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22 results

Page 1 of 2

  • SOME COMPLETENESS THEOREMS IN THE DYNAMIC DOXASTIC LOGIC OF ITERATED BELIEF REVISION
  • KRISTER SEGERBERG
  • Journal: The Review of Symbolic Logic / Volume 3 / Issue 2 / June 2010
  • Published online by Cambridge University Press: 19 March 2010, pp. 228-246
  • Print publication: June 2010
  • View abstract

    The success of the AGM paradigm—the theory of belief change initiated by Alchourrón, Gärdenfors, and Makinson—is remarkable, as even a quick look at the literature it has generated will testify. But it is also remarkable, at least in hindsight, how limited was the original effort. For example, the theory concerns the beliefs of just one agent; all incoming information is accepted; belief change is uniquely determined by the new information; there is no provision for nested beliefs. And perhaps most surprising: there is no analysis of iterated change.

    In this paper it is that last restriction that is at issue. Our medium of study is dynamic doxastic logic (DDL). The success of the AGM paradigm The particular contribution of the paper is detailed completeness proofs for three dynamic doxastic logics of iterated belief revision.

    The problem of extending the AGM paradigm to include iterated change has been discussed for years, but systematic discussions have appeared only recently (see Segerberg, 2007 and forthcoming, but also van Benthem, 2007; Rott, 2006; Zvesper, 2007).

  • Intension, intention
  • Edited by Reinhard Kähle, Universidade de Coimbra, Portugal
  • Book: Intensionality
  • Published online: 30 March 2017
  • Print publication: 02 March 2005, pp 174-186
  • View extract

    Summary

    Abstract. Intensionality has generally been of more concern to logicians than intentionality. But also the latter merits their interest. This paper, a contribution to the logic of action, involves both concepts—the former implicitly, the latter explicitly.

    Informal background. Many logicians and philosophers, the present writer included, are familiar with the term “intension” (with an s) but rather less familiar with the term “intention” (with a t). Outside philosophy and logic the situation is reverse: “intention” is used by all, “intension” by few, if any. A miniature history of the development of the two terms was given by E. J. Lemmon [6]:

    The medieval term intentio was originally employed as a translation of the Arabic termma'na, a formin the soul identified with a meaning or a notion, and meant throughout medieval epistemology a natural sign in the soul. Later the Port Royal Logic distinguished between the comprehension and extension of a general term in something of the way in which Mill later distinguished connotation and denotation: whilst the extension is the set of things to which the term applies, its comprehension is the set of attributes which it implies. Sir William Hamilton replaced “comprehension” by “intension”, faultily spelling the word with an “s” by analogy with “extension”. Since then, the term “intentionality” has gone one way, via Brentano to Chisholm, and the word “intensionality” another via Carnap to Quine.

    This elegant quotation is offered for what it is worth. It is of some help in explaining philosophers’ terminology, but unfortunately it leaves unexplained the connexion with everyday usage in the context of action. And it is the latter that is of concern in this paper.

    We study a system in which one agent (“the agent”) operates in some environment (“the world”). The world may or may not be dynamic, in the sense that things can happen even if the agent does not do anything; when it is, it is convenient to postulate yet another agent, called “Nature”.

  • 14 - Representing facts
  • Edited by Cristina Bicchieri, Maria Luisa Dalla Chiara
  • Book: Knowledge, Belief, and Strategic Interaction
  • Published online: 05 November 2011
  • Print publication: 28 August 1992, pp 239-256
  • View extract

    Summary

    Without the concept of action there would be no social science. Much work can be (and is) done without a detailed examination of this concept, but ultimately there is a need for a full conceptual analysis of action. Even though philosophers are already addressing that task, work of a more formal nature is still in its infancy. In this chapter some suggestions toward a formal analysis of action are offered, in the belief that philosophical work of this kind ought eventually to result in formal modelings.

    We take our lead from Georg Henrik von Wright, to whom we should like to attribute the insight contained in the slogan “to act is to bring about a fact.” As a first step, then, one ought to analyze the notion of a fact; this is attempted in the first five sections, the bulk of this chapter. The last two sections contain some suggestions – sketchy, to be sure – for how a theory of action, in the spirit of von Wright, might be based on our analysis of facts.

    FACTS ACCORDING TO VON WRIGHT

    When a (contingent) proposition is true there corresponds to it a fact in the world. It is a well-known view that truth ‘consists’ in a correspondence between proposition and fact.

    This observation was made by von Wright in his book Norm and Action ([14], p. 25), and he went on to distinguish three types of fact: states-of-affairs, events, and processes.

  • The truth about some Post numbers
  • Krister Segerberg
  • Journal: The Journal of Symbolic Logic / Volume 41 / Issue 1 / March 1976
  • Published online by Cambridge University Press: 12 March 2014, pp. 239-244
  • Print publication: March 1976
  • View extract

    There is a mistake in [6], discovered by Robert V. Kohn: contrary to the claim on p. 714, the set {◊X i : i ≥ 2} is not independent in S3. As a result three problems thought to be settled are open once more, viz., whether the Post numbers of S2, S3, and K4 are denumerable. In [6] it was claimed they are not. Now we shall prove that that claim is indeed correct for S2 and K4 but, surprisingly enough, not for S3.

  • Post completeness in modal logic
  • Krister Segerberg
  • Journal: The Journal of Symbolic Logic / Volume 37 / Issue 4 / December 1972
  • Published online by Cambridge University Press: 12 March 2014, pp. 711-715
  • Print publication: December 1972
  • View extract

    Let ⊥, →, and □ be primitive, and let us have a countable supply of propositional letters. By a (modal) logic we understand a proper subset of the set of all formulas containing every tautology and being closed under modus ponens and substitution. A logic is regular if it contains every instance of □A ∧ □B ↔ □(A ∧ B) and is closed under the rule

    A regular logic is normal if it contains □⊤. The smallest regular logic we denote by C (the same as Lemmon's C2), the smallest normal one by K. If L and L' are logics and L ⊆ L′, then L is a sublogic of L', and L' is an extension of L; properly so if L ≠ L'. A logic is quasi-regular (respectively, quasi-normal) if it is an extension of C (respectively, K).

    A logic is Post complete if it has no proper extension. The Post number, denoted by p(L), is the number of Post complete extensions of L. Thanks to Lindenbaum, we know that

    There is an obvious upper bound, too:

    Furthermore,

    .

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