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## Über dieses Buch

This LNCS volume is part of FoLLI book serie and contains the papers presented at the 6th International Workshop on Logic, Rationality and Interaction/ (LORI-VI), held in September 2017 in Sapporo, Japan.
The focus of the workshop is on following topics: Agency, Argumentation and Agreement, Belief Revision and Belief Merging, Belief Representation, Cooperation, Decision making and Planning, Natural Language, Philosophy and Philosophical Logic, and Strategic Reasoning.

## Inhaltsverzeichnis

### A Logical Framework for Graded Predicates

In this position paper we present a logical framework for modelling reasoning with graded predicates. We distinguish several types of graded predicates and discuss their ubiquity in rational interaction and the logical challenges they pose. We present mathematical fuzzy logic as a set of logical tools that can be used to model reasoning with graded predicates, and discuss a philosophical account of vagueness that makes use of these tools. This approach is then generalized to other kinds of graded predicates. Finally, we propose a general research program towards a logic-based account of reasoning with graded predicates.

Petr Cintula, Carles Noguera, Nicholas J. J. Smith

### Evidence Logics with Relational Evidence

We introduce a family of logics for reasoning about relational evidence: evidence that involves an ordering of states in terms of their relative plausibility. We provide sound and complete axiomatizations for the logics. We also present several evidential actions and prove soundness and completeness for the associated dynamic logics.

Alexandru Baltag, Andrés Occhipinti

### Rational Coordination with no Communication or Conventions

We study pure coordination games where in every outcome, all players have identical payoffs, ‘win’ or ‘lose’. We identify and discuss a range of ‘purely rational principles’ guiding the reasoning of rational players in such games and analyse which classes of coordination games can be solved by such players with no preplay communication or conventions. We observe that it is highly nontrivial to delineate a boundary between purely rational principles and other decision methods, such as conventions, for solving such coordination games.

Valentin Goranko, Antti Kuusisto, Raine Rönnholm

### Towards a Logic of Tweeting

In this paper we study the logical principles of a common type of network communication events that haven’t been studied from a logical perspective before, namely network announcements, or tweeting, i.e., simultaneously sending a message to all your friends in a social network. In particular, we develop and study a minimal modal logic for reasoning about propositional network announcements. The logical formalisation helps elucidate core logical principles of network announcements, as well as a number of assumptions that must be made in such reasoning. The main results are sound and complete axiomatisations.

Zuojun Xiong, Thomas Ågotnes, Jeremy Seligman, Rui Zhu

### Multi-Path vs. Single-Path Replies to Skepticism

In order to reply to the contemporary skeptic’s argument for the conclusion that we don’t have any empirical knowledge about the external world, several authors have suggested different fallibilist theories of knowledge that reject the epistemic closure principle. Holliday [8], however, shows that almost all of them suffer from either the problem of containment or the problem of vacuous knowledge. Furthermore, Holliday [9] suggests that the fallibilist should allow a proposition to have multiple sets of relevant alternatives, each of which is sufficient while none is necessary, if all its members are eliminated, for knowing that proposition. Not completely satisfied with Holliday’s multi-path reply to the skeptic, the author suggests a new single-path relevant alternative theory of knowledge and argues that it can avoid both the problem of containment and the problem of vacuous knowledge while rejecting skepticism.

Wen-fang Wang

### An Extended First-Order Belnap-Dunn Logic with Classical Negation

In this paper, we investigate an extended first-order Belnap-Dunn logic with classical negation. We introduce a Gentzen-type sequent calculus FBD+ for this logic and prove theorems for syntactically and semantically embedding FBD+ into a Gentzen-type sequent calculus for first-order classical logic. Moreover, we show the cut-elimination theorem for FBD+ and prove the completeness theorems with respect to both valuation and many-valued semantics for FBD+.

