Krister Segerberg Research Articles

Revocable Belief Revision

Krister Segerberg proposed irrevocable belief revision, to be contrasted with standard belief revision, in a setting wherein belief of propositional formulas is modelled explicitly. This suggests that in standard belief revision is revocable: one should be able to unmake (`revoke') the fresh belief in the revision formula, given yet further information that contradicts it. In a dynamic epistemic logical setting for belief revision, for multiple agents, we investigate what the requirements are for revocable belief revision. By this we not merely mean recovering belief in non-modal propositions, as in the recovery principle for belief contraction, but recovering belief in modal propositions: beliefs about beliefs. These requirements are almost never met, a surprising result.

Interrogative Belief Revision in Modal Logic

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.

Irrevocable belief revision and epistemic entrenchment

In recent papers [10, 11] Krister Segerberg introduced Irrevocable Belief Revision, as closely related to AGM revision [2]. In this paper we present irrevocable belief revision in terms of an epistemic entrenchment relation. 1

Ddl Unlimited: Dynamic Doxastic Logic for Introspective Agents

The theories of belief change developed within the AGM-tradition are not logics in the proper sense, but rather informal axiomatic theories of belief change. Instead of characterizing the models of belief and belief change in a formalized object language, the AGM-approach uses a natural language — ordinary mathematical English — to characterize the mathematical structures that are under study. Recently, however, various authors such as Johan van Benthem and Maarten de Rijke have suggested representing doxastic change within a formal logical language: a dynamic modal logic.1 Inspired by these suggestions Krister Segerberg has developed a very general logical framework for reasoning about doxastic change: dynamic doxastic logic (DDL).2 This framework may be seen as an extension of standard Hintikka-style doxastic logic (Hintikka 1962) with dynamic operators representing various kinds of transformations of the agent's doxastic state. Basic DDL describes an agent that has opinions about the external world and an ability to change these opinions in the light of new information. Such an agent is non-introspective in the sense that he lacks opinions about his own belief states. Here we are going to discuss various possibilities for developing a dynamic doxastic logic for introspective agents: full DDL or DDL unlimited. The project of constructing such a logic is faced with difficulties due to the fact that the agent’s own doxastic state now becomes a part of the reality that he is trying to explore: when an introspective agent learns more about the world, then the reality he holds beliefs about

Third international workshop on deontic logic in computer science

The Third International Workshop on Deontic Logic in Computer Science (ΔEON'96) took place in Sesimbra, Portugal, from 11–13 January 1996. It consisted of 12 refereed technical presentations and four invited talks. The invited speakers were Nuel Belnap (Pittsburgh University, USA), Andrew Jones (Oslo University, Norway), Krister Segerberg (Uppsala University, Sweden) and Marek Sergot (Imperial College, UK).

Intentions, actions and routines: A problem in Krister Segerberg's theory of action

The aim of this paper is to make a critical assessment of Krister Segerberg's theory of action. The first part gives a critical presentation of the key concepts in Segerberg's informal theory of action. These are the ideas that motivate the formal models he develops. In the second part it is argued that if one takes all of Segerberg's motivating ideas seriously, problems are forthcoming. The main problem is that on this theory the agents seem to be bound to realize all of their intentions, a problem that stems from Segerberg's attempt to individuate actions in terms of the agent's intentions. On the ground that this unfortunate result is forthcoming in both of Segerberg's approaches to the logic of action it is concluded that the conceptual basis of the theory is problematic.

Robert Bull and Krister Segerberg. Basic modal logic. Handbook of philosophical logic, Volume II, Extensions of classical logic, edited by D. Gabbay and F. Guenthner, Synthese library, vol. 165, D. Reidel Publishing Company, Dordrecht, Boston, and Lancaster, 1984, pp. 1–88. - John P. Burgess. Basic tense logic. Handbook of philosophical logic, Volume II, Extensions of classical logic, edited by D.

