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Domain Theory, Coalgebras and Dualities: Leicester-Birmingham collaborationA brief description
Future and past seminarsSeminar programme
Seminar detailsConcrete Coalgebraic Modal Logic Liang-Ting Chen (U. of Birmingham) Coalgebraic logic is mainly tailored for Set coalgebras so far and only few works are involved with different categories, e.g. the category of posets by K. Kapulkin and locally presentable categories by B. Klin. In this introduction to our on-going project, we formulate logics as a dual adjunction of concrete categories induced by a dualising object as known as schizophrenic object. Concepts in coalgebraic logic, e.g. predicate liftings, behavioural equivalence and logical equivalence are generalised naturally to this setting. I will prove the adequacy in one step but leave the expressivity problem unsolved.
Bilattices with modal operators Umberto Rivieccio (University of Birmingham) Umberto's slides are here. Some authors have recently started to consider modal expansions of the well-know Belnap four-valued logic, either with implication (S. Odintsov, H. Wansing et al.) or without it (G. Priest). Given that some bilattice logics are four-valued (conservative) expansions of the Belnap logic, one may ask whether it makes sense to consider modal expansions of bilattice logics and their algebraic counterpart, which would be bilattices with modal operators. I will present a few ideas on how this can be done.
A visit of Fredrik Nordvall Forsberg (PhD Student of Anton Setzer, Swansea) Fredrik Nordvall Forsberg (Department of Computer Science, University of Swansea) Rob Myers (IC London) (tentative) Priestley duality for bilattices/some extensions of Dunn-Belnap logic dr Umberto Rivieccio (University of Genoa, University of Birmingham) Umberto can give a talk from either this or this set of slides, depending on preferences of the audience.
A farewell seminar for Katsuhiko Sano Dr Dirk Pattinson, dr Katsuhiko Sano and dr Tadeusz Litak Suggested and potential items:
Canonical extensions and the Rasiowa-Sikorski Lemma Olaf Klinke and dr Tadeusz Litak
In the first part of the seminar, Olaf reported on results obtained with Drew during his stay in California. More specifically, the discussion focused on the use of results and insights in the recent PhD Thesis of Jacob Vosmaer for bitopological theory of Stone duality. In the second part, I explained the topological meaning of the Rasiowa-Sikorski Lemma (more specifically, its connection with the Baire Category Theorem) using two classical papers of Rob Goldblatt. This was intended as a background to the talk given the previous day by our guest, dr Yoshihito Tanaka from Kyushu Sangyo University (currently on sabbatical with Frank Wolter in Liverpool), explaining the use of the Rasiowa-Sikorski Lemma in completeness proofs for infinitary/predicate modal/superintuitionistic logics.
Continuous algebras and their presentations Prof. Achim Jung, Dr Alexander Kurz, Olaf Klinke et al A farewell seminar for prof. Moshier The whole Leicester-Birmingham team Summary of the work done last week with Drew
Canonical extensions for MLS and skew lattices Prof. Achim Jung and prof. M. Andrew Moshier
We were working on generalization of standard construction of canonical extension (for lattices/distributive lattices/bounded lattice expansions) to the case of MLS and skew lattices.
Fine's completeness proof for GML/welcome seminar for prof. Moshier Dr Katsuhiko Sano (JSPS Research Fellow, Kyoto University)
Tentative plan: in the first part, Katsuhiko will tell us about Fine's completeness proof for graded modal logic and we'll investigate its coalgebraic meaning (see July 16 meeting for Katsuhiko's own results on GML). In the second part, we'll return to subjects discussed during Drew's last visit in spring.