Norihiro Kamide, Hitoshi Omori

### A Characterization Theorem for Trackable Updates

The information available to some agents can be represented with several mathematical models, depending on one’s purpose. These models differ not only in their level of precision, but also in how they evolve when the agents receive new data. The notion of tracking was introduced to describe the matching of information dynamics, or ‘updates’, on different structures.We expand on the topic of tracking, focusing on the example of plausibility and evidence models, two central structures in the literature on formal epistemology. Our main result is a characterization of the trackable updates of a certain class, that is, we give the exact condition for an update on evidence models to be trackable by a an update on plausibility models. For the positive cases we offer a procedure to compute the other update, while for the negative cases we give a recipe to construct a counterexample to tracking. To our knowledge, this is the first result of this kind in the literature.

Giovanni Cinà

### Convergence, Continuity and Recurrence in Dynamic Epistemic Logic

The paper analyzes dynamic epistemic logic from a topological perspective. The main contribution consists of a framework in which dynamic epistemic logic satisfies the requirements for being a topological dynamical system thus interfacing discrete dynamic logics with continuous mappings of dynamical systems. The setting is based on a notion of logical convergence, demonstratively equivalent with convergence in Stone topology. Presented is a flexible, parametrized family of metrics inducing the latter, used as an analytical aid. We show maps induced by action model transformations continuous with respect to the Stone topology and present results on the recurrent behavior of said maps.

Dominik Klein, Rasmus K. Rendsvig

### Dynamic Logic of Power and Immunity

We present a dynamic logic for modelling legal competences, and in particular for the Hohfeldian categories of power and immunity. We argue that this logic improves on existing models by explicitly capturing the norm-changing character of legal competences, while at the same time providing a sophisticated reduction of the latter to static normative positions. The logic is shown to be completely axiomatizable; an analysis of its resulting dynamic normative positions is provided; and it is finally applied to a concrete case in German contract law to illustrate how the logic can distinguish legal ability and legal permissibility.

Huimin Dong, Olivier Roy

### A Propositional Dynamic Logic for Instantial Neighborhood Models

We propose a new perspective on logics of computation by combining instantial neighborhood logic INL with bisimulation safe operations adapted from PDL and dynamic game logic. INL is a recently proposed modal logic, based on a richer extension of neighborhood semantics which permits both universal and existential quantification over individual neighborhoods. We show that a number of game constructors from game logic can be adapted to this setting to ensure invariance for instantial neighborhood bisimulations, which give the appropriate bisimulation concept for INL. We also prove that our extended logic IPDL is a conservative extension of dual-free game logic, and its semantics generalizes the monotone neighborhood semantics of game logic. Finally, we provide a sound and complete system of axioms for IPDL, and establish its finite model property and decidability.

Johan van Benthem, Nick Bezhanishvili, Sebastian Enqvist

### Contradictory Information as a Basis for Rational Belief

As agents faced with fallible information, we frequently find ourselves in situations where we are forced to base our beliefs on evidence which is in some way or another contradictory. We nevertheless want these beliefs to be rational. This paper presents a simple probabilistic model of what it means for a belief based on a contradictory body of evidence to be rational. In this approach, we model contradictions in the evidence available to us as resulting from random noise, and we model our task as rational agents as reconstructing the most likely states of affairs given the evidence available to us. Our main result consists in providing several equivalent descriptions of the non-reflexive and non-monotonic consequence relation which formalizes the notion that it is reasonable to accept that a proposition is true given good evidence supporting some set of propositions.

### Stability in Binary Opinion Diffusion

The paper studies the stabilization of the process of diffusion of binary opinions on networks. It first shows how such dynamics can be modeled and studied via techniques from binary aggregation, which directly relate to neighborhood frames. It then characterizes stabilization in terms of such neighborhood structures, and shows how the monotone $$\mu$$μ-calculus can express relevant properties of them. Finally, it illustrates the scope of these results by applying them to specific diffusion models.

Zoé Christoff, Davide Grossi

### Quotient Dynamics: The Logic of Abstraction

We propose a Logic of Abstraction, meant to formalize the act of “abstracting away” the irrelevant features of a model. We give complete axiomatizations for a number of variants of this formalism, and explore their expressivity. As a special case, we consider the “logics of filtration”.

