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We propose a dynamic-epistemic analysis of perceptual knowledge placing structured observational events at center stage. Our starting point is the specific entanglement of epistemic accessibility with the relation of ‘closeness’ or... more
We propose a dynamic-epistemic analysis of perceptual knowledge placing structured observational events at center stage. Our starting point is the specific entanglement of epistemic accessibility with the relation of ‘closeness’ or similarity, that is claimed in the so-called Margin of Error principle. While we find the standard formulation of this principle to be defective, we think that it contains valuable intuitions for a joint logic of closeness and uncertainty, whose contours we develop. In particular, our analysis explains how imprecise observation can lead to higher-precision knowledge.
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Monotonicity-based inference is a fundamental notion in the logical semantics of natural language, and also in logic in general. Start- ing in generalized quantifier theory, we distinguish three senses of the notion, study their... more
Monotonicity-based inference is a fundamental notion in the logical semantics of natural language, and also in logic in general. Start- ing in generalized quantifier theory, we distinguish three senses of the notion, study their relations, and use these to connect monotonicity to logics of model change. At the end we return to natural language and consider monotonicity inference in linguistic settings with vocabulary for various forms of change. While we mostly raise issues in this paper, we do make a number of new observations backing up our distinctions.
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KNAW Narcis. Back to search results. Publication Games at the Institute for Logic, Language and Computation (2005). Pagina-navigatie: Main. ...
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Abstract. This paper looks at deontic logic as resulting from both a betterness ordering on states (ie, a 'deontic preference') and a priority ordering on properties (ie, a 'law'explicitly representing a standard of... more
Abstract. This paper looks at deontic logic as resulting from both a betterness ordering on states (ie, a 'deontic preference') and a priority ordering on properties (ie, a 'law'explicitly representing a standard of behavior). The correspondence between these two orderings offers a rich perspective from which to look at deontic scenarios and puzzles, and in particular at contrary-to-duties. The framework naturally lends itself to describing dynamics involving both orderings, thereby providing a new analysis of norm change as 'betterness ...
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This chapter gives an overview of current dynamic logics that describe belief update and revision, both for single agents and in multi-agent settings. We employ a mixture of ideas from AGM belief revision theory and dynamic-epistemic... more
This chapter gives an overview of current dynamic logics that describe belief update and revision, both for single agents and in multi-agent settings. We employ a mixture of ideas from AGM belief revision theory and dynamic-epistemic logics of information-driven agency. After describing the basic background, we review logics of various kinds of beliefs based on plausibility models, and then go on to various sorts of belief change engendered by changes in current models through hard and soft information. We present matching complete logics with dynamic-epistemic recursion axioms, and develop a very general perspective on belief change by the use of event models and priority update. The chapter continues with three topics that naturally complement the setting of single steps of belief change: connections with probabilistic approaches to belief change, long-term temporal process structure including links with formal learning theory, and multi-agent scenarios of information flow and bel...
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Imagine for a moment that you are given the opportunity of a trip to the ancient state of Qi (齊) in a suitably reliable time machine. Your destination is the famous Jixia (稷下) academy, which was founded during the reign of the King Wei of... more
Imagine for a moment that you are given the opportunity of a trip to the ancient state of Qi (齊) in a suitably reliable time machine. Your destination is the famous Jixia (稷下) academy, which was founded during the reign of the King Wei of Qi (齊威王, 356–321 BC). When you arrive, the halls will be full of scholars debating such topics as the importance of ritual lǐ (禮), how to determine what is right yì (義), the relationship between names míng (名) and objects/reality shí (實), and of course, human nature xìng (性). Equipped with the tools of ...
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Analyzing the behavior of agents in a dynamic environment requires describing the evolution of their knowledge as they receive new information. But equally crucial are agents ’ beliefs over time, since most of our decisions and actions... more
Analyzing the behavior of agents in a dynamic environment requires describing the evolution of their knowledge as they receive new information. But equally crucial are agents ’ beliefs over time, since most of our decisions and actions involve uncertainty, from going to work to selling shares. Beliefs, too, are information-based, and when refuted, they have to be revised in systematic ways. These phenomena have been studied in many different formal frameworks, including, game theory [14, 5], belief revision theory [1], and formal learning theory [24, 22]. In this paper, however, we are concerned with two logic-based approaches. One are dynamic logics for changing beliefs that have been developed recently (van Benthem [7], Baltag and Smets [3]) using plausibility relations between worlds to represent agents ’ beliefs and conditional beliefs. An act of revision is then a single step of change in such a relation, triggered by some new incoming, hard or soft, information. Of course, suc...
