The well known AGM framework for belief revision has recently been extended to include a model of the research agenda of the agent, i.e. a set of questions to which the agent wishes to find answers (Olsson & Westlund in Erkenntnis , 65 , 165–183, 2006 ). The resulting model has later come to be called interrogative belief revision . While belief revision has been studied extensively from the point of view of modal logic, so far interrogative belief revision has (...) only been dealt with in the metalanguage approach in which AGM was originally presented. In this paper, I show how to model interrogative belief revision in a modal object language using a class of operators for questions. In particular, the solution I propose will be shown to capture the notion of K-truncation , a method for agenda update in the case of expansion constructed by Olsson & Westlund. Two case studies are conducted: first, an interrogative extension of Krister Segerberg’s system DDL, and then a similar extension of Giacomo Bonanno’s modal logic for belief revision. Sound and complete axioms will be provided for both of the resulting logics. (shrink)

In the paper "On the role of the research agenda in epistemic change", Olsson and Westlund have suggested that the notion of epistemic state employed in the standard framework of belief revision (Alchourrón et al. 1985; Gärdenfors 1988) should be extended to include a representation of the agent's research agenda (Olsson and Westlund 2006). The resulting framework will here be referred to as interrogative belief revision. In this paper, I attempt to deal with the problem of how research agendas should (...) change in contraction, a problem largely left open by Olsson and Westlund. Two desiderata of an appropriate solution are suggested: one is a principle of continuity, stating that changes in the research agenda should somehow reflect that certain long term research interests are kept fixed. The other desideratum, which is based on part of Olsson and Westlund's motivation for adding research agendas to the epistemic states, is that we should be able to account for how contraction may serve to open up new, fruitful hypotheses for investigation. In order to achieve these desiderata, I base my solution on a revised version of Olsson and Westlund's notion of epistemic state. (shrink)

There are several known Lindström-style characterization results for basic modal logic. This paper proves a generic Lindström theorem that covers any normal modal logic corresponding to a class of Kripke frames definable by a set of formulas called strict universal Horn formulas. The result is a generalization of a recent characterization of modal logic with the global modality. A negative result is also proved in an appendix showing that the result cannot be strengthened to cover every first-order elementary class of (...) frames. This is shown by constructing an explicit counterexample. (shrink)

I develop a dynamic logic for reasoning about "interrogative belief revision", a new branch of belief revision theory that has been developed in a small number of papers, beginning with E. J. Olsson and D. Westlund's paper "On the role of the research agenda in epistemic change" [12]. In interrogative belief revision, epistemic states are taken to include a research agenda, consisting of questions the agent seeks to answer. I present a logic for revision of such epistemic states based on (...) the notion of an epistemic strategy, a stable plan of action that determines changes in the agent's research agenda. This idea is a further development of an idea put forward in [6], that changes in the research agenda of an agent should be determined by stable, "long term" research interests. I provide complete axioms and a decidability result for the logic. (shrink)

In a recent article, Alexander Kurz and Yde Venema establish a Lindström theorem for coalgebraic modal logic that is shown to imply a modal Lindström theorem by Maarten de Rijke. A later modal Lindström theorem has been established by Johan van Benthem, and this result still lacks a coalgebraic formulation. The main obstacle has so far been the lack of a suitable notion of ‘submodels’ in coalgebraic semantics, and the problem is left open by Kurz and Venema. In this article, (...) we propose a solution to this problem and derive a general coalgebraic Lindström theorem along the lines of van Benthem's result. We provide several applications of the result. (shrink)

This thesis deals with the theory of interrogative belief revision, a recent development in the subfield of philosophical logic known as belief revision theory. While classical belief revision theory deals with the dynamics of an agent’s beliefs, interrogative belief revision aims to describe the dynamics of the agent’s questions about the world, or research agenda, as well. Great emphasis is put on the interaction between belief change and changes in the research agenda. I develop both the technical framework for this (...) theory by constructing and investigating modal logics for reasoning about the dynamics of research interests, as well as pursuing further the philosophical foundations and applications of the theory. Among the contributions of the thesis are: - a novel interpretation of the theory founded on a notion of epistemic strategies - a solution to the previously open problem of contraction and revision in this context - several systems of modal logic that can be used to reason about interrogative belief revision - completeness results and decidability results for these logics - a characterization of a class of relevant conditionals based on a notion of agenda relevance. (shrink)