Alexandru Baltag, Nick Bezhanishvili, Julia Ilin, Aybüke Özgün

### The Dynamics of Group Polarization

Exchange of arguments in a discussion often makes individuals more radical about their initial opinion. This phenomenon is known as Group-induced Attitude Polarization. A byproduct of it are bipolarization effects, where the distance between the attitudes of two groups of individuals increases after the discussion. This paper is a first attempt to analyse the building blocks of information exchange and information update that induce polarization. I use Argumentation Frameworks as a tool for encoding the information of agents in a debate relative to a given issue a. I then adapt a specific measure of the degree of acceptability of an opinion (Matt and Toni 2008). Changes in the degree of acceptability of a, prior and posterior to information exchange, serve here as an indicator of polarization. I finally show that the way agents transmit and update information has a decisive impact on polarization and bipolarization.

Carlo Proietti

### Doing Without Nature

We show that every indeterministic n-agent choice model $$M^i$$Mi can be transformed into a deterministic n-agent choice model $$M^d$$Md, such that $$M^i$$Mi is a bounded morphic image of $$M^d$$Md. This generalizes an earlier result from Van Benthem and Pacuit [16] about finite two-player choice models. It further strengthens the link between STIT logic and game theory, because deterministic choice models correspond in a straightforward way to normal game forms, and choice models are generally used to interpret STIT logic.

Frederik Van De Putte, Allard Tamminga, Hein Duijf

### Axiomatizing Epistemic Logic of Friendship via Tree Sequent Calculus

This paper positively solves an open problem if it is possible to provide a Hilbert system to Epistemic Logic of Friendship (EFL) by Seligman, Girard and Liu. To find a Hilbert system, we first introduce a sound, complete and cut-free tree (or nested) sequent calculus for EFL, which is an integrated combination of Seligman’s sequent calculus for basic hybrid logic and a tree sequent calculus for modal logic. Then we translate a tree sequent into an ordinary formula to specify a Hilbert system of EFL and finally show that our Hilbert system is sound and complete for an intended two-dimensional semantics.

Katsuhiko Sano

### The Dynamic Logic of Stating and Asking: A Study of Inquisitive Dynamic Modalities

Inquisitive dynamic epistemic logic (IDEL) extends public announcement logic incorporating ideas from inquisitive semantics. In IDEL, the standard public announcement action can be extended to a more general public utterance action, which may involve a statement or a question. While uttering a statement has the effect of a standard announcement, uttering a question typically leads to new issues being raised. In this paper, we investigate the logic of this general public utterance action. We find striking commonalities, and some differences, with public announcement logic. We show that dynamic modalities admit a set of reduction axioms, which allow us to turn any formula of IDEL into an equivalent formula of static inquisitive epistemic logic. This leads us to establish several complete axiomatizations of IDEL, corresponding to known axiomatizations of public announcement logic.

Ivano Ciardelli

### The Stubborn Non-probabilist—‘Negation Incoherence’ and a New Way to Block the Dutch Book Argument

We rigorously specify the class of nonprobabilistic agents which are, we argue, immune to the classical Dutch Book argument. We also discuss the notion of expected value used in the argument as well as sketch future research connecting our results to those concerning incoherence measures.

Leszek Wroński, Michał Tomasz Godziszewski

### Conjunction and Disjunction in Infectious Logics

In this paper we discuss the extent to which conjunction and disjunction can be rightfully regarded as such, in the context of infectious logics. Infectious logics are peculiar many-valued logics whose underlying algebra has an absorbing or infectious element, which is assigned to a compound formula whenever it is assigned to one of its components. To discuss these matters, we review the philosophical motivations for infectious logics due to Bochvar, Halldén, Fitting, Ferguson and Beall, noticing that none of them discusses our main question. This is why we finally turn to the analysis of the truth-conditions for conjunction and disjunction in infectious logics, employing the framework of plurivalent logics, as discussed by Priest. In doing so, we arrive at the interesting conclusion that —in the context of infectious logics— conjunction is conjunction, whereas disjunction is not disjunction.

