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Within ZFC, we develop a general technique to topologize trees that provides a uniform approach to topological completeness results in modal logic with respect to zerodimensional Hausdorff spaces. Embeddings of these spaces into wellknown extremally disconnected spaces then gives new completeness results for logics extending S4.2. 

We study logic translations from an abstract perspective, without any commitment to the structure of sentences and the nature of logical entailment, which also means that we cover both proof theoretic and modeltheoretic entailment. We show how logic translations induce notions of logical expressiveness, consistency strength and sublogic, leading to an explanation of paradoxes that have been described in the literature. Connectives and quantifiers, although not present in the definition of logic and logic translation, can be recovered by their abstract (...) 

The paper aims at studying, in full generality, logics defined by imposing a variable inclusion condition on a given logic \. We prove that the description of the algebraic counterpart of the left variable inclusion companion of a given logic \ is related to the construction of Płonka sums of the matrix models of \. This observation allows to obtain a Hilbertstyle axiomatization of the logics of left variable inclusion, to describe the structure of their reduced models, and to locate (...) 

The aim of this paper is to initiate a systematic exploration of the model theory of epistemic plausibility models (EPMs). There are two subtly different definitions in the literature: one by van Benthem and one by Baltag and Smets. Because van Benthem's notion is the most general, most of the paper is dedicated to this notion. We focus on the notion of bisimulation, and show that the most natural generalization of bisimulation to van Benthemtype EPMs fails. We then introduce parametrized (...) 

This paper studies Aumann’s agreeing to disagree theorem from the perspective of dynamic epistemic logic. This was first done by Dégremont and Roy (J Phil Log 41:735–764, 2012) in the qualitative framework of plausibility models. The current paper uses a probabilistic framework, and thus stays closer to Aumann’s original formulation. The paper first introduces enriched probabilistic Kripke frames and models, and various ways of updating them. This framework is then used to prove several agreement theorems, which are natural formalizations of (...) 

Epistemic logic with its possible worlds semantic model is a powerful framework that allows us to represent an agent’s information not only about propositional facts, but also about her own information. Nevertheless, agents represented in this framework are logically omniscient: their information is closed under logical consequence. This property, useful in some applications, is an unrealistic idealisation in some others. Many proposals to solve this problem focus on weakening the properties of the agent’s information, but some authors have argued that (...) 

Supervaluationism is a well known theory of vagueness. Subvaluationism is a less well known theory of vagueness. But these theories cannot be taken apart, for they are in a relation of duality that can be made precise. This paper provides an introduction to the subvaluationist theory of vagueness in connection to its dual, supervaluationism. A survey on the supervaluationist theory can be found in the Compass paper of Keefe (2008); our presentation of the theory in this paper will be short (...) 

Hybrid languages are introduced in order to evaluate the strength of “minimal” mereologies with relatively strong frame definability properties. Appealing to a robust form of nominalism, I claim that one investigated language \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{69pt} \begin{document}$\mathcal {H}_{\textsf {m}}$\end{document} is maximally acceptable for nominalistic mereology. In an extension \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{69pt} \begin{document}$\mathcal {H}_{\textsf {gem}}$\end{document} of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{69pt} \begin{document}$\mathcal {H}_{\textsf {m}}$\end{document}, a modal analog (...) 

Sahlqvist formulas are a syntactically specified class of modal formulas proposed by Hendrik Sahlqvist in 1975. They are important because of their firstorder definability and canonicity, and hence axiomatize complete modal logics. The firstorder properties definable by Sahlqvist formulas were syntactically characterized by Marcus Kracht in 1993. The present paper extends Kracht's theorem to the class of ‘generalized Sahlqvist formulas' introduced by Goranko and Vakarelov and describes an appropriate generalization of Kracht formulas. 

The general verificationist thesis says that What is true can be known or formally: φ → ◊Kφ VT Fitch's argument trivializes this principle. It uses a weak modal epistemic logic to show that VT collapses truth and knowledge, by taking a clever substitution instance for φ: P ∧ ¬KP → ◊ K(P ∧ ¬KP) Then we have the following chain of three conditionals (a) ◊ K(P ∧ ¬KP) → ◊ (KP ∧ K¬KP) in the minimal modal logic for the knowledge (...) 

This paper presents a new modal logic for ceteris paribus preferences understood in the sense of "all other things being equal". This reading goes back to the seminal work of Von Wright in the early 1960's and has returned in computer science in the 1990' s and in more abstract "dependency logics" today. We show how it differs from ceteris paribus as "all other things being normal", which is used in contexts with preference defeaters. We provide a semantic analysis and (...) 