in UndeterminedInterrogative belief revision is a relatively recent framework for belief revision theory, in which the epistemic state of an agent includes a representation of that agent's research agenda, i.e. the set of questions the agent wants to have answers to. This added structure opens new possibilites for various types of epistemic change that cannot be distinguished in traditional belief revision. In this article I use the so-called 'action model' approach known from the literature on dynamic epistemic logic to provide (...) a unified framework in which we can reason about these various types of epistemic changes. I show how to model some natural examples of epistemic changes involving change of the research agenda in this framework. The action models give rise to a dynamic logic which is proven to be decidable. (shrink)

Belief revision theory and philosophy of science both aspire to shed light on the dynamics of knowledge – on how our view of the world changes in the light of new evidence. Yet these two areas of research have long seemed strangely detached from each other, as witnessed by the small number of cross-references and researchers working in both domains. One may speculate as to what has brought about this surprising, and perhaps unfortunate, state of affairs. One factor may be (...) that while belief revision theory has traditionally been pursued in a bottom- up manner, focusing on the endeavors of single inquirers, philosophers of science, inspired by logical empiricism, have tended to be more interested in science as a multi-agent or agent-independent phenomenon. (shrink)

We present a new notion of game equivalence that captures basic powers of interacting players. We provide a representation theorem, a complete logic, and a new game algebra for basic powers. In doing so, we establish connections with imperfect information games and epistemic logic. We also identify some new open problems concerning logic and games.

We propose a new perspective on logics of computation by combining instantial neighborhood logic INL\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathsf {INL}$$\end{document} with bisimulation safe operations adapted from PDL\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathsf {PDL}$$\end{document}. INL\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathsf {INL}$$\end{document} is a recent modal logic, based on an extended neighborhood semantics which permits quantification over individual neighborhoods plus their contents. This system has a natural interpretation as a (...) logic of computation in open systems. Motivated by this interpretation, we show that a number of familiar program constructors can be adapted to instantial neighborhood semantics to preserve invariance for instantial neighborhood bisimulations, the appropriate bisimulation concept for INL\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathsf {INL}$$\end{document}. We also prove that our extended logic IPDL\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathsf {IPDL}$$\end{document} 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\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathsf {IPDL}$$\end{document}, and establish its finite model property and decidability. (shrink)

We introduce a path-based cyclic proof system for first-order $\mu $-calculus, the extension of first-order logic by second-order quantifiers for least and greatest fixed points of definable monotone functions. We prove soundness of the system and demonstrate it to be as expressive as the known trace-based cyclic systems of Dam and Sprenger. Furthermore, we establish cut-free completeness of our system for the fragment corresponding to the modal $\mu $-calculus.

We characterize the expressive power of the modal mu-calculus on monotone neighborhood structures, in the style of the Janin-Walukiewicz theorem for the standard modal mu-calculus. For this purpose we consider a monadic second-order logic for monotone neighborhood structures. Our main result shows that the monotone modal mu-calculus corresponds exactly to the fragment of this second-order language that is invariant for neighborhood bisimulations.

We present sound and complete sequent calculi for the modal mu-calculus with converse modalities, aka two-way modal mu-calculus. Notably, we introduce a cyclic proof system wherein proofs can be represented as finite trees with back-edges, i.e., finite graphs. The sequent calculi incorporate ordinal annotations and structural rules for managing them. Soundness is proved with relative ease as is the case for the modal mu-calculus with explicit ordinals. The main ingredients in the proof of completeness are isolating a class of non-wellfounded (...) proofs with sequents of bounded size, called slim proofs, and a counter-model construction that shows slimness suffices to capture all validities. Slim proofs are further transformed into cyclic proofs by means of re-assigning ordinal annotations. (shrink)

Ocherk 1. Voprosy ontologii -- Ocherk 2. Voprosy ėtiki i ėstetiki -- Ocherk 3. Voprosy gnoseologii i aksiologii.