This handbook provides a systematic survey of the central areas of philosophical logic. It is divided into four volumes, each devoted to a major sub-field within the disciplines. The articles should be of value to general philosophers, linguists, logicians, mathematicians and computer scientists. Volume 1, Elements of Classical Logic, deals with the background to what has come to be considered the standard formulation of predicate logic - both as far as its semantics and proof theory are concerned. The central chapter on predicate logic is followed by chapters outlining various alternative, but essentially equivalent ways of constructing the semantics for first-order logic as well as its proof theory. In addition, this volume contains a discussion of higher-order extensions of first-order logic and a compendium of the algorithmic and decision-theoretic prerequisites in the study of logical systems. Volume 2, Extensions of Classical Logic, surveys the most significant extensions of predicate logic and their applications to various philosophical fields of inquiry. The 12 chapters in this volume together provide a succinct introduction to a variety of intensional frameworks, a discussion of the most well-known logical systems, as well as an overview of major applications and of the open problems in the respective fields. Volume 3, Alternatives to Classical Logic, consists of a series of surveys of some of the alternatives to the basic assumptions of classical logic. These include many-valued logic, partial logic, free logic, relevance and entailment logics, dialogue logic, quantum logic and intuitionism. Volume 4, Topics in the Philosophy of Language, presents a panorama of the applications of logical tools and methods in the formal analysis of natural language. Since a number of developments in philosophical logic were originally stimulated by concern arising in the semantic analysis of natural language discourse, the chapters in this volume provide some criteria of evaluation of the applications of work in philosophical logic. In revealing both the adequacies and inadequacies of logical investigations in the semantic structures of natural discourse, these chapters also point the way to future developments in philosophical logic in general and thus close again the circle of inquiry relating logic and language.

Robert Bull and Krister Segerberg. Basic modal logic. Handbook of philosophical logic, Volume II, Extensions of classical logic, edited by D. Gabbay and F. Guenthner, Synthese library, vol. 165, D. Reidel Publishing Company, Dordrecht, Boston, and Lancaster, 1984, pp. 1–88. - John P. Burgess. Basic tense logic. Handbook of philosophical logic, Volume II, Extensions of classical logic, edited by D.

Robert Bull and Krister Segerberg. Basic modal logic. Handbook of philosophical logic, Volume II, <i><b>Extensions of classical logic</b></i>, edited by D. Gabbay and F. Guenthner, Synthese library, vol. 165, D. Reidel Publishing Company, Dordrecht, Boston, and Lancaster, 1984, pp. 1–88. - John P. Burgess. Basic tense logic. Handbook of philosophical logic, Volume II, <i><b>Extensions of classical logic</b></i>, edited by D.

Krister Segerberg. The logic of deliberate action. Journal of philosophical logic, vol. 11 (1982),pp. 233–254.

Krister Segerberg. The logic of deliberate action. Journal of philosophical logic, vol. 11 (1982),pp. 233–254.

Vaughan R. Pratt. Semantical considerations on Floyd–Hoare logic. 17th Annual Symposium on Foundations of Computer Science, Institute of Electrical and Electronics Engineers, New York1976, pp. 109–121. - Michael J. Fischer and Richard E. Ladner. Propositional dynamic logic of regular programs. Journal of computer and system sciences, vol. 18 (1979), pp. 194–211. - Krister Segerberg. A completeness theorem in the modal

This paper deals with logics of programs. The objective is to formalize a notion of program description and to give both plausible (semantic) and effective (syntactic) criteria for the notion of truth of a description. A novel feature of this treatment is the development of the mathematics underlying Floyd-Hoare axiom systems independently of such systems. Other directions that such research might take are also considered. This paper grew out of, and is intended to be usable as, class notes for an introductory semantics course. The three sections of the paper are: 1) A frame work for the logic of programs. Programs and their partial correctness theories are treated as binary relations on states and formulae respectively. Truth-values are assigned to partial correctness assertions in a plausible (Tarskian) but not directly usable way. 2) Particular Programs. Effective criteria for truth are established for some programs using the Tarskian criteria as a benchmark. This leads directly to a sound, complete, effective axiom system for the theories of these programs. The difficulties involved in finding such effective criteria for other programs are explored. 3) Variations and extensions of the framework. Alternatives to binary relations for both programs and theories are speculated on, and their possible roles in semantics are considered. We discuss a hierarchy of varieties of programs and the importance of this hierarchy to the issues of definability and describability. Modal logic is considered as a first-order alternative to Floyd-Hoare logic. We give an appropriate axiom system which is complete for loop-free programs and also puts conventional predicate calculus in a different light by lumping quantifiers with non-logical assignments rather than treating them as logical concepts.

