Untangled: A Complete Dynamic Topological Logic

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F23%3A00603039" target="_blank" >RIV/67985807:_____/23:00603039 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1609/aaai.v37i5.25782" target="_blank" >http://dx.doi.org/10.1609/aaai.v37i5.25782</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1609/aaai.v37i5.25782" target="_blank" >10.1609/aaai.v37i5.25782</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Untangled: A Complete Dynamic Topological Logic

Popis výsledku v původním jazyce

Dynamical systems are general models of change or movement over time with a broad area of applicability to many branches of science, including computer science and AI. Dynamic topological logic (DTL) is a formal framework for symbolic reasoning about dynamical systems. DTL can express various liveness and reachability conditions on such systems, but has the drawback that the only known axiomatisation requires an extended language. In this paper, we consider dynamic topological logic restricted to the class of scattered spaces. Scattered spaces appear in the context of computational logic as they provide semantics for provability and enjoy definable fixed points. We exhibit the first sound and complete dynamic topological logic in the original language of DTL. In particular, we show that the version of DTL based on the class of scattered spaces is finitely axiomatisable, and that the natural axiomatisation is sound and complete.

Název v anglickém jazyce

Untangled: A Complete Dynamic Topological Logic

Popis výsledku anglicky

Dynamical systems are general models of change or movement over time with a broad area of applicability to many branches of science, including computer science and AI. Dynamic topological logic (DTL) is a formal framework for symbolic reasoning about dynamical systems. DTL can express various liveness and reachability conditions on such systems, but has the drawback that the only known axiomatisation requires an extended language. In this paper, we consider dynamic topological logic restricted to the class of scattered spaces. Scattered spaces appear in the context of computational logic as they provide semantics for provability and enjoy definable fixed points. We exhibit the first sound and complete dynamic topological logic in the original language of DTL. In particular, we show that the version of DTL based on the class of scattered spaces is finitely axiomatisable, and that the natural axiomatisation is sound and complete.

Druh

D - Stať ve sborníku

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA22-01137S" target="_blank" >GA22-01137S: Metamatematika substrukturálních modálních logik</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2023

Kód důvěrnosti údajů

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

Název statě ve sborníku

Proceedings of the AAAI Conference on Artificial Intelligence 2023

ISBN

—

ISSN

2159-5399

e-ISSN

—

Počet stran výsledku

8

Strana od-do

6355-6362

Název nakladatele

AAAI Press

Místo vydání

Palo Alto

Místo konání akce

Washington, D. C.

Datum konání akce

7. 2. 2023

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

001243718500105