Hitoshi Omori, Damian Szmuc

### On the Concept of a Notational Variant

In the study of modal and nonclassical logics, translations have frequently been employed as a way of measuring the inferential capabilities of a logic. It is sometimes claimed that two logics are “notational variants” if they are translationally equivalent. However, we will show that this cannot be quite right, since first-order logic and propositional logic are translationally equivalent. Others have claimed that for two logics to be notational variants, they must at least be compositionally intertranslatable. The definition of compositionality these accounts use, however, is too strong, as the standard translation from modal logic to first-order logic is not compositional in this sense. In light of this, we will explore a weaker version of this notion that we will call schematicity and show that there is no schematic translation either from first-order logic to propositional logic or from intuitionistic logic to classical logic.

Alexander W. Kocurek

### Conditional Doxastic Logic with Oughts and Concurrent Upgrades

In this paper, we model the behavior of an epistemic agent that faces a deliberation against a background of oughts, beliefs and information. We do this by introducing a dynamic epistemic logic where ought operators are defined and release of information makes beliefs and oughts co-vary. The static part of the logic extends single-agent Conditional Doxastic Logic by combining dyadic operators for conditional beliefs and oughts that are interpreted over two distinct preorders. The dynamic part of the logic introduces concurrent upgrade operators, which are interpreted on operations that change the two preorders in the same way, thus generating the covariation of beliefs and oughts. The effect of the covariation is that, after receiving new information, the agent will change both her beliefs and her oughts accordingly, and in deliberating, she will pick up the best states among those she takes to be the most plausible.

Roberto Ciuni

### On Subtler Belief Revision Policies

This paper proposes three subtle revision policies that are not propositionally successful (after a single application the agent might not believe the given propositional formula), but nevertheless are not propositionally idempotent (further applications might affect the agent’s epistemic state). It also compares them with two well-known revision policies, arguing that the subtle ones might provide a more faithful representation of humans’ real-life revision processes.

### Topo-Logic as a Dynamic-Epistemic Logic

We extend the ‘topologic’ framework [13] with dynamic modalities for ‘topological public announcements’ in the style of Bjorndahl [5]. We give a complete axiomatization for this “Dynamic Topo-Logic”, which is in a sense simpler than the standard axioms of topologic. Our completeness proof is also more direct (making use of a standard canonical model construction). Moreover, we study the relations between this extension and other known logical formalisms, showing in particular that it is co-expressive with the simpler (and older) logic of interior and global modality [1, 4, 10, 14]. This immediately provides an easy decidability proof (both for topologic and for our extension).

Alexandru Baltag, Aybüke Özgün, Ana Lucia Vargas Sandoval

### Strategic Knowledge of the Past in Quantum Cryptography

We propose an epistemic strategy logic with future and past time operators, called $$\text {SLKP}$$SLKP, for Strategy Logic with Knowledge of the Past. With $$\text {SLKP}$$SLKP we can model mutually observed moves/actions in strategic contexts. In a semantic game, agents may completely or partially observe other agents’ moves, their moves may depend on their knowledge of other players’ strategies, and their knowledge may depend on the history of their own or other’s moves. The logic $$\text {SLKP}$$SLKP also allows us to describe temporal properties involving past, future, and composed tenses such as future perfect or counterfactual assertions. We illustrate SLKP by formalising the quantum cryptography protocol BB84, with the purpose to initiate an integrated epistemic and strategic treatment of agent interactions in quantum systems.

