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59On Topological Issues of IndeterminismErkenntnis 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
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21Twenty-sixth annual meeting of the association for symbolic logicJournal of Symbolic Logic 25 (4): 384-393. 1960.
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41On not strengthening intuitionistic logicNotre 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 AâAâ..., Aâ I- B, where AâAâ..., Aâ(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
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190Funny business in branching space-times: infinite modal correlationsSynthese 164 (1): 141-159. 2008.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
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112The Revision Theory of TruthMIT 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..
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32New Foundations for Branching Space-TimesStudia 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
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52CIFOL: Case-Intensional First Order Logic: Toward a Theory of SortsJournal 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
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79CIFOL: Case-Intensional First Order Logic: Toward a Theory of SortsJournal 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
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89BH-CIFOL: Case-Intensional First Order LogicJournal 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
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59BH-CIFOL: Case-Intensional First Order Logic: Branching HistoriesJournal 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
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17Branching Space-Times: Theory and ApplicationsOxford University Press. 2020."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
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6Entailment: The Logic of Relevance and Necessity Vol. 2 (edited book)Princeton University Press. 1992.
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Approaches to the Semantics of Questions in Natural LanguageIn Rainer Bäuerle, Christoph Schwarze & Arnim von Stechow (eds.), Meaning, Use, and Interpretation of Language, De Gruyter. pp. 22--29. 1968.
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95Branching 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)
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Questions and Answers in Montague GrammarIn Stanley Peters & Esa Saarinen (eds.), Processes, Beliefs, and Questions. Essays on Formal Semantics of Natural Language and Natural Language Processing, Reidel. pp. 165--198. 1982.
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Åqvist’s Correction-Accumulating Question-SequencesIn J. W. Davis (ed.), Philosophical logic, D. Reidel. pp. 122--134. 1969.
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Questions: Their Preuppositions, and How They Can Fail to AriseIn Karel Lambert (ed.), The Logical Way of Doing Things, Yale University Press. pp. 23--37. 1969.
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Double Time References: Speech-act Reports as a Modalitites in an Indeterminist SettingIn Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic, Csli Publications. pp. 37-58. 1998.
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59A simple treatment of truth functionsJournal 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).
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247Modalities in Ackermann's “rigorous implication”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
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22David Harrah. A logic of questions and answers. Philosophy of science, vol. 28 , pp. 40–46. - David Harrah. Communication: A logical model. The M.I.T. Press, Cambridge, Massachusetts, 1963, xi + 118 pp. - David Harrah. A model for applying information and utility functions. Philosophy of science, vol. 30 , pp. 267–273 (review)Journal of Symbolic Logic 29 (3): 136-138. 1964.
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26R. B. Angell. A propositional logic with subjunctive conditionals. The journal of symbolic logic, vol. 27 no. 3 , pp. 327–343Journal of Symbolic Logic 35 (3): 464-465. 1970.
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Double Time References: Speech-act Reports as a Modalitites in an Indeterminist SettingIn Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic, Csli Publications. pp. 37-58. 1998.
Pittsburgh, Pennsylvania, United States of America
Areas of Interest
Metaphysics |
Logic and Philosophy of Logic |