On October 14 – 16, 2013, a large group of Chinese and foreign logicians gathered at Tsinghua University to present a broad and lively picture of the field of logic in its various ramifications today. As can be seen in the scientific... more
On October 14 – 16, 2013, a large group of Chinese and foreign logicians gathered at Tsinghua University to present a broad and lively picture of the field of logic in its various ramifications today. As can be seen in the scientific program at the webpage www.tsinghualogic.net, topics at the international conference “Logic across the University: Foundations and Applications” ranged from mathematics, philosophy, and linguistics to computer science and the cognitive and social sciences. In addition, two evening lectures highlighted major outside interfaces of logic with society and industry. The interested reader can find the material of this conference in the Proceedings, prepared by the editors of the current piece, that appeared with College Publications London. Moreover, reports for a more general audience on various aspects of the conference have appeared in China Science Daily and Chinese Social Sciences Today. While participants came from a wide range of disciplinary backgroun...
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... more
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.
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Classical epistemic logic describes implicit knowledge of agents about facts and knowledge of other agents, based on semantic information. The latter is produced by acts of observation or communication, that are described well by dynamic... more
Classical epistemic logic describes implicit knowledge of agents about facts and knowledge of other agents, based on semantic information. The latter is produced by acts of observation or communication, that are described well by dynamic epistemic logics. What these logics do not describe, however, is how significant information is also produced by acts of inference – and key axioms of the system merely postulate “deductive closure”. In this paper, we take the view that all information is produced by acts, and hence we also need a dynamic logic of inference steps showing what effort on the part of the agent makes a conclusion explicit knowledge. Strong omniscience properties of agents should be seen not as static idealizations, but as the result of dynamic processes that agents engage in. This raises two questions: (a) how to define suitable information states of agents and matching notions of explicit knowledge, (b) how to define natural processes over these states that generate ne...
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Modern logic has the tools for becoming a broad science of reasoning and other information directed behavior that plays an important role in connecting the humanities, exact sciences and social sciences at the university, and which is... more
Modern logic has the tools for becoming a broad science of reasoning and other information directed behavior that plays an important role in connecting the humanities, exact sciences and social sciences at the university, and which is part of the bedrock of our information society. This paper is a revised version of a valedictory lecture delivered on 26 September 2014 as a University Professor of Pure and Applied Logic in the main auditorium of the University of Amsterdam. It traces the history of modern logic, illustrates the emergence of new trends in logic and agency, and discusses the most important future challenges facing it.
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The filtration method for proving decidability in a focused minimal manner is a highlight of modal logic, widely used, but also posing a bit of a challenge as to its scope and what makes it tick. In this paper, we bring together a number... more
The filtration method for proving decidability in a focused minimal manner is a highlight of modal logic, widely used, but also posing a bit of a challenge as to its scope and what makes it tick. In this paper, we bring together a number of modern perspectives on filtration, including model-theoretic and proof-theoretic ones. We also include a few more unusual recent connections with dynamic logics of model change and logics of questions and issues. Finally, we analyze where the filtration method fails in full first-order logic, and what it still has to say there.
Two of the authors (van Benthem and Pacuit) recently introduced evidence logic as a way to model epistemic agents faced with possibly contradictory evidence from different sources. For this the authors used neighborhood semantics, where a... more
Two of the authors (van Benthem and Pacuit) recently introduced evidence logic as a way to model epistemic agents faced with possibly contradictory evidence from different sources. For this the authors used neighborhood semantics, where a neighborhood N indicates that the agent has reason to believe that the true state of the world lies in N. A normal belief modality is defined in terms of the neighborhood structure. In this paper we consider four variants of evidence logic which hold for different classes of evidence models. For each of these logics we give a representation theorem using extended evidence models, where the belief operator is replaced by a standard relational modality. With this, we axiomatize all four logics, and determine whether each has the finite model property.
On 26 September 2014, Johan van Benthem, Professor of Pure and Applied Logic, delivered his valedictory lecture in the auditorium of the University of Amsterdam. Modern logic is the broad, exact science of information directed behaviour... more
On 26 September 2014, Johan van Benthem, Professor of Pure and Applied Logic, delivered his valedictory lecture in the auditorium of the University of Amsterdam. Modern logic is the broad, exact science of information directed behaviour that plays an important role in connecting the humanities, exact sciences and social sciences at the university, and which forms the bedrock of our information society. In his valedictory lecture, van Benthem illustrates the creation of this scientific field and the most important future challenges facing it.
If logic is the general study of a priori valid reasoning, then where is the paradigmatic area where we see this reasoning in its full glory? To some, this is clearly mathematics, where precision is relentless, and strings of inferences... more
If logic is the general study of a priori valid reasoning, then where is the paradigmatic area where we see this reasoning in its full glory? To some, this is clearly mathematics, where precision is relentless, and strings of inferences are taken to impressive lengths. But on another view, the highest form of reasoning is displayed in the ordinary world of common sense – say, when engaging in conversation about something that matters, where pure information is deeply intertwined with evaluation and goals, and where, crucially, we are surrounded by further agents like us that we must interact with. On the first view, to simplify things a bit, logic is about mathematical proof and related processes like computation, making mathematical logic and foundations of mathematics the heart of the field. Agency is not even needed, and no human aspects are modeled. On the second view (frankly speaking: my own), logic is about interactive agency and all that entails, making philosophical logic a...