Christophe Chareton, Hans van Ditmarsch

### Enumerative Induction and Semi-uniform Convergence to the Truth

I propose a new definition of identification in the limit, also called convergence to the truth, as a new success criterion that is meant to complement, but not replace, the classic definition due to Putnam (1963) and Gold (1967). The new definition is designed to explain how it is possible to have successful learning in a kind of scenario that the classic account ignores—the kind of scenario in which the entire infinite data stream to be presented incrementally to the learner is not presupposed to completely determine the correct learning target. For example, suppose that a scientists is interested in whether all ravens are black, and that she will never observe a counterexample in her entire life. This still leaves open whether all ravens (in the universe) are black. From a purely mathematical point of view, the proposed definition of convergence to the truth employs a convergence concept that generalizes net convergence and sits in between pointwise convergence and uniform convergence. Two results are proved to suggest that the proposed definition provides a success criterion that is by no means weak: (i) Between the proposed identification in the limit and the classic one, neither implies the other. (ii) If a learning method identifies the correct target in the limit in the proposed sense, any U-shaped learning involved therein has to be essentially redundant. I conclude that we should have (at least) two success criteria that correspond to two senses of identification in the limit: the classic one and the one proposed here. They are complementary: meeting any one of the two is good; meeting both at the same time, if possible, is even better.

Hanti Lin

### How to Make Friends: A Logical Approach to Social Group Creation

This paper studies the logical features of social group creation. We focus on the mechanisms which indicate when agents can form a team based on the correspondence in their set of features (behavior, opinions, etc.). Our basic approach uses a semi-metric on the set of agents, which is used to construct a network topology. Then it is extended with epistemic features to represent the agents’ epistemic states, allowing us to explore group-creation alternatives where what matters is not only the agent’s differences but also what they know about them. We use tools of dynamic epistemic logic to study the properties of different strategies to network formations.

### Examining Network Effects in an Argumentative Agent-Based Model of Scientific Inquiry

In this paper we present an agent-based model (ABM) of scientific inquiry aimed at investigating how different social networks impact the efficiency of scientists in acquiring knowledge. The model is an improved variant of the ABM introduced in [3], which is based on abstract argumentation frameworks. The current model employs a more refined notion of social networks and a more realistic representation of knowledge acquisition than the previous variant. Moreover, it includes two criteria of success: a monist and a pluralist one, reflecting different desiderata of scientific inquiry. Our findings suggest that, given a reasonable ratio between research time and time spent on communication, increasing the degree of connectedness of the social network tends to improve the efficiency of scientists.

AnneMarie Borg, Daniel Frey, Dunja Šešelja, Christian Straßer

### Substructural Logics for Pooling Information

This paper puts forward a generalization of the account of pooling information – offered by standard epistemic logic – based on intersection of sets of possible worlds. Our account is based on information models for substructural logics and pooling is represented by fusion of information states. This approach yields a representation of pooling related to structured communication within groups of agents. It is shown that the generalized account avoids some problematic features of the intersection-based approach. Our main technical result is a sound and complete axiomatization of a substructural epistemic logic with an operator expressing pooling.

Vít Punčochář, Igor Sedlár

### Logical Argumentation Principles, Sequents, and Nondeterministic Matrices

The concept of “argumentative consequence” is introduced, involving only the attack relations in Dung-style abstract argumentation frames. Collections of attack principles of different strength, referring to the logical structure of claims of arguments, lead to new characterizations of classical and nonclassical consequence relations. In this manner systematic relations between structural constraints on abstract argumentation frames, sequent rules, and nondeterministic matrix semantics for corresponding calculi emerge.

Esther Anna Corsi, Christian G. Fermüller

### Non-triviality Done Proof-Theoretically

It is well known that naive theories of truth based on the three-valued schemes K3 and LP are non-trivial.

Rohan French, Shawn Standefer

### Sette’s Logics, Revisited

One of the simple approaches to paraconsistent logic is in terms of three-valued logics. Assuming the standard behavior with respect to the “classical"values, there are only two possibilities for paraconsistent negation, namely the negation of the Logic of Paradox and the negation of Sette’s logic P$$^1$$1. From a philosophical perspective, the paraconsistent negation of P$$^1$$1 is less discussed due to the lack of an intuitive reading of the third value. Based on these, the aim of this paper is to fill in the gap by presenting a semantics for P$$^1$$1 à la Jaśkowski which sheds some light on the intuitive understanding of Sette’s logic. A variant of P$$^1$$1 known as I$$^1$$1 will be also discussed.

