bookmark   2 citations  
  • Nested Sequents for Intuitionistic Modal Logics via Structural Refinement.Tim Lyon - 2021 - In Anupam Das & Sara Negri (eds.), Automated Reasoning with Analytic Tableaux and Related Methods: TABLEAUX 2021. 93413 Cham, Germany: pp. 409-427.
    We employ a recently developed methodology -- called "structural refinement" -- to extract nested sequent systems for a sizable class of intuitionistic modal logics from their respective labelled sequent systems. This method can be seen as a means by which labelled sequent systems can be transformed into nested sequent systems through the introduction of propagation rules and the elimination of structural rules, followed by a notational translation. The nested systems we obtain incorporate propagation rules that are parameterized with formal grammars, (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  • Refining Labelled Systems for Modal and Constructive Logics with Applications.Tim Lyon - 2021 - Dissertation, Technischen Universität Wien
    This thesis introduces the "method of structural refinement", which serves as a means of transforming the relational semantics of a modal and/or constructive logic into an 'economical' proof system by connecting two proof-theoretic paradigms: labelled and nested sequent calculi. The formalism of labelled sequents has been successful in that cut-free calculi in possession of desirable proof-theoretic properties can be automatically generated for large classes of logics. Despite these qualities, labelled systems make use of a complicated syntax that explicitly incorporates the (...)
    Download  
     
    Export citation  
     
    Bookmark   3 citations