Dates: Saturday, October 29th, 2016
Venue: Faculty of Technology, Policy and Management, Delft University of Technology. Jaffalaan 5, 2628 BX Delft.
Room: Classrooms I and J, first floor, turn right twice after the stairs.
VENUE: Aula Congrescentrum, Building number: 20, Mekelweg 5, 2628 CC Delft.
ROOM: Commissiekamer 4, Tag: COM4, Location: 10.
For directions, see here.
The event will be held right after the Lorentz Workshop: Logics, Decision, and Interactions, October 24 - 28.
Aims and Scope
Dynamics in Logic will keep its goal of bringing together a small group of people who are currently very active in the area of logic and information dynamics.
> Marta Bílková (Faculty of Arts, Charles University in Prague - Department of Logic)
Title: Epistemic Logics Based On Information States Semantics
(The work has been supported by the project SEGA: From Shared Evidence to Group Agency of Czech Science Foundation and DFG no. 16-07954J)
To model knowledge or belief of rational agents logically, specifying what kind of agents and, consequently, what notion of knowledge and belief one has in mind is essential. A prototypical rational agent for us is a scientist working with collections of data--and those, in contrast with complete and consistent descriptions of a state of the world, might be incomplete and inconsistent. The agent, by weighting the evidence supported by the available data carefully, eventually accepts some of the available information as known or believed. But only confirmed data coming from a reliable source might be accepted (cf. e.g. with the notion of scientific or rational scepticism).
The background propositional logic we use to model collections of data is therefore a par- ticular logic of information states, where collections of data are modeled as not necessarily consistent or complete theories. We allow for some information states to act as reliable sources of confirmation of data available at the current state. The modal part of the logic then consists of epistemic operators of knowledge and belief confirmed by a reliable source, which are, in contrast to standard approaches, diamond-like operators. Such logics have been studied in , based on distributive substructural logics.
In this talk, we present a multiagent version of such logics extended with common knowledge and belief operators. The semantics is now given by information frames, which, inspired by , are based on semilattices. The principal epistemic relation between the states is the one of being a reliable source of information and the epistemic operators are modeled as backward-looking diamond modalities. This actually is not so strange as prominent examples of such frames can be extracted from monotone neighborhood models where knowledge or belief is modeled as a box modality.
We in particular address the following points: axiomatization, proof theory and strong completeness for the underlying modal logic, and strongly complete infinitary proof theory for the logic with common knowledge and common belief operators in spirit of [2, 3].
 Bílková, M., O. Majer and M. Peliš, Epistemic logics for sceptical agents, Journal of Logic and Computation, first published online March 21, 2015.
 G. Jager, M. Kretz, T. Studer, Canonical completeness of infinitary μ, The Journal of Logic and Algebraic Programming 76 (2008), 270–292.
 G. Renardel de Lavalette, B. Kooi, R. Verbrugge, Strong Completeness and Limited Canonicity for PDL, Journal of Logic, Language and Information, 2008, Volume 17, Issue 1, pp. 69–87.
 V. PunčochářSpaces of Information States, Under review.
> Davide Grossi (University of Liverpoll - Department of Computer Science)
Title: Aggregation, Fixpoints, And Liquid Democracy
(Joint work with Zoé Christoff)
The talk focuses on the issue of aggregation of binary opinions in a group of agents, or judgment aggregation. I will explore some formal interfaces between a special form of aggregation known as proxy voting (aka liquid democracy) and a process of opinion diffusion on networks where each agent’s opinion may be dictated by a (unique) influencer (Boolean DeGroot Processes). The study sheds novel light on the relation between processes of aggregation and of opinion diffusion.
> Guillaume Aucher (University of Rennes 1)
Title: Expedition In The Update Universe
Dynamic epistemic logic (DEL) is a logic dealing with knowledge and belief change based on the concepts of event model and product update. In DEL, the product update accounts for the way we update our knowledge and beliefs about situations when events occur. However, DEL does not account for the way we update our knowledge and beliefs about events when other events occur. Indeed, events are assumed to occur instantaneously in DEL and this idealization precludes to study this kind of update. Our first contribution is to provide a logical analysis of updates without this assumption. It leads us to identify a graph structure for events based on their relative dependence and to introduce a generic product update. The DEL product update is a specific instance of this generic product update. Our second contribution is an investigation in the construction of Kripke models and event models. We introduce a parallel composition operator. This operator combines a set of Kripke models into a single Kripke model. When these Kripke models represent events, the resulting combination represents the occurrence of all these events at the same time. We prove that every finite Kripke model is bisimilar to the parallel composition and the product update of a finite set of Kripke models taken from a fixed and finitely generated set. We apply this general result to the construction of event models. Our third contribution is to define a logical language based on these different kinds of operators that refines the classical DEL language.We identify the fragment of this logic which has the same expressiveness as DEL and epistemic logic.