Hitoshi Omori

### Multi-agent Belief Revision Using Multisets

Revising a belief set K with a proposition a results in a theory that entails a. We consider the case of a multiset of beliefs, representing the beliefs of multiple agents, and define its revision with a multiset of desired beliefs the group of agents should have. We give graph theoretic semantics to this revision operation and we postulate two classes of distance-based revision operators. Further, we show that this multiset revision operation can express the merging of the beliefs of multiple agents.

Konstantinos Georgatos

### Boosting Distance-Based Revision Using SAT Encodings

Belief revision has been studied for more than 30 years, and the theoretical properties of the belief revision operators are now well-known. Contrastingly, there are almost no practical applications of these operators. One of the reasons is the computational complexity of the corresponding inference problem, which is typically NP-hard and coNP-hard. Especially, existing implementations of belief revision operators are capable to solve toy instances, but are still unable to cope with real-size problem instances. However, the improvements achieved by SAT solvers for the past few years have been very impressive and they allow to tackle the solving of instances of inference problems located beyond NP. In this paper we describe and evaluate SAT encodings for a large family of distance-based belief revision operators. The results obtained pave the way for the practical use of belief revision operators in large-scale applications.

Sébastien Konieczny, Jean-Marie Lagniez, Pierre Marquis

### Counterfactuals in Nelson Logic

We motivate and develop an extension of Nelson’s constructive logic N3 that adds a counterfactual conditional to the existing setup. After developing the semantics, we will outline how our account will be able to give a nice analysis of natural language counterfactuals. In particular, the account does justice to the intuitions and arguments that have lead Alan Hájek to claim that most conditionals are false, but assertable, without actually forcing us to endorse that rather uncomfortable claim.

Andreas Kapsner, Hitoshi Omori

### A Dynamic Approach to Temporal Normative Logic

State commands refer to states, not actions. They have a temporal dimension explicitly or implicitly. They indirectly change what we are permitted, forbidden or obligated to do. This paper presents $${{\mathrm{\mathsf {DTNL}}}}{}$$DTNL, a deontic logic meant to handle state commands based on the branching-time temporal logic $$\mathsf {PCTL}^*$$PCTL∗. The models of $${{\mathrm{\mathsf {DTNL}}}}{}$$DTNL are trees with bad states, which are identified by a propositional constant $$\mathfrak {b}$$b introduced in the language. To model state commands, a dynamic operator that adds states to the extension of $$\mathfrak {b}$$b is introduced.

Fengkui Ju, Gianluca Grilletti

### Labelled Sequent Calculus for Inquisitive Logic

A contraction-free and cut-free labelled sequent calculus $$\mathsf {GInqL}$$GInqL for inquisitive logic is established. Labels are defined by a set-theoretic syntax. The completeness of $$\mathsf {GInqL}$$GInqL is shown by the equivalence between the Hilbert-style axiomatic system and sequent system.

Jinsheng Chen, Minghui Ma

### Testing Minimax for Rational Ignorant Agents

Richard Pettigrew [13, 14] defends the following theses: (1) epistemic disutility can be measured with strictly proper scoring rules (like the Brier score) and (2) at the beginning of their credal lives, rational agents ought to minimize their worst-case epistemic disutility (Minimax). This leads to a Principle of Indifference for ignorant agents. However, Pettigrew offers no argument in favour of Minimax, suggesting that the epistemic conservatism underlying it is a “normative bedrock.” Is there a way to test Minimax? In this paper, we argue that, since Pettigrew’s Minimax is impermissive, an argument against credence permissiveness constitutes an argument in favour of Minimax, and that arguments for credence permissiveness are arguments against Minimax.

Marc-Kevin Daoust, David Montminy

### A Reconstruction of Ex Falso Quodlibet via Quasi-Multiple-Conclusion Natural Deduction

This paper is intended to offer a philosophical analysis of the propositional intuitionistic logic formulated as $$\textit{NJ}$$NJ. This system has been connected to Prawitz and Dummett’s proof-theoretic semantics and its computational counterpart. The problem is, however, there has been no successful justification of ex falso quodlibet (EFQ): “From the absurdity ‘$$\bot$$⊥’, an arbitrary formula follows.” To justify this rule, we propose a novel intuitionistic natural deduction with what we call quasi-multiple conclusion. In our framework, EFQ is no longer an inference deriving everything from ‘$$\bot$$⊥’, but rather represents a “jump” inference from the absurdity to the other possibility.

