Safety and Strong Completeness via Reducibility for Many-Valued Coalgebraic Dynamic Logics

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F25%3A00638085" target="_blank" >RIV/67985807:_____/25:00638085 - isvavai.cz</a>

Result on the web

<a href="https://drops.dagstuhl.de/storage/00lipics/lipics-vol342-calco2025/LIPIcs.CALCO.2025.9/LIPIcs.CALCO.2025.9.pdf" target="_blank" >https://drops.dagstuhl.de/storage/00lipics/lipics-vol342-calco2025/LIPIcs.CALCO.2025.9/LIPIcs.CALCO.2025.9.pdf</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.4230/LIPIcs.CALCO.2025.9" target="_blank" >10.4230/LIPIcs.CALCO.2025.9</a>

Result language

angličtina

Original language name

Safety and Strong Completeness via Reducibility for Many-Valued Coalgebraic Dynamic Logics

Original language description

We present a coalgebraic framework for studying generalisations of dynamic modal logics such as PDL and game logic in which both the propositions and the semantic structures can take values in an algebra A of truth-degrees. More precisely, we work with coalgebraic modal logic via A-valued predicate liftings where A is an FLew-algebra, and interpret actions (abstracting programs and games) as F-coalgebras where the functor F represents some type of A-weighted system. We also allow combinations of crisp propositions with A-weighted systems and vice versa. We introduce coalgebra operations and tests, with a focus on operations which are reducible in the sense that modalities for composed actions can be reduced to compositions of modalities for the constituent actions. We prove that reducible operations are safe for bisimulation and behavioural equivalence, and prove a general strong completeness result, from which we obtain new strong completeness results for 2-valued iteration-free PDL with A-valued accessibility relations when A is a finite chain, and for many-valued iteration-free game logic with many-valued strategies based on finite Lukasiewicz logic.

Czech name

—

Czech description

—

Type

D - Article in proceedings

CEP classification

—

OECD FORD branch

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Project

<a href="/en/project/EH23_025%2F0008724" target="_blank" >EH23_025/0008724: Biography of Fake News with a Touch of AI: Dangerous Phenomenon through the Prism of Modern Human Sciences</a><br>

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2025

Confidentiality

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

Article name in the collection

11th Conference on Algebra and Coalgebra in Computer Science (CALCO 2025)

ISBN

978-3-95977-383-6

ISSN

1868-8969

e-ISSN

—

Number of pages

23

Pages from-to

9

Publisher name

Schloss Dagstuhl – Leibniz-Zentrum für Informatik

Place of publication

Dagstuhl

Event location

Glasgow

Event date

Jun 16, 2025

Type of event by nationality

WRD - Celosvětová akce

UT code for WoS article

001585185500009