Stone duality for nominal boolean algebras Daniela Petrişan Daniela discussed her recent work with Jamie Gabbay and myself
Goldblatt-Thomason-style Theorems for Graded Modal Language Katsuhiko Sano (JSPS Research Fellow, Kyoto University) We establish two main Goldblatt-Thomason-style Theorems for graded modal language in Kripke semantics: a full Goldblatt-Thomason Theorem for elementary classes and the relative Goldblatt-Thomason Theorem within the class of finite transitive frames. The following two different semantic views to GML allow us to show these results: neighborhood semantics and graph semantics. By neighborhood semantic view, we can define a natural generalization of Jankov-Fine formula of GML to establish the relative Goldblatt-Thomason Theorem. By extracting graph semantics from Fine (1972)'s completeness proof of GML, we introduce the new notion of graded ultrafilter images to establish the full Goldblatt-Thomason Theorem. Therefore, we revive Fine's old idea in the new context of Goldblatt-Thomason-style characterization. This is a joint work with Minghui Ma (Tsinghua University).
Announcements:
The London-Leicester Coalgebra Meeting
Speakers from London (IC), Leicester, Birmingham and Oxford
Sam van Gool and Umberto Rivieccio Sam and Umberto are PhD students visiting Achim. They will talk about their work - click on the links to their websites to learn more.
Achim and Alexander
Cancelled due to Achim's unforeseen circumstances. We meet next week.
A Farewell Seminar for Drew Moshier Prof. M. Andrew Moshier et al. We'll sum up the work we did in last months, discuss last ideas and agree on how to proceed after Drew Moshier's return to US. Update: In fact, thanks to Alexander and Achim, we spent most of the time on an immensely useful discussion of the connection between Lawvere theories and finitary monads.
Towards Logic for Predicate Liftings on SCS's and Frames Prof. M. Andrew Moshier
We discussed whether it is possible to define generalize tools and techniques of coalgebraic logic to a more general setting than functors on Set/BAs.
Towards Logic for Bitopological Spaces Prof. M. Andrew Moshier and dr Alexander Kurz
We discussed possible notions of expressiveness, completeness, bisimilarity and implication in the context of bitopological spaces.
Scalars, Monads, and Categories Prof. Bart Jacobs (TU Eindhoven and Radboud University Nijmegen)
We discuss ideas introduced in [CJ:SMC10].
Labelled Markov Processes as Generalised Stochastic Relations Dr Alexander Kurz (University of Leicester)
We discuss ideas introduced in [MPV:LMPGSR].
Giry Monad and Labeled Markov Processes Prof. Achim Jung (University of Birmingham)
At Prof. Moshier absence, we continue to discuss ideas introduced the previous week
A Logic for Probabilities in Semantics II Prof. M. Andrew Moshier (Chapman University)
Building on the background from the last talk, we introduce the probabilistic powerdomain in MLS, and perhaps just
start a discussion of how to build a logic (in MLS) for labeled Markov processes, i.e., for a final coalgebra of a functor like: 1 + PP(X)^A
(terminating processes with A-labelled transitions).
A Logic for Probabilities in Semantics I Prof. M. Andrew Moshier (Chapman University)
This talk is based on [JM:LPSCSL02].
Separation axioms for d-frames Olaf Klinke (University of Birmingham) I will give a different view on the structure of a d-frame and the collection of axioms called "reasonable". We look at several topologically motivated axioms which correspond to separation axioms on the spacial side. I claim that when translating topology into the language of d-frames, one follows two paradigms: One must identify hidden bitopology, and one must use complement operations. As an application I will present a striking similarity between compact regular d-frames and regular normal d-frames, together with a compactification construction. Unpublished printable work can be found at http://www.cs.bham.ac.uk/~okk/papers/
On the Bitopological Nature of Stone Duality II Prof. Achim Jung (University of Birmingham) On the Bitopological Nature of Stone Duality I Prof. Achim Jung (University of Birmingham)
The talk is based on a recent joint work with M. Andrew Moshier [JM:BNSD06]
Dr Alexander Kurz (University of Leicester)
I will present the first section of [PT:CD91].
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Author: Tadeusz Litak (tml12 if_you're_a_spambot_this_underlined_part_is_to_confuse_you at mcs.le.ac.uk), T: +44 (0) 116 252 2593. |
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