Yosuke Fukuda, Ryosuke Igarashi

### A Nonmonotonic Modal Relevant Sequent Calculus

Motivated by semantic inferentialism and logical expressivism proposed by Robert Brandom, in this paper, I submit a nonmonotonic modal relevant sequent calculus equipped with special operators, □ and R. The base level of this calculus consists of two different types of atomic axioms: material and relevant. The material base contains, along with all the flat atomic sequents (e.g., Γ0, p |~0 p), some non-flat, defeasible atomic sequents (e.g., Γ0, p |~0 q); whereas the relevant base consists of the local region of such a material base that is sensitive to relevance. The rules of the calculus uniquely and conservatively extend these two types of nonmonotonic bases into logically complex material/relevant consequence relations and incoherence properties, while preserving Containment in the material base and Reflexivity in the relevant base. The material extension is supra-intuitionistic, whereas the relevant extension is stronger than a logic slightly weaker than R. The relevant extension also avoids the fallacies of relevance. Although the extended material consequence relation is defeasible and insensitive to relevance, it has local regions of indefeasibility and relevance (the latter of which is marked by the relevant extension). The newly introduced operators, □ and R, codify these local regions within the same extended material consequence relation.

Shuhei Shimamura

### A Formalization of the Greater Fools Theory with Dynamic Epistemic Logic

The greater fools explanation of financial bubbles says that traders are willing to pay more for an asset than they deem it worth, because they anticipate they might be able to sell it to someone else for an even higher price. As agents’ beliefs about other agents’ beliefs are at the heart of the greater fools theory, this paper comes to formal terms with the theory by translating the phenomenon into the language and models of dynamic epistemic logic. By presenting a formalization of greater fools reasoning, structural insights are obtained pertaining to the structure of its higher-order content and the role of common knowledge.

Hanna S. van Lee

### On Axiomatization of Epistemic GDL

The Game Description Language (GDL) has been introduced as an official language for specifying games in the AAAI General Game Playing Competition since 2005. It was originally designed as a declarative language for representing rules of arbitrary games with perfect information. More recently, an epistemic extension of GDL, called EGDL, has been proposed for representing and reasoning about imperfect information games. In this paper, we develop an axiomatic system for a variant of EGDL and prove its soundness and completeness with respect to the semantics based on the epistemic state transition model. With a combination of action symbols, temporal modalities and epistemic operators, the completeness proof requires novel combinations of techniques used for completeness of propositional dynamic logic and epistemic temporal logic. We demonstrate how to use the proof theory for inferring game properties from game rules.

Guifei Jiang, Laurent Perrussel, Dongmo Zhang

### Putting More Dynamics in Revision with Memory

We have proposed in previous works [14, 15] a construction that allows to define operators for iterated revision from classical AGM revision operators. We called these operators revision operators with memory and show that the operators obtained have nice logical properties. But these operators can be considered as too conservative, since the revision policy of the agent, encoded as a faithful assignment, does not change during her life. In this paper we propose an extension of these operators, that aims to add more dynamics in the revision process.

Sébastien Konieczny, Ramón Pino Pérez

### An Empirical Route to Logical ‘Conventionalism’

The laws of classical logic are taken to be logical truths, which in turn are taken to hold objectively. However, we might question our faith in these truths: why are they true? One general approach, proposed by Putnam [8] and more recently Dickson [3] or Maddy [5], is to adopt empiricism about logic. On this view, logical truths are true because they are true of the world alone – this gives logical truths an air of objectivity. Putnam and Dickson both take logical truths to be true in virtue of the world’s structure, given by our best empirical theory, quantum mechanics. This assumes a determinate logical structure of the world given by quantum mechanics. Here, I argue that this assumption is false, and that the world’s logical structure, and hence the related ‘true’ logic, are underdetermined. This leads to what I call empirical conventionalism.