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 evidence. We conclude with some coalgebraic perspectives on what is achieved in this paper. Many of these final themes suggest follow-up work of independent interest. (shrink)

We propose a new perspective on logics of computation by combining instantial neighborhood logic \ with bisimulation safe operations adapted from \. \ is a recent modal logic, based on an extended neighborhood semantics which permits quantification over individual neighborhoods plus their contents. This system has a natural interpretation as a logic of computation in open systems. Motivated by this interpretation, we show that a number of familiar program constructors can be adapted to instantial neighborhood semantics to preserve invariance for (...) instantial neighborhood bisimulations, the appropriate bisimulation concept for \. We also prove that our extended logic \ 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 \, and establish its finite model property and decidability. (shrink)

We present a new notion of game equivalence that captures basic powers of interacting players. We provide a representation theorem, a complete logic, and a new game algebra for basic powers. In doing so, we establish connections with imperfect information games and epistemic logic. We also identify some new open problems concerning logic and games.

Prologue, invitation to thinking about God In the Hebrew Bible? -- Part I, questions about God? -- Why does God in the Bible have a body? -- What do God's body parts in the Bible mean? -- Why is God angry in the Bible? -- Does God in the Bible have gender or sexuality? -- Part II, questions about God in the world? -- What can creation tell us about God? -- Who-or what-is the Satan? -- Why do people suffer (...) according to the Hebrew Bible? -- Epilogue, God in the Bible and beyond. (shrink)

Many books explain what is known about the universe. This book investigates what cannot be known. Rather than exploring the amazing facts that science, mathematics, and reason have revealed to us, this work studies what science, mathematics, and reason tell us cannot be revealed. In The Outer Limits of Reason, Noson Yanofsky considers what cannot be predicted, described, or known, and what will never be understood. He discusses the limitations of computers, physics, logic, and our own thought processes. Yanofsky describes (...) simple tasks that would take computers trillions of centuries to complete and other problems that computers can never solve; perfectly formed English sentences that make no sense; different levels of infinity; the bizarre world of the quantum; the relevance of relativity theory; the causes of chaos theory; math problems that cannot be solved by normal means; and statements that are true but cannot be proven. He explains the limitations of our intuitions about the world -- our ideas about space, time, and motion, and the complex relationship between the knower and the known. Moving from the concrete to the abstract, from problems of everyday language to straightforward philosophical questions to the formalities of physics and mathematics, Yanofsky demonstrates a myriad of unsolvable problems and paradoxes. Exploring the various limitations of our knowledge, he shows that many of these limitations have a similar pattern and that by investigating these patterns, we can better understand the structure and limitations of reason itself. Yanofsky even attempts to look beyond the borders of reason to see what, if anything, is out there. (shrink)

This chapter develops a perceptual solution to the epistemological problem of other minds, relying on central ideas from Maurice Merleau-Ponty's phenomenology. The Merleau-Pontian account is contrasted with another attempted perceptual solution to the other minds problem, and it is argued that only the former meets the phenomenologists' desideratum of providing an alternative to inferential solutions. The chapter also provides responses to various objections to the perceptual solution, including a pair of objections recently put forward by Alec Hyslop.

Richard Janko's acclaimed translation of Aristotle's _Poetics_ is accompanied by the most comprehensive commentary available in English that does not presume knowledge of the original Greek. Two other unique features are Janko's translations with notes of both the _Tractatus Coislinianus_, which is argued to be a summary of the lost second book of the Poetics, and fragments of Aristotle’s dialogue On Poets, including recently discovered texts about catharsis, which appear in English for the first time.

Study of Hans-Georg Gadamer's and Julius Stenzel's interpretations of Plato.

"Williams's masterful translation satisfies (at last!) a long-standing need. There are lots of good translations of Augustine's great work, but until now we have been forced to choose between those that strive to replicate in English something of the majesty and beauty of Augustine's Latin style and those that opt instead to convey the careful precision of his philosophical terminology and argumentation. Finally, Williams has succeeded in capturing both sides of Augustine's mind in a richly evocative, impeccably reliable, elegantly readable (...) presentation of one of the most impressive achievements in Western thought--Augustine's Confessions." --Scott MacDonald, Professor of Philosophy and Norma K. Regan Professor in Christian Studies, Cornell University. (shrink)

Treatise, with commentaries, on Navya-Nyāya philosophy.