University of Leicester

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Domain Theory, Coalgebras and Dualities: Leicester-Birmingham collaboration

A brief description

Usually Thursdays 10:30-14:00 in G4. Usually held on Monday afternoons this semester. From January 2011, we are back to Thursday morning schedule. Made possible by Alexander and Achim's EPSRC grant (see also EPSRC website). Its long-term goal is to understand how the three subjects in the title are connected and to prove suitable transfer results. A systematic study of these connections is long overdue. To fully utilize Achim's time, participants are encouraged to bring their own sandwiches or ready-made meals to avoid breaking for lunch.

Future and past seminars

Seminar programme


Seminar details

Concrete Coalgebraic Modal Logic

Liang-Ting Chen (U. of Birmingham)
Thu, 1 Mar 2012, 10:45 in G4

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)
Thu, 23 Feb 2012, 11:00 in PHY LTD (Physics Ground Floor LR LTD), after 13:00 continued in G4

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)
Nov 3, 2011, 11:00 in G4

A visit of dr Rob Myers

Rob Myers (IC London)
Oct 24, 2011, 15:00 in G4

(tentative) Priestley duality for bilattices/some extensions of Dunn-Belnap logic

dr Umberto Rivieccio (University of Genoa, University of Birmingham)
Thursday, 3 March 2011, 12:00 in G4

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
Thursday, 17 February 2011, 11:20 in G4

Suggested and potential items:

  • Katsuhiko is willing to talk about his recent work on products of coalgebraic hybrid logics, more than fittingly for his farewell seminar.
  • Recently, I wrote a set of unreadable notes on various completeness notions in coalgebraic logic, where I tried to systematize the outcome of our discussions with Alexander and Katsuhiko + some of material found in literature (including numerous papers by Dirk, Lutz, Alexander et al...). I can go briefly through them, with members of the audience (particularly Dirk and Alexander) correcting me and filling the gaps wherever necessary. This can be a good starting point for an overview discussion, especially given that there were two papers published recently with "strong completeness" in the title: one by Alexander and Jiř and another one by Dirk and Lutz.
  • We can also publicly continue the discussion on coalgebraic FOL, which is perhaps the main goal of Dirk's visit anyway. In this context, maybe we can also return to Dirk's correspondence paper with Lutz and if Dirk feels so inclined, he can tell us a bit more, e.g., on Van Benthem theorem in coalgebraic context.
  • Needless to say, if only Dirk feels so inclined, he can also tell us more about any of his recent papers, arbitrarily chosen...

Canonical extensions and the Rasiowa-Sikorski Lemma

Olaf Klinke and dr Tadeusz Litak
Thursday, 27 January 2011, 11:00 in ATT 205 Attenborough Second Floor TR 205

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
Monday, 22 November 2010, 14:00 in G4

(tentative) We will discuss possible generalizations of results from the "Presenting dcpos" paper.

A farewell seminar for prof. Moshier

The whole Leicester-Birmingham team
Monday, 25 October 2010, 14:00 in FJ SW SR1 Fielding Johnson South Wing Basement The Ogden Lewis Seminar Suite 1

Summary of the work done last week with Drew

Canonical extensions for MLS and skew lattices

Prof. Achim Jung and prof. M. Andrew Moshier
Friday, 22 October 2010, 10:30 in reading room (exceptionally)

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)
Monday, 18 October 2010, 14:00 in tba

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
Monday, 11 October 2010, 14:00 in ATT 204 (Attenborough Second Floor TR 204)

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)
Friday, 16 July 2010, 10:00 in Attenborough Seminar Block First Floor SR SB1.05

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:

  1. A draft version of the paper is available to anyone interested in details - just e-mail me.
  2. Katsuhiko will give another talk on the same day at 14:00 on products of hybrid logics. This will be announced separately by Alexander as one of CS Department Internal Seminars
  3. Leicester-Birmingham seminar is suspended until the beginning of August: this week we're having two replacement events (including Katsuhiko's talk) and for next two weeks Achim and myself are away

The London-Leicester Coalgebra Meeting

Speakers from London (IC), Leicester, Birmingham and Oxford
Monday, 12 July 2010, 11:00-18:30 in London, Imperial College

See webpage

guest speakers

Sam van Gool and Umberto Rivieccio
Thursday, 1 July 2010, 10:20-16:20 in FJ L66 Fielding Johnson First Floor (Law Dept) LR L66

Sam and Umberto are PhD students visiting Achim. They will talk about their work - click on the links to their websites to learn more.

tba

Achim and Alexander
CANCELLED: Thursday, 24 June 2010, 13:00 (!) in ATT SB2.08

Our first meeting this month---notice unusual time!

Cancelled due to Achim's unforeseen circumstances. We meet next week.

A Farewell Seminar for Drew Moshier

Prof. M. Andrew Moshier et al.
Thursday, 27 May 2010, 10:30 in G4

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
Thursday, 20 May 2010, 9:30 in G4

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
Thursday, 13 May 2010, 10:30 in FJ L17

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)
Thursday, 6 May 2010, 11:00 in KE 214

We discuss ideas introduced in [CJ:SMC10].
[CJ:SMC10] Dion Coumans and Bart Jacobs.
Scalars, Monads, and Categories.

Labelled Markov Processes as Generalised Stochastic Relations

Dr Alexander Kurz (University of Leicester)
Thursday, 2 April 2010, 12:30 in G4

We discuss ideas introduced in [MPV:LMPGSR].
[MPV:LMPGSR] Michael Mislove, Dusko Pavlovic and James Worrell.
Labelled Markov Processes as Generalised Stochastic Relations. ENTCS 172 (2007), 459--478.

Giry Monad and Labeled Markov Processes

Prof. Achim Jung (University of Birmingham)
Thursday, 25 March 2010, 10:30 in G4

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)
Thursday, 18 March 2010, 11:00 in G4

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)
Thursday, 11 March 2010, 10:30 in G4

This talk is based on [JM:LPSCSL02].
[JM:LPSCSL02] M. Andrew Moshier and Achim Jung.
A Logic for Probabilities in Semantics. In Julian Bradfield (editor), Proceedings of CSL'02. LNCS 2471 (2002), 216--231. Springer Verlag.

Separation axioms for d-frames

Olaf Klinke (University of Birmingham)
Thursday, 4 March 2010, 10:30 in G4

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)
Thursday, 25 February 2010, 10:30 in G4

The talk is a continuation of the one given last week based on [JM:BNSD06]

On the Bitopological Nature of Stone Duality I

Prof. Achim Jung (University of Birmingham)
Thursday, 18 February 2010, 10:30 in we meet in the coffee room, from 11:00 ATT SBB.10 (Attenborough Seminar Block Basement TR SBB.10)

The talk is based on a recent joint work with M. Andrew Moshier [JM:BNSD06]
[JM:BNSD06] Achim Jung and M. Andrew Moshier.
On the bitopological nature of Stone duality, Technical Report, School of Computer Science, University of Birmingham CSR-06-13 (December 2006).

Concrete Dualities

Dr Alexander Kurz (University of Leicester)
Thursday, 11 February 2010, 9:30 in G4

I will present the first section of [PT:CD91].
[PT:CD91] H.-E. Porst and W. Tholen.
Concrete Dualities. In H. Herrlich and H.-E. Porst (editors), Category Theory at Work, 111–136. Heldermann Verlag (1991).

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.
University of Leicester 12 Feb 2010. Last modified: 27th February 2012, 13:49:00.
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