Lattice logic properly displayed

  • G. Greco*
  • , Alessandra Palmigiano
  • *Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

Abstract

We introduce a proper display calculus for (non-distributive) Lattice Logic which is sound, complete, conservative, and enjoys cut-elimination and subformula property. Properness (i.e. closure under uniform substitution of all parametric parts in rules) is the main interest and added value of the present proposal, and allows for the smoothest Belnap-style proof of cut-elimination, and for the most comprehensive account of axiomatic extensions and expansions of Lattice Logic in a single overarching framework. Our proposal builds on an algebraic and order-theoretic analysis of the semantic environment of lattice logic, and applies the guidelines of the multi-type methodology in the design of display calculi.
Original languageEnglish
Title of host publicationLogic, Language, Information, and Computation (WoLLIC 2017)
Subtitle of host publication24th International Workshop, WoLLIC 2017 - London, UK, July 18-21, 2017 - Proceedings
PublisherSpringer
Pages153-169
Volume10388
EditionLNCS
ISBN (Electronic)978-3-662-55386-2
ISBN (Print)978-3-662-55385-5
DOIs
Publication statusPublished - 2017
Externally publishedYes

Publication series

NameLecture Notes in Computer Science
Volume10388
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Keywords

  • Lattice logic
  • substructural logic
  • algebraic proof theory
  • sequent calculi
  • cut elimination
  • display calculi
  • multi-type calculi

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