Biological modalities play an important explanatory role in biological practice. However, biological modalities lack truth conditions and the inferential relationship between biological and other modalities is unclear. This thesis addresses these problems, first, by improving upon Daniel Dennett's Library of Mendel. Second, a family of modal logics is introduced. In the simplest model, states are interpreted as codons, the binary relation is interpreted as single substitution mutation and the valuation induces a partition of blocks of codons that code for some (...) 

Large databases of linguistic annotations are used for testing linguistic hypotheses and for training language processing models. These linguistic annotations are often syntactic or prosodic in nature, and have a hierarchical structure. Query languages are used to select particular structures of interest, or to project out large slices of a corpus for external analysis. Existing languages suffer from a variety of problems in the areas of expressiveness, efficiency, and naturalness for linguistic query. We describe the domain of linguistic trees and (...) 

Statements not only update our current knowledge, but also have other dynamic effects. In particular, suggestions or commands ?upgrade' our preferences by changing the current order among worlds. We present a complete logic of knowledge update plus preference upgrade that works with dynamicepistemicstyle reduction axioms. This system can model changing obligations, conflicting commands, or ?regret'. We then show how to derive reduction axioms from arbitrary definable relation changes. This style of analysis also has a product update version with preferences between (...) 

This article presents an overview of the basic philosophical motivations for, and some recent work in, modal set theory. 

In this investigation we explore a general strategy for constructing modal theories where the modal notion is conceived as a predicate. The idea of this strategy is to develop modal theories over axiomatic theories of truth. In this first paper of our two part investigation we develop the general strategy and then apply it to the axiomatic theory of truth FriedmanSheard. We thereby obtain the theory Modal FriedmanSheard. The theory Modal FriedmanSheard is then discussed from three different perspectives. First, we (...) 

Preference is a key area where analytic philosophy meets philosophical logic. I start with two related issues: reasons for preference, and changes in preference, first mentioned in von Wright’s book The Logic of Preference but not thoroughly explored there. I show how these two issues can be handled together in one dynamic logical framework, working with structured twolevel models, and I investigate the resulting dynamics of reasonbased preference in some detail. Next, I study the foundational issue of entanglement between preference (...) 

This paper argues that relativity of truth to a world plays no significant role in empirical semantic theory, even as it is done in the modeltheoretic tradition relying on intensional type theory. Some philosophical views of content provide an important notion of truth at a world, but they do not constrain the empirical domain of semantic theory in a way that makes this notion empirically significant. As an application of this conclusion, this paper shows that a potential motivation for relativism (...) 

We investigate the process of truthseeking by iterated belief revision with higherlevel doxastic information . We elaborate further on the main results in Baltag and Smets (Proceedings of TARK, 2009a , Proceedings of WOLLIC’09 LNAI 5514, 2009b ), applying them to the issue of convergence to truth . We study the conditions under which the belief revision induced by a series of truthful iterated upgrades eventually stabilizes on true beliefs. We give two different conditions ensuring that beliefs converge to “full” (...) 

We investigate an aspect of defeasibility that has somewhat been overlooked by the nonmonotonic reasoning community, namely that of defeasible modes of reasoning. These aim to formalise defeasibility of the traditional notion of necessity in modal logic, in particular of its different readings as action, knowledge and others in specific contexts, rather than defeasibility of conditional forms. Building on an extension of the preferential approach to modal logics, we introduce new modal osperators with which to formalise the notion of defeasible (...) 

This paper investigates and develops generalizations of twodimensional modal logics to any finite dimension. These logics are natural extensions of multidimensional systems known from the literature on logics for a priori knowledge. We prove a completeness theorem for propositional ndimensional modal logics and show them to be decidable by means of a systematic tableau construction. 

In this paper, we present several extensions of epistemic logic with update operators modelling public information change. Next to the wellknown public announcement operators, we also study public substitution operators. We prove many of the results regarding expressivity and completeness using socalled reduction axioms. We develop a general method for using reduction axioms and apply it to the logics at hand. 

In this paper I study intentions of the form, that is, intentions with a wecontent, and their role in interpersonal coordination. I focus on the notion of epistemic support for such intentions. Using tools from epistemic game theory and epistemic logic, I cast doubt on whether such support guarantees the other agents' conditional mediation in the achievement of such intentions, something that appears important if intentions with a wecontent are to count as genuine intentions. I then formulate a stronger version (...) 

In this paper we provide frame definability results for weak versions of classical modal axioms that can be expressed in Fitting's manyvalued modal languages. These languages were introduced by M. Fitting in the early '90s and are built on Heyting algebras which serve as the space of truth values. The possibleworlds frames interpreting these languages are directed graphs whose edges are labelled with an element of the underlying Heyting algebra, providing us a form of manyvalued accessibility relation. Weak axioms of (...) 

