BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Helle Hvid Hansen DTSTART:20260604T170000Z DTEND:20260604T180000Z DTSTAMP:20260604T125422Z UID:ToposInstituteColloquium/215 DESCRIPTION:Title: Coalgebraic Dynamic Logics\nby Helle Hvid Hansen as part of Topos Institute Colloquium\n\nInteractive livestream: https://top os-institute.zoom.us/j/84392523736?pwd=bjdVS09wZXVscjQ0QUhTdGhvZ3pUdz09\nP assword hint: 65537\nView-only livestream: https://www.youtube.com/live/Jz pYEkvi-wM\n\nAbstract\nWe present a coalgebraic framework for studying dyn amic modal logics such as Propositional Dynamic Logic (PDL) and Parikh's G ame Logic\, which are logics for reasoning about program correctness and s trategic ability in games\, respectively. A characteristic feature of thes e logics is that their syntax is two-sorted\, combining program/game const ructs with modal logic syntax. Semantically\, programs/games are modelled as T-coalgebras for a monad T on Set\, and program/game constructs are int erpreted as operations on T-coalgebras. The axiomatisation of PDL consists of extending normal modal logic K with reduction axioms that capture the interplay between program structure and propositions. Similarly\, an axiom atisation based on monotonic modal logic M plus reduction axioms has been proposed for Game Logic. This modularity of axiomatisations was the starti ng point for developing dynamic logics in the setting of coalgebraic modal logic. The framework of coalgebraic dynamic logic is parametric in the co algebra type functor T and a choice of modalities. In recent work\, it has been extended from Boolean-valued to many-valued logics\, with the underl ying algebra A of truth values as an additional parameter. The main techni cal results include a compositionality theorem for behavioural equivalence and conditions for strong completeness (without iteration\, many-valued) and weak completeness (with iteration\, Boolean-valued).\n\nThis is joint work with Clemens Kupke\, Raul Leal\, and Wolfgang Poiger.\n LOCATION:https://researchseminars.org/talk/ToposInstituteColloquium/215/ URL:https://topos-institute.zoom.us/j/84392523736?pwd=bjdVS09wZXVscjQ0QUhT dGhvZ3pUdz09 URL:https://www.youtube.com/live/JzpYEkvi-wM END:VEVENT END:VCALENDAR