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#### Chairs: Alexandru Baltag & Sonja Smets

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# Abstracts Invited Lectures

##### Jan van Eijck *Probabilistic Update Logic and Semantic Concept Learning*

We show how probabilistic update logic can be used for analyzing what goes on when speakers of a language learn the use of new concepts. (Based on joint work with Shalom Lappin.) [Slides]

##### Dietmar Berwanger *Acting as if there were no secrets -- Imperfect information and game*

transformations

Uncertainty is an inherent feature of interaction. Much of the effort for solving games is marked by the tension between predicting undetermined events and prescribing deterministic action rules. One approach, common to different solution procedures, consists in re-modelling games to expose their implicit perfect-information structure. Determinisation of nondeterministic automata can be viewed as one simple example in this direction. We survey game transformations that support reasoning about games with imperfect information in terms of perfect information, with particular focus on challenges raised by games of infinite duration.

##### Alessandra Palmigiano *Epistemic updates on algebras*

We introduce a methodology, based on duality theory, which makes it possible to study epistemic updates from an algebraic perspective. We focus on public announcements, which are the simplest epistemic actions, and hence on Public Announcement Logic (PAL) without the common knowledge operator. As is well known, the epistemic action of publicly announcing a given proposition is semantically represented as a process of relativization of the model encoding the current epistemic setup of the given agents; from the given model to its submodel relativized to the announced proposition. We give the dual characterization of the corresponding submodel-injection map, as a certain pseudo-quotient map between the complex algebras respectively associated with the given model and with its relativized submodel. As is well known, these complex algebras are complete atomic BAOs (Boolean algebras with operators). The dual characterization we provide naturally generalizes to much wider classes of algebras, which include, but are not limited to, arbitrary BAOs and arbitrary modal expansions of Heyting algebras (HAOs). In this way, we access the benefits and the wider scope of applications given by a point-free, intuitionistic theory of epistemic updates. As an application of this dual characterization, we axiomatize the intuitionistic analogue of PAL, which we refer to as IPAL, and prove soundness and completeness of IPAL w.r.t. both algebraic and relational models. [Slides]

# Abstracts Contributed Lectures

##### Patrick Allo *The Dynamics of Adaptive Proofs: a Modal Perspective*

Adaptive logics are logics for defeasible inference that are characterised by, on the one hand, a formula preferential semantics, and, on the other hand, a dynamic proof-theory. Because adaptive logics rely on a truly dynamic perspective on logical inference, one would expect that a comparison and integration of adaptive logics with other dynamic logics should be a fruitful enterprise. It does, for instance, make sense to define a class of Kripke-style models that allow us to reformulate the adaptive consequence relation with the standard tools of modal logic, or to develop a dynamic doxastic logic where the relation between an agent's knowledge (or firm beliefs) and defeasible beliefs is governed by an adaptive logic. In either case, we get a better idea of how adaptive logics are related to modal logics, but we still miss out on the one crucial aspect of adaptive logics: its dynamic proof-theory. The main aim of this paper is to fill this gap. [Slides]

##### Francien Dechesne and Mohammadreza Mousavi In processes, we believe! On Marrying Process Algebra and Epistemic Logic

Process algebras are a widely used formalism in theoretical computer science for the specification of protocols. From a more philosophical tradition, epistemic logics provide a formalism for the specification of knowledge properties. While the two formal frameworks have developed largely in parallel, the combination of both behavioral and epistemic aspects is called for in a context like security protocols, for properties like anonymity and secrecy. We work towards bridging the gap between two approaches by proposing a combined framework, which allows for modeling the behavior of a protocol in a process language with an operational semantics, and supports reasoning about properties expressed in a rich logic which combines temporal and epistemic operators. We show how this framework can be extended with cryptographic constructs, and we are relate our semantic framework to the interpreted systems model of Halpern and Vardi. [Slides]

##### Alexander Horn, Prakash Panangaden and Mehrnoosh Sadrzadeh *Knowing where you are: an algebraic approach to navigation*

We present a new update axiom for a dynamic epistemic logic for navigation problems. The framework builds on the algebraic semantics developed by the third author in her doctoral dissertation and is based on an extension of the idea of resource quantales. The novel features of the framework here are: (1) a distinction between real and virtual actions and (2) a converse action that allows one to step back in time *in the model* but not in reality.

##### Tadeusz Litak, Dirk Pattinson and Katsuhiko Sano *Coalgebraic Predicate Logic: First Steps*

C.C. Chang in a somewhat forgotten paper on "Modal Model Theory" (written shortly after Montague's death and dedicated to his memory) set out to simplify model theory for what Montague called "pragmatics" and to replace Montague's many-sorted setting by one without sorts. In contemporary terminology, Chang's paper dealt with model and correspondence theory for neighbourhood frames: coalgebras for double contravariant powerset functor. The paper provided suitable notions of (elementary) submodel/extension, elementary chain of models and ultraproduct and suitable variants of Tarski-Vaught, downward and upward Lowenheim-Skolem and compactness theorems. It is questionable whether Montague would accept Chang's invention as an account of pragmatics, but as noted by Chang himself, the resulting language is particularly well-tailored for reasoning about social situations and relationships between an individual and sets of individuals. Moreover, the notion of predicate lifting allows to turn Chang's invention into a generic correspondence language for arbitrary coalgebras. In our paper, we discuss examples of expressible properties and introduce our particularly simple version of standard translation for coalgebraic modal formulas. As it turns out, the resulting language is equipollent with expressive variants of coalgebraic hybrid logic (just like in the Kripke case) and this allows to use recent results of Schroeder and Pattinson to prove axiomatization and completeness results for a wide classes of functors and predicate liftings, including both the Kripke and the neighbourhood case. We also briefly discuss the status of van Benthem-Rosen characterization results.

##### Jonas De Vuyst *Minimal Revision and Classical Kripke Models: First Results*

Dynamic modal logics are modal logics that have statements of the form [π]ψ. The truth value of such statements, when evaluated in a pointed model (M, w), is determined by the truth value that ψ takes in some or all of the pointed models (M , w) that stand in a relation −π→ to (M, w). This paper introduces new dynamic operators that minimally revise finite classical Kripke models to make almost any satisfiable modal formula φ true. To this end, we define two minimal revision relations −†φ→ and −‡φ→. The first revises only the valuation function whereas the second relation also changes the frame. Our approach is different from others in that (i) our revision expressions π do not refer to abstract semantic objects such as accessibility relations or ‘action models’, (ii) we do not add extra semantic structure to our models, and (iii) yet we can make almost any formula true. Patrick Allo. The Dynamics of Adaptive Proofs: a Modal Perspective Abstract: Adaptive logics are logics for defeasible inference that are characterised by, on the one hand, a formula preferential semantics, and, on the other hand, a dynamic proof-theory. Because adaptive logics rely on a truly dynamic perspective on logical inference, one would expect that a comparison and integration of adaptive logics with other dynamic logics should be a fruitful enterprise. It does, for instance, make sense to define a class of Kripke-style models that allow us to reformulate the adaptive consequence relation with the standard tools of modal logic, or to develop a dynamic doxastic logic where the relation between an agent's knowledge (or firm beliefs) and defeasible beliefs is governed by an adaptive logic. In either case, we get a better idea of how adaptive logics are related to modal logics, but we still miss out on the one crucial aspect of adaptive logics: its dynamic proof-theory. The main aim of this paper is to fill this gap. [Slides]