Fictional truth, or truth in fiction/pretense, has been the object of extended scrutiny among philosophers and logicians in recent decades. Comparatively little attention, however, has been paid to its inferential relationships with time and with certain deliberate and contingent human activities, namely, the creation of fictional works. The aim of the paper is to contribute to filling the gap. Toward this goal, a formal framework is outlined that is consistent with a variety of conceptions of fictional truth and based upon (...) 

We provide a Hilbertstyle axiomatization of the logic of , as well as a twodimensional semantics with respect to which our logics are sound and complete. Our completeness results are quite general, pertaining to all such actuality logics that extend a normal and canonical modal basis. We also show that our logics have the strong finite model property and permit straightforward firstorder extensions. 

In this paper I use the distinction between hard and soft information from the dynamic epistemic logic tradition to extend prior work on informational conceptions of logic to include nonmonotonic consequencerelations. In particular, I defend the claim that at least some nonmonotonic logics can be understood on the basis of soft or “belieflike” logical information, and thereby question the orthodox view that all logical information is hard, “knowledgelike”, information. 

In this work we summarise the concept of bisimulation, widely used both in computational sciences and in modal logic, that characterises modal structures with the same behaviour in terms of accessibility relations. Then, we offer a sketch of categorical interpretation of bisimulation between modal structures, which comprise both the structure and the valuation from a propositional language. 

Duality in Logic and Language [draftdo not cite this article] Duality phenomena occur in nearly all mathematically formalized disciplines, such as algebra, geometry, logic and natural language semantics. However, many of these disciplines use the term ‘duality’ in vastly different senses, and while some of these senses are intimately connected to each other, others seem to be entirely … Continue reading Duality in Logic and Language →. 

While standard firstorder modal logic is quite powerful, it cannot express even very simple sentences like “I could have been taller than I actually am” or “Everyone could have been smarter than they actually are”. These are examples of crossworld predication, whereby objects in one world are related to objects in another world. Extending firstorder modal logic to allow for crossworld predication in a motivated way has proven to be notoriously difficult. In this paper, I argue that the standard accounts (...) 

In this paper, we study indiscernibility relations and complementarity relations in hyper arrow structures. A firstorder characterization of indiscernibility and complementarity is obtained through a duality result between hyper arrow structures and certain structures of relational type characterized by firstorder conditions. A modal analysis of indiscernibility and complementarity is performed through a modal logic which modalities correspond to indiscernibility relations and complementarity relations in hyper arrow structures. 

In the paper we present a technique for eliminating quantifiers of arbitrary order, in particular of firstorder. Such a uniform treatment of the elimination problem has been problematic up to now, since techniques for eliminating firstorder quantifiers do not scale up to higherorder contexts and those for eliminating higherorder quantifiers are usually based on a form of monotonicity w.r.t implication and are not applicable to the firstorder case. We make a shift to arbitrary relations “ordering” the underlying universe. This allows (...) 

The Moral Law is fulfilled iff everything that ought to be the case is the case, and The Good is realised in a possible world w at a time t iff w is deontically accessible from w at t. In this paper, I will introduce a set of temporal modal deontic systems with propositional quantifiers that can be used to prove some interesting theorems about The Moral Law and The Good. First, I will describe a set of systems without any (...) 

Analogues of Scott's isomorphism theorem, Karp's theorem as well as results on lack of compactness and strong completeness are established for infinitary propositional relevant logics. An "interpolation theorem" for the infinitary quantificational boolean logic Linfinity omega. holds. This yields a preservation result characterizing the expressive power of infinitary relevant languages with absurdity using the modeltheoretic relation of relevant directed bisimulation as well as a Beth definability property. 

O presente volume se trata de uma coletânea de artigos que reúne alguns dos trabalhos propostos para o evento “III International Colloquium of Analytic Epistemology and VII Conference of Social Epistemology”, realizado entre os dias 27 e 30 de Novembro de 2018, na Universidade Federal de Santa Maria. O “III International Colloquium of Analytic Epistemology and VII Conference of Social Epistemology” é um dos principais eventos de Epistemologia analítica da América Latina e reúne especialistas do Brasil e do exterior para (...) 

Special issue: "Reflecting on the Legacy of C.I. Lewis: Contemporary and Historical Perspectives on Modal Logic". 

