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  • 1.
    Prawitz, Dag
    Stockholm University, Faculty of Humanities, Department of Philosophy.
    The Fundamental Problem of General Proof Theory2019In: Studia Logica: An International Journal for Symbolic Logic, ISSN 0039-3215, E-ISSN 1572-8730, Vol. 107, no 1, p. 11-29Article in journal (Refereed)
    Abstract [en]

    I see the question what it is that makes an inference valid and thereby gives a proof its epistemic power as the most fundamental problem of general proof theory. It has been surprisingly neglected in logic and philosophy of mathematics with two exceptions: Gentzen's remarks about what justifies the rules of his system of natural deduction and proposals in the intuitionistic tradition about what a proof is. They are reviewed in the paper and I discuss to what extent they succeed in answering what a proof is. Gentzen's ideas are shown to give rise to a new notion of valid argument. At the end of the paper I summarize and briefly discuss an approach to the problem that I have proposed earlier.

  • 2. van Benthem, Johan
    et al.
    Bezhanishvili, Nick
    Enqvist, Sebastian
    Stockholm University, Faculty of Humanities, Department of Philosophy.
    A Propositional Dynamic Logic for Instantial Neighborhood Semantics2019In: Studia Logica: An International Journal for Symbolic Logic, ISSN 0039-3215, E-ISSN 1572-8730, Vol. 107, no 4, p. 719-751Article in journal (Refereed)
    Abstract [en]

    We propose a new perspective on logics of computation by combining instantial neighborhood logic INL with bisimulation safe operations adapted from PDL. INL 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. 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.

  • 3.
    Westerståhl, Dag
    et al.
    Stockholm University, Faculty of Humanities, Department of Philosophy.
    Kontinen, Juha
    University of Helsinki.
    Väänänen, Jouko
    University of Helsinki.
    Editorial introduction: Special issue: Dependence and Independence in Logic2013In: Studia Logica: An International Journal for Symbolic Logic, ISSN 0039-3215, E-ISSN 1572-8730, Vol. 101, no 1, p. 233-236Article in journal (Other academic)
    Abstract [en]

    The goal of the study of dependence and independence in logic is to establish a basic theory of dependence and independence phenomena underlying seemingly unrelated subjects such as game theory, random variables, database theory, scientific experiments, and probably many others. The monograph Dependence Logic (J. Väänänen, Cambridge UP, 2007) stimulated an avalanche of new results which have demonstrated remarkable convergence in this area. The concepts of (in)dependence in the different fields of science have surprising similarity and a common logic is starting to emerge. This special issue will give an overview of the state of the art of this new field.

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