COULD HAVE BUT DID NOT

Pacific Philosophical QuarterlyVolume 64, Issue 3 p. 230-241 Article COULD HAVE BUT DID NOT Krister Segerberg, Krister Segerberg University of Auckland, Auckland, New ZealandSearch for more papers by this author Krister Segerberg, Krister Segerberg University of Auckland, Auckland, New ZealandSearch for more papers by this author First published: July 1983 https://doi.org/10.1111/j.1468-0114.1983.tb00196.xAboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat Volume64, Issue3July 1983Pages 230-241 RelatedInformation

The decidability of normal K5 logics

The literature on modal logic includes a number of general completeness and decidability results. The work of Schiller Joe Scroggs [5], R.A. Bull [1], Kit Fine [2], and Krister Segerberg [6] provide examples.Scroggs showed that the proper extensions of S5 have the finite model property and are axiomatizable. (Harrop [3] then argued that logics having these properties are decidable.) Bull extended Scroggs' result by showing that the normal extensions of S4.3 have the finite model property. Fine subsequently provided a model-theoretic proof of Bull's result and also proved the axiomatizability of these logics. In a different direction Segerberg proved that every normal logic containing the characteristic axioms of Lewis' systems S4 and S5 is decidable.The present paper is in this tradition. We extend the results of Scroggs and Segerberg by showing that every normal modal logic containing the S5 axiom has the finite model property, is axiomatizable, and thus is decidable.

E. J. Lemmon. An introduction to modal logic, ir. collaboration with Dana Scott, edited by Krister Segerberg. American philosophical quarterly monograph series, no. 11. Basil Blackwell, Oxford1977, x + 94 pp.

E. J. Lemmon. An introduction to modal logic, ir. collaboration with Dana Scott, edited by Krister Segerberg. American philosophical quarterly monograph series, no. 11. Basil Blackwell, Oxford1977, x + 94 pp. - Volume 44 Issue 4

A completeness proof for an infinitary tense‐logic

In his forthcoming examination of G. H. von Wright's tense-logic [4], Krister Segerberg studies certain infinitary extensions of the original tense-logic created by von Wright. For one of these extensions the completeness problem turned out to be harder than was expected at first sight. This paper is devoted to a proof of a completeness theorem for the extension in question, called Wl by Segerberg. We use a countable language of ordinary prepositional logic supplied with two modal operators: O (tomorrow) and D (always). The relevant semantics for tense-logic based on this language uses the frame 9^ = , where the successorrelation is the accessibility-relation for O and n A is true at k. We assume that the reader is familiar with ordinary Kripkesemantics for modal languages and, in particular, that he understands what it means that 9ft is a model on the frame 9^. We shall use O(A] as a shorthand for

Krister Segerberg. Some modal logics based on a three-valued logic. Theoria (Lund), vol. 33 (1967), pp. 53–71.

Krister Segerberg. Some modal logics based on a three-valued logic. Theoria (Lund), vol. 33 (1967), pp. 53–71.

Propositional Logics Related to Heyting's and Johansson's

TheoriaVolume 34, Issue 1 p. 26-61 Propositional Logics Related to Heyting's and Johansson's KRISTER SEGERBERG, KRISTER SEGERBERG Uppsala University and Stanford UniversitySearch for more papers by this author KRISTER SEGERBERG, KRISTER SEGERBERG Uppsala University and Stanford UniversitySearch for more papers by this author First published: April 1968 https://doi.org/10.1111/j.1755-2567.1968.tb00337.xCitations: 74AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Citing Literature Volume34, Issue1April 1968Pages 26-61 RelatedInformation

Decidability of four modal logics

TheoriaVolume 34, Issue 1 p. 21-25 Decidability of four modal logics KRISTER SEGERBERG, KRISTER SEGERBERG Uppsala Univeristy and Stanford UniversitySearch for more papers by this author KRISTER SEGERBERG, KRISTER SEGERBERG Uppsala Univeristy and Stanford UniversitySearch for more papers by this author First published: April 1968 https://doi.org/10.1111/j.1755-2567.1968.tb00336.xCitations: 8AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Citing Literature Volume34, Issue1April 1968Pages 21-25 RelatedInformation

A contribution to nonsense‐logics

TheoriaVolume 31, Issue 3 p. 199-217 A contribution to nonsense-logics KRISTER SEGERBERG, KRISTER SEGERBERG Uppsala UniversitySearch for more papers by this author KRISTER SEGERBERG, KRISTER SEGERBERG Uppsala UniversitySearch for more papers by this author First published: December 1965 https://doi.org/10.1111/j.1755-2567.1965.tb00579.xCitations: 27Read the full textAboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat Citing Literature Volume31, Issue3December 1965Pages 199-217 RelatedInformation