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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 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 (...) 

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. 

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 (...) 

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 (...) 

Abstract 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 Hm is maximally acceptable for nominalistic mereology. In an extension Hgem of Hm, a modal analog for the classical systems of Leonard and Goodman (J Symb Log 5:45–55, 1940) and Lesniewski (1916) is introduced and shown to be complete with respect to 0 deleted Boolean algebras. We characterize (...) 

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. 

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 (...) 

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 (...) 

In the literature there are at least two main formal structures to deal with situations of interactive epistemology: Kripke models and type spaces. As shown in many papers :149–225, 1999; Battigalli and Siniscalchi in J Econ Theory 106:356–391, 2002; Klein and Pacuit in Stud Log 102:297–319, 2014; Lorini in J Philos Log 42:863–904, 2013), both these frameworks can be used to express epistemic conditions for solution concepts in game theory. The main result of this paper is a formal comparison between (...) 

This paper contributes to the principled construction of tableaubased decision procedures for hybrid logic with global, difference, and converse modalities. We also consider reflexive and transitive relations. For conversefree formulas we present a terminating control that does not rely on the usual chainbased blocking scheme. Our tableau systems are based on a new model existence theorem. 



The paper sketches an analysis of the notion of a selffulfilling belief in terms of doxastic modal logic. We point out a connection between selffulfilling beliefs and Moore’s paradox. Then we look at selffulfilling beliefs in the context of neighborhood semantics. We argue that the analysis of several interesting selffulfilling beliefs has to make essential use of propositional quantification. 

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

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 (...) 

In the tradition of quantified modal logic, it was assumed that significantly different linguistic systems underlie reference to individuals, to times and to 'possible worlds'. Various results from recent research in formal semantics suggest that this is not so, and that there is in fact a pervasive symmetry between the linguistic means with which we refer to these three domains. Reference to individuals, times and worlds is uniformly effected through generalized quantifiers, definite descriptions, and pronouns, and in each domain grammatical (...) 

McCall (1984) offered a semantics of counterfactual conditionals based on “real possible worlds” that avoids using the vague notion of similarity between possible worlds. I will propose an interpretation of McCall’s counterfactuals in a formal framework based on BaltagMossSolecki events and protocols. Moreover, I will argue that using this interpretation one can avoid an objection raised by Otte (1987). 

We study set algebras with an operator (SAO) that satisfy the axioms of S5 knowledge. A necessary and sufficient condition is given for such SAOs that the knowledge operator is defined by a partition of the state space. SAOs are constructed for which the condition fails to hold. We conclude that no logic singles out the partitional SAOs among all SAOs. 

In this paper we define and examine frame constructions for the family of manyvalued modal logics introduced by M. Fitting in the '90s. Every language of this family is built on an underlying space of truth values, a Heyting algebra H. We generalize Fitting's original work by considering complete Heyting algebras as truth spaces and proceed to define a suitable notion of Hindexed families of generated subframes, disjoint unions and bounded morphisms. Then, we provide an algebraic generalization of the canonical (...) 

The main aim of this paper is to present a way to improve the e.ciency of an intelligent alarm correlation module by means of an abductive reasoner. The alarm correlation module is integrated in a more complex system that performs monitoring and control tasks over a tract of a highway. On the basis of a specific theory on the domain, explanations of anomalous traffic patterns can be provided taking into account those situations not directly detected by data acquisition technology. The (...) 

We present a modal logic called (logic of intention and attempt) in which we can reason about intention dynamics and intentional action execution. By exploiting the expressive power of , we provide a formal analysis of the relation between intention and action and highlight the pivotal role of attempt in action execution. Besides, we deal with the problems of instrumental reasoning and intention persistence. 

The metaphor of a branching tree of future possibilities has a number of important philosophical and logical uses. In this paper we trace this metaphor through some of its uses and argue that the metaphor works the same way in physics as in philosophy. We then give an overview of formal systems for branching possibilities, viz., branching time and (briefly) branching spacetimes. In a next step we describe a number of different notions of possibility, thereby sketching a landscape of possibilities. (...) 

Timothy Williamson has argued that in the debate on modal ontology, the familiar distinction between actualism and possibilism should be replaced by a distinction between positions he calls contingentism and necessitism. He has also argued in favor of necessitism, using results on quantified modal logic with plurally interpreted secondorder quantifiers showing that necessitists can draw distinctions contingentists cannot draw. Some of these results are similar to wellknown results on the relative expressivity of quantified modal logics with socalled inner and outer (...) 

Since the early days of physics, space has called for means to represent, experiment, and reason about it. Apart from physicists, the concept of space has intrigued also philosophers, mathematicians and, more recently, computer scientists. This longstanding interest has left us with a plethora of mathematical tools developed to represent and work with space. Here we take a special look at this evolution by considering the perspective of Logic. From the initial axiomatic efforts of Euclid, we revisit the major milestones (...) 



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 (...) 

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 (...) 

(2012). Modal logics for reasoning about infinite unions and intersections of binary relations. Journal of Applied NonClassical Logics: Vol. 22, No. 4, pp. 275294. doi: 10.1080/11663081.2012.705960. 