Eugene Chua

### Beating the Gatecrasher Paradox with Judiciary Narratives

A probabilistic model for the narrative approach to reasoning in legal fact-finding is developed and applied to the gatecrasher paradox.

Rafal Urbaniak

### Distributed Knowledge Whether

(Extended Abstract)

As is known, by putting their knowledge together, agents can obtain distributed knowledge. However, by pooling their non-ignorance, agents can only obtain distributed knowledge as to whether something holds, rather than distributed knowledge (of something).

Jie Fan

### A Note on Belief, Question Embedding and Neg-Raising

The epistemic verb to believe does not embed polar questions, unlike the verb to know. After reviewing this phenomenon, I propose an explanation which connects the neg-raising behavior of belief with its embedding patterns (following [14]). I use dynamic epistemic logic to model the presuppositions and the effects associated with belief assertions.

Michael Cohen

### Distributed Knowing Whether

(Extended Abstract)

Standard epistemic logic studies reasoning patterns about ‘knowing that’, where interesting group notions of ‘knowing that’ arise naturally, such as distributed knowledge and common knowledge. In recent research, other notions of knowledge are also studied, such as ‘knowing whether’, ‘knowing how’, and so on. It is natural to ask what are the group notions of these non-standard knowledge expressions. This paper makes an initial attempt in this line, by looking at the notion corresponding to distributed knowledge in the setting of ‘knowing whether’. We introduce the distributed know-whether operator, and give complete axiomatizations of the resulting logics over arbitrary or $$\mathcal {S}$$S5 frames, based on the corresponding axiomatizations of ‘knowing whether’.

Xingchi Su

### A Causal Theory of Speech Acts

In speech acts, a speaker utters sentences that might affect the belief state of a hearer. To formulate causal effects in assertive speech acts, we introduce a logical theory that encodes causal relations between speech acts, belief states of agents, and truth values of sentences. We distinguish trustful and untrustful speech acts depending on the truth value of an utterance, and distinguish truthful and untruthful speech acts depending on the belief state of a speaker. Different types of speech acts cause different effects on the belief state of a hearer, which are represented by the set of models of a causal theory. Causal theories of speech acts are also translated into logic programs, which enables one to represent and reason about speech acts in answer set programming.

Chiaki Sakama

### An Axiomatisation for Minimal Social Epistemic Logic

A two-dimensional modal logic, intended for applications in social epistemic logic, with one dimension for agents and the other for epistemic states is given. The language has hybrid logic devices for agents, as proposed in earlier papers by Seligman, Liu and Girard. We give an axiomatisation and a proof of its completeness.

Liang Zhen

### Relief Maximization and Rationality

This paper introduces the concept of relief maximization in decisions and games and shows how it can explain experimental behavior, such as asymmetric dominance and decoy effects. Next, two possible evolutionary explanations for the survival of relief-based behavior are sketched.

Paolo Galeazzi, Zoi Terzopoulou

### Reason to Believe

In this paper we study the relation between nonmonotonic reasoning and belief revision. Our main conceptual contribution is to suggest that nonmonotonic reasoning guides but does not determine an agent’s belief revision. To be adopted as beliefs, defeasible conclusions should remain stable in the face of certain bodies of information. This proposal is formalized in what we call a two-tier semantics for nonmonotonic reasoning and belief revision. The main technical result is a sound and complete axiomatization for this semantic.

Chenwei Shi, Olivier Roy

### Justification Logic with Approximate Conditional Probabilities

The importance of logics with approximate conditional probabilities is reflected by the fact that they can model non-monotonic reasoning. We introduce a new logic of this kind, $$\mathsf {CPJ}$$CPJ, which extends justification logic and supports non-monotonic reasoning with and about evidences.

Zoran Ognjanović, Nenad Savić, Thomas Studer

### From Concepts to Predicates Within Constructivist Epistemology

In this research constructivist epistemology provides a ground for conceptual analysis of concept construction, conception production, and concept learning processes. Relying on a constructivist model of knowing, this research will make an epistemological and logical linkage between concepts and predicates.