Proof systems for Moss' coalgebraic logic

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11210%2F14%3A10279707" target="_blank" >RIV/00216208:11210/14:10279707 - isvavai.cz</a>

Výsledek na webu

<a href="http://www.sciencedirect.com/science/article/pii/S0304397514004423" target="_blank" >http://www.sciencedirect.com/science/article/pii/S0304397514004423</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.tcs.2014.06.018" target="_blank" >10.1016/j.tcs.2014.06.018</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Proof systems for Moss' coalgebraic logic

Popis výsledku v původním jazyce

We study Gentzen-style proof theory of the finitary version of the coalgebraic logic introduced by L. Moss. The logic captures the behaviour of coalgebras for a large class of set functors. The syntax of the logic, defined uniformly with respect to a finitary coalgebraic type functor T, uses a single modal operator of arity given by the functor T itself, and its semantics is defined in terms of a relation lifting functor. An axiomatization of the logic, consisting of modal distributive laws, has been given together with an algebraic completeness proof in work of C. Kupke, A. Kurz and Y. Venema. In this paper, following our previous work on structural proof theory of the logic in the special case of the finitary powerset functor, we present cut-free, one- and two-sided sequent calculi for the finitary version of Moss' coalgebraic logic for a general finitary functor T in a uniform way. For the two-sided calculi to be cut-free we use a language extended with the boolean dual of the nabla

Název v anglickém jazyce

Proof systems for Moss' coalgebraic logic

Popis výsledku anglicky

We study Gentzen-style proof theory of the finitary version of the coalgebraic logic introduced by L. Moss. The logic captures the behaviour of coalgebras for a large class of set functors. The syntax of the logic, defined uniformly with respect to a finitary coalgebraic type functor T, uses a single modal operator of arity given by the functor T itself, and its semantics is defined in terms of a relation lifting functor. An axiomatization of the logic, consisting of modal distributive laws, has been given together with an algebraic completeness proof in work of C. Kupke, A. Kurz and Y. Venema. In this paper, following our previous work on structural proof theory of the logic in the special case of the finitary powerset functor, we present cut-free, one- and two-sided sequent calculi for the finitary version of Moss' coalgebraic logic for a general finitary functor T in a uniform way. For the two-sided calculi to be cut-free we use a language extended with the boolean dual of the nabla

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

IN - Informatika

OECD FORD obor

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Projekt

<a href="/cs/project/GPP202%2F11%2FP304" target="_blank" >GPP202/11/P304: Teorie důkazů modální koalgebraické logiky</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2014

Kód důvěrnosti údajů

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

Název periodika

Theoretical Computer Science

ISSN

0304-3975

e-ISSN

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Svazek periodika

neuveden

Číslo periodika v rámci svazku

549

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

25

Strana od-do

36-60

Kód UT WoS článku

000341551400003

EID výsledku v databázi Scopus

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