•  59
    On Topological Issues of Indeterminism
    Erkenntnis 79 (S3): 1-34. 2014.
    Indeterminism, understood as a notion that an event may be continued in a few alternative ways, invokes the question what a region of chanciness looks like. We concern ourselves with its topological and spatiotemporal aspects, abstracting from the nature or mechanism of chancy processes. We first argue that the question arises in Montague-Lewis-Earman conceptualization of indeterminism as well as in the branching tradition of Prior, Thomason and Belnap. As the resources of the former school are …Read more
  •  64
  •  38
  •  41
    On not strengthening intuitionistic logic
    with H. Leblanc and R. H. Thomason
    Notre Dame Journal of Formal Logic 4 (4): 313-320. 1963.
    tic sequenzen-kalkul of Gentzen, into rules for PCc, the classical sequenzenkalkul. We shall limit ourselves here to sequenzen or turnstile statements of the form A„A„..., A„ I- B, where A„A„..., A„(n ~ 0), and B are wffs consisting of propositional variables, zero or more of the connectives '5', "v', ' ', ')', and '=', and zero or more parentheses. One can pass from PCi to PCc by amending the intelim rules for ' a result of long standing, or by amending the intelim rules for either …Read more
  •  190
    The theory of branching space-times is designed as a rigorous framework for modelling indeterminism in a relativistically sound way. In that framework there is room for "funny business", i.e., modal correlations such as occur through quantummechanical entanglement. This paper extends previous work by Belnap on notions of "funny business". We provide two generalized definitions of "funny business". Combinatorial funny business can be characterized as "absence of prima facie consistent scenarios",…Read more
  •  1
    Nondesignating Singular Terms
    Journal of Symbolic Logic 25 (1): 87-88. 1960.
  •  112
    The Revision Theory of Truth
    with A. Gupta
    MIT Press. 1993.
    In this rigorous investigation into the logic of truth Anil Gupta and Nuel Belnap explain how the concept of truth works in both ordinary and pathological..
  •  32
    New Foundations for Branching Space-Times
    Studia Logica 109 (2): 239-284. 2020.
    The theory of branching space-times, put forward by Belnap, considers indeterminism as local in space and time. In the axiomatic foundations of that theory, so-called choice points mark the points at which the possible future can turn out in different ways. Working under the assumption of choice points is suitable for many applications, but has an unwelcome topological consequence that makes it difficult to employ branching space-times to represent a range of possible physical space-times. There…Read more
  •  52
    CIFOL: Case-Intensional First Order Logic: Toward a Theory of Sorts
    Journal of Philosophical Logic 43 (2-3): 393-437. 2014.
    This is part I of a two-part essay introducing case-intensional first order logic, an easy-to-use, uniform, powerful, and useful combination of first-order logic with modal logic resulting from philosophical and technical modifications of Bressan’s General interpreted modal calculus. CIFOL starts with a set of cases; each expression has an extension in each case and an intension, which is the function from the cases to the respective case-relative extensions. Predication is intensional; identity…Read more
  •  79
    CIFOL: Case-Intensional First Order Logic: Toward a Theory of Sorts
    Journal of Philosophical Logic 43 (2-3): 393-437. 2014.
    This is part I of a two-part essay introducing case-intensional first order logic, an easy-to-use, uniform, powerful, and useful combination of first-order logic with modal logic resulting from philosophical and technical modifications of Bressan’s General interpreted modal calculus. CIFOL starts with a set of cases; each expression has an extension in each case and an intension, which is the function from the cases to the respective case-relative extensions. Predication is intensional; identity…Read more
  •  89
    BH-CIFOL: Case-Intensional First Order Logic
    Journal of Philosophical Logic (2-3): 1-32. 2013.
    This paper follows Part I of our essay on case-intensional first-order logic (CIFOL; Belnap and Müller (2013)). We introduce a framework of branching histories to take account of indeterminism. Our system BH-CIFOL adds structure to the cases, which in Part I formed just a set: a case in BH-CIFOL is a moment/history pair, specifying both an element of a partial ordering of moments and one of the total courses of events (extending all the way into the future) that that moment is part of. This fram…Read more
  •  59
    BH-CIFOL: Case-Intensional First Order Logic: Branching Histories
    Journal of Philosophical Logic 43 (5): 835-866. 2014.
    This paper follows Part I of our essay on case-intensional first-order logic ). We introduce a framework of branching histories to take account of indeterminism. Our system BH-CIFOL adds structure to the cases, which in Part I formed just a set: a case in BH-CIFOL is a moment/history pair, specifying both an element of a partial ordering of moments and one of the total courses of events that that moment is part of. This framework allows us to define the familiar Ockhamist temporal/modal connecti…Read more
  •  84
    The pure calculus of entailment
    with Alan Ross Anderson
    Journal of Symbolic Logic 27 (1): 19-52. 1962.
  •  17
    "This book develops a rigorous theory of indeterminism as a local and modal concept. Its crucial insight is that our world contains events or processes with alternative, really possible outcomes. The theory aims at clarifying what this assumption involves, and it does it in two ways. First, it provides a mathematically rigorous framework for local and modal indeterminism. Second, we support that theory by spelling out the philosophically relevant consequences of this formulation and by showing i…Read more
  •  6
    Entailment: The Logic of Relevance and Necessity Vol. 2 (edited book)
    with Alan Ross Anderson and J. Michael Dunn
    Princeton University Press. 1992.
  • Approaches to the Semantics of Questions in Natural Language
    In Rainer Bäuerle, Christoph Schwarze & Arnim von Stechow (eds.), Meaning, Use, and Interpretation of Language, De Gruyter. pp. 22--29. 1968.
  •  95
    Branching with Uncertain Semantics: Discussion Note on Saunders and Wallace, 'Branching and Uncertainty'
    British Journal for the Philosophy of Science 61 (3): 681-696. 2010.
    (No abstract is available for this citation)
  • Double Time References: Speech-act Reports as a Modalitites in an Indeterminist Setting
    In Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic, Csli Publications. pp. 37-58. 1998.
  •  59
    A simple treatment of truth functions
    with Alan Ross Anderson
    Journal of Symbolic Logic 24 (4): 301-302. 1959.
    In this note we present an axiomatization of the classical two-valued propositional calculus, for which proofs of decidability, consistency, completeness, and independence, are almost trivial (given an understanding of truth tables).
  •  247
    Modalities in Ackermann's “rigorous implication”
    with Alan Ross Anderson
    Journal of Symbolic Logic 24 (2): 107-111. 1959.
    Following a suggestion of Feys, we use “rigorous implication” as a translation of Ackermann's strenge Implikation ([1]). Interest in Ackermann's system stems in part from the fact that it formalizes the properties of a strong, natural sort of implication which provably avoids standard implicational paradoxes, and which is consequently a good candidate for a formalization of entailment (considered as a narrower relation than that of strict implication). Our present purpose will not be to defend t…Read more
  • Double Time References: Speech-act Reports as a Modalitites in an Indeterminist Setting
    In Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic, Csli Publications. pp. 37-58. 1998.