> Zeinab Bakhtiari (Université de Lorraine)
Title: Neighbourhood Contingency Bisimulation
(Joint work with: H. van Ditmarsch and H. H. Hansen)
We introduce a notion of bisimulation for contingency logic interpreted on neighbourhood structures, characterize this logic as bisimulation invariant fragment of modal logic and of first-order logic, and compare it with existing notions in the literature.
> Helle Hvid Hansen (TU Delft - Department of Engineering Systems and Services)
Title: Coalgebraic Dynamic Logics
(Joint work with Clemens Kupke)
In Propositional Dynamic Logic (PDL) programs are interpreted as relations, and program constructs as operations on relations. The axiomatisation of PDL essentially consists of modal logic K together with reduction axioms for program constructs. Similarly, in Parikh's Game Logic (GL), games are interpreted as monotonic neighbourhood functions, and game constructs by operations on these. Completeness of Game Logic remains an open question, but the proposed axiomatisation is essentially monotonic modal logic M together with reduction axioms. These similarities suggest that a more general picture exists that encompasses both.
In this talk I will present a coalgebraic generalisation of PDL and GL in which programs (or games) are coalgebras for a monad T, the program constructs arise from Kleisli composition and algebraic structure on T, and the axioms of these logics correspond to certain compatibility requirements between the modalities and this structure. This setup allows us to prove two general completeness results: strong completeness without iteration, and (weak) completeness with iteration and "negation-free" pointwise operations.
> Alexander Kurz (University of Leicester - Department of Computer Science)
Title: Tool Support For Multi-Type Display Calculi
> Michael Moortgat (Utrecht Institute of Linguistics OTS - Language, logic and information)
Title: Resource Control In Grammar Logics
To recover the expressivity of intuitionistic logic, linear logic uses the `!' modality which brings back copying and deletion (Contraction, Weakening) in a controlled form.
In grammar logics, the need for controlled resource management makes itself felt in a similar way. Natural language resources (words, phrases) may be linearly ordered (absence of commutativity for the composition operation) or configured into trees (absence of associativity). As in the linear logic case, the point is not so much to ban reordering/restructuring completely, but to have the means to control them.
To achieve structural control, [KM97] introduce an adjoint pair of modalities which are then used to define back-and-forth translations between logics with a stricter and with a more liberal resource management regime.
In the talk, I will present the linguistic motivation for this approach, and discuss what happens when one extends the `intuitionistic' Lambek-style grammar logics to bilinear systems of the type originally proposed by Grishin. In the latter, next to multiplicative conjunction (resource composition, fusion), one finds a multiplicative disjunction (decomposition, fission), and linear distributivities relating the two.
[KM97] Kurtonina N. and M. Moortgat (1997), "Structural control". In P. Blackburn and M. de Rijke, Specifying Syntactic Structures, CSLI Publications, pp. 75--113.
> Aybüke Özgün ( LORIA, Université de Lorraine - ILLC, University of Amsterdam)
Title: Justified Belief, Knowledge and the Topology of Evidence
(Joint work with Alexandru Baltag, Nick Bezhanishvili and Sonja Smets)
In this talk, I will present a topological semantics for evidence-based belief, as well as for a notion of (“soft”, defeasible) knowledge, and explore their connections with various notions of evidence possession. We will not only focus on truthful evidence but also formalize conceptions of possibly false and misleading evidence. The basic pieces of evidence possessed by an agent are modelled as non-empty sets of possible worlds and form a primitive component of our models.This setting builds on the evidence model framework of van Benthem and Pacuit (van Benthem et al., 2011), as well as our own previous work (Baltag et al., 2013) on (a topological semantics for) Stalnaker’s doxastic-epistemic axioms (Stalnaker, 2006). We prove completeness, decidability and finite model property for the associated logics.
Workshop attendance is free of cost, but we have a limited amount of places. If you are interested in participating, please send an email to Sabine Frittella (S dot S dot A dot Frittella at tudelft dot nl) or Giuseppe Greco (G dot Greco at tudelft dot nl).
> Dynamics in Logic III, 2015
> Dynamics in Logic II, 2012
> Dynamics in Logic I, 2011
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> Guillaume Aucher (University of Rennes 1)
> Giuseppe Greco (TU Delft)
> Sabine Frittella (TU Delft)
> Fan Yang (TU Delft)