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This piece is not a paper reporting on original research, but rather a slightly expanded write-up of some notes for a concluding discussion at the 2012 Workshop on ‘Modeling Strategic Reasoning’ at the Lorentz Center in Leiden, an... more
This piece is not a paper reporting on original research, but rather a slightly expanded write-up of some notes for a concluding discussion at the 2012 Workshop on ‘Modeling Strategic Reasoning’ at the Lorentz Center in Leiden, an interdisciplinary meeting on the importance of strategies in many fields, from game theory to linguistics, computer science, and cognitive science, that was the incubator for the present volume on the logic-based analysis of strategies and how we reason with, and about them. My modest purpose here is to highlight a few general, somewhat unresolved, decision points about this proposed program that seemed to resonate with the audience at the Workshop, but that may also present food for thought to a more general reader of this book. The emphasis in the presentation that follows is on logic, a view of strategies that figures prominently in my own work on logic and games, cf. [9]. Still, there are certainly other equally viable and illuminating formal viewpoints on the study of strategies, coming, for instance, from automata theory or dynamical systems, cf. [16, 31].
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This paper presents a simple decidable logic of functional dependence LFD, based on an extension of classical propositional logic with dependence atoms plus dependence quantifiers treated as modalities, within the setting of generalized... more
This paper presents a simple decidable logic of functional dependence LFD, based on an extension of classical propositional logic with dependence atoms plus dependence quantifiers treated as modalities, within the setting of generalized assignment semantics for first order logic. The expressive strength, complete proof calculus and meta-properties of LFD are explored. Various language extensions are presented as well, up to undecidable modal-style logics for independence and dynamic logics of changing dependence models. Finally, more concrete settings for dependence are discussed: continuous dependence in topological models, linear dependence in vector spaces, and temporal dependence in dynamical systems and games.
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This paper explores a new language of neighbourhood structures where existential information can be given about what kind of worlds occur in a neighbourhood of a current world. The resulting system of ‘instantial neighbourhood logic’ INL... more
This paper explores a new language of neighbourhood structures where existential information can be given about what kind of worlds occur in a neighbourhood of a current world. The resulting system of ‘instantial neighbourhood logic’ INL has a nontrivial mix of features from relational semantics and from neighbourhood semantics. We explore some basic model-theoretic behavior, including a matching notion of bisimulation, and give a complete axiom system for which we prove completeness by a new normal form technique. In addition, we relate INL to other modal logics by means of translations, and determine its precise SAT complexity. Finally, we discuss proof-theoretic fine-structure of INL in terms of semantic tableaux and some expressive fine-structure in terms of fragments, while discussing concrete illustrations of the instantial neighborhood language in topological spaces, in games with powers for players construed in a new way, as well as in dynamic logics of acquiring or deleting...
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Intensional logic is the technical study of such intensional phenomena in human reasoning as modality, knowledge, or flow of time. These all require a richer semantic picture than standard truth values in one static environment. Such a... more
Intensional logic is the technical study of such intensional phenomena in human reasoning as modality, knowledge, or flow of time. These all require a richer semantic picture than standard truth values in one static environment. Such a picture is provided by so-called possible worlds semantics, a paradigm which is surveyed in this book, both as to its external sources of motivation and as to the internal dynamics of the resulting program. In particular, Manual of Intensional Logic presents the major classical topics, including modal logic, tense logic, and conditional logic, all of which illustrate motivations coming from philosophy and linguistics. The Book also discusses recent computational applications in computer science and AI. Finally, Manual of Intensional Logic takes up recent developments in the study of language and information making themselves felt in the area. The Book examines the role of partial information--with illustrations drawn from different branches of Intensional Logic--and various influences stemming from current theories of the semantics of natural language, involving generalized quantifiers and theories of types.
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This chapter gives an overview of current dynamic logics that describe belief update and revision, both for single agents and in multi-agent settings. We employ a mixture of ideas from AGM belief revision theory and dynamic-epistemic... more
This chapter gives an overview of current dynamic logics that describe belief update and revision, both for single agents and in multi-agent settings. We employ a mixture of ideas from AGM belief revision theory and dynamic-epistemic logics of information-driven agency. After describing the basic background, we review logics of various kinds of beliefs based on plausibility models, and then go on to various sorts of belief change engendered by changes in current models through hard and soft information. We present matching complete logics with dynamic-epistemic recursion axioms, and develop a very general perspective on belief change by the use of event models and priority update. The chapter continues with three topics that naturally complement the setting of single steps of belief change: connections with probabilistic approaches to belief change, long-term temporal process structure including links with formal learning theory, and multi-agent scenarios of information flow and belief revision in games and social networks. We end with a discussion of alternative approaches, further directions, and windows to the broader literature, while links with relevant philosophical traditions are discussed throughout.