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Proof Systems for the Coalgebraic Cover Modality

Result description

We investigate an alternative presentation of classical and positive modal logic where the coalgebraic cover modality is taken as primitive. For each logic, we present a sound and complete Hilbert-style axiomatization. Moreover, we give a two-sided soundand complete sequent calculus for the negation-free language, and for the language with negation we provide a one-sided sequent calculus which is sound, complete and cut-free.

Keywords

modal logicderivation systemcoalgebracoalgebraic modalityGentzen calculuscompleteness

The result's identifiers

Alternative languages

  • Result language

    angličtina

  • Original language name

    Proof Systems for the Coalgebraic Cover Modality

  • Original language description

    We investigate an alternative presentation of classical and positive modal logic where the coalgebraic cover modality is taken as primitive. For each logic, we present a sound and complete Hilbert-style axiomatization. Moreover, we give a two-sided soundand complete sequent calculus for the negation-free language, and for the language with negation we provide a one-sided sequent calculus which is sound, complete and cut-free.

  • Czech name

    Důkazové systémy pro koalgebraickou modalitu

  • Czech description

    Článek zkoumá alternativní prezentaci klasické a positivní modální logiky v jazyce s koalgebraickou modalitou pokrytí jako primitivním operátorem. Pro obě logiky prezentujeme korektní a úplnou hilbertovskou axiomatizaci, korektní a úplný sekventový kalkul s oboustrannými sekventy a korektní, úplný a bezřezový sekventový kalkul s jednostrannými sekventy.

Classification

  • Type

    D - Article in proceedings

  • CEP classification

    BA - General mathematics

  • OECD FORD branch

Result continuities

Others

  • Publication year

    2008

  • Confidentiality

    S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Data specific for result type

  • Article name in the collection

    Advances in Modal Logic

  • ISBN

    978-1-904987-68-0

  • ISSN

  • e-ISSN

  • Number of pages

    21

  • Pages from-to

  • Publisher name

    College Publications

  • Place of publication

    London

  • Event location

    Nancy

  • Event date

    Sep 9, 2008

  • Type of event by nationality

    WRD - Celosvětová akce

  • UT code for WoS article

Result type

D - Article in proceedings

D

CEP

BA - General mathematics

Year of implementation

2008