In this paper, I will develop a set of boulesicdoxastic tableau systems and prove that they are sound and complete. Boulesicdoxastic logic consists of two main parts: a boulesic part and a doxastic part. By ‘boulesic logic’ I mean ‘the logic of the will’, and by ‘doxastic logic’ I mean ‘the logic of belief’. The first part deals with ‘boulesic’ concepts, expressions, sentences, arguments and theorems. I will concentrate on two types of boulesic expression: ‘individual x wants it to be (...) 

The Interrogative Model of Inquiry and Dynamic Epistemic Logics are two central paradigms in formal epistemology. This paper is motivated by the observation of a significant complementarity between them: on the one hand, the IMI provides a framework for investigating inquiry represented as an idealized game between an Inquirer and Nature, along with an account of the interaction between questions and inferences in informationseeking processes, but is lacking a formulation in the multiagent case; on the other hand, DELs model various (...) 



Epistemic naturalism holds that the results or methodologies from the cognitive sciences are relevant to epistemology, and some have maintained that scientific methods are more compatible with externalist theories of justification than with internalist theories. But practically all discussions about naturalized epistemology are framed exclusively in terms of cognitive psychology, which is only one of the cognitive sciences. The question addressed in this essay is whether a commitment to naturalism really does favor externalism over internalism, and we offer reasons for (...) 

This paper supersedes an ealier version, entitled "A NonStandard Semantics for Inexact Knowledge with Introspection", which appeared in the Proceedings of "Rationality and Knowledge". The definition of token semantics, in particular, has been modified, both for the single and the multiagent case. 

The picture of information acquisition as the elimination of possibilities has proven fruitful in many domains, serving as a foundation for formal models in philosophy, linguistics, computer science, and economics. While the picture appears simple, its formalization in dynamic epistemic logic reveals subtleties: given a valid principle of information dynamics in the language of dynamic epistemic logic, substituting complex epistemic sentences for its atomic sentences may result in an invalid principle. In this article, we explore such failures of uniform substitution. (...) 

The impossibility theorem of Dekel, Lipman and Rustichini has been thought to demonstrate that standard statespace models cannot be used to represent unawareness. We first show that Dekel, Lipman and Rustichini do not establish this claim. We then distinguish three notions of awareness, and argue that although one of them may not be adequately modeled using standard state spaces, there is no reason to think that standard state spaces cannot provide models of the other two notions. In fact, standard space (...) 

Recent years witnessed a growing interest in nonstandard epistemic logics of knowing whether, knowing how, knowing what, knowing why and so on. The new epistemic modalities introduced in those logics all share, in their semantics, the general schema of ∃x◻φ, e.g., knowing how to achieve φ roughly means that there exists a way such that you know that it is a way to ensure that φ. Moreover, the resulting logics are decidable. Inspired by those particular logics, in this work, we (...) 

Notions of kasimulation and asimulation are introduced as asymmetric counterparts to kbisimulation and bisimulation, respectively. It is proved that a firstorder formula is equivalent to a standard translation of an intuitionistic propositional formula iff it is invariant with respect to kasimulations for some k, and then that a firstorder formula is equivalent to a standard translation of an intuitionistic propositional formula iff it is invariant with respect to asimulations. Finally, it is proved that a firstorder formula is equivalent to a (...) 

We prove that every firstorder formula that is invariant under quasiinjective bisimulations is equivalent to a formula of the hybrid logic . Our proof uses a variation of the usual unravelling technique. We also briefly survey related results, and show in a standard way that it is undecidable whether a firstorder formula is invariant under quasiinjective bisimulations. 

In this paper we investigate a logic for modelling individual and collective acceptances that is called acceptance logic. The logic has formulae of the form $A_{Gx} \phi $ reading 'if the agents in the set of agents G identify themselves with institution x then they together accept that φ'. We extend acceptance logic by two kinds of dynamic modal operators. The first kind are public announcements of the form x!ψ, meaning that the agents learn that ψ is the case in (...) 

We continue the work initiated in Herzig and Lorini (J Logic Lang Inform, in press) whose aim is to provide a minimalistic logical framework combining the expressiveness of dynamic logic in which actions are firstclass citizens in the object language, with the expressiveness of logics of agency such as STIT and logics of group capabilities such as CL and ATL. We present a logic called ( Deterministic Dynamic logic of Agency ) which supports reasoning about actions and joint actions of (...) 

This paper is a study of higherorder contingentism – the view, roughly, that it is contingent what properties and propositions there are. We explore the motivations for this view and various ways in which it might be developed, synthesizing and expanding on work by Kit Fine, Robert Stalnaker, and Timothy Williamson. Special attention is paid to the question of whether the view makes sense by its own lights, or whether articulating the view requires drawing distinctions among possibilities that, according to (...) 