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  1. Semantics and Proof Theory of the Epsilon Calculus.Richard Zach - 2017 - In Ghosh Sujata & Prasad Sanjiva (eds.), Logic and Its Applications. ICLA 2017. Springer. pp. 27-47.
    The epsilon operator is a term-forming operator which replaces quantifiers in ordinary predicate logic. The application of this undervalued formalism has been hampered by the absence of well-behaved proof systems on the one hand, and accessible presentations of its theory on the other. One significant early result for the original axiomatic proof system for the epsilon-calculus is the first epsilon theorem, for which a proof is sketched. The system itself is discussed, also relative to possible semantic interpretations. The problems facing (...)
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  • Existence Assumptions and Logical Principles: Choice Operators in Intuitionistic Logic.Corey Edward Mulvihill - 2015 - Dissertation, University of Waterloo
    Hilbert’s choice operators τ and ε, when added to intuitionistic logic, strengthen it. In the presence of certain extensionality axioms they produce classical logic, while in the presence of weaker decidability conditions for terms they produce various superintuitionistic intermediate logics. In this thesis, I argue that there are important philosophical lessons to be learned from these results. To make the case, I begin with a historical discussion situating the development of Hilbert’s operators in relation to his evolving program in the (...)
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  • A relational formulation of the theory of types.Reinhard Muskens - 1989 - Linguistics and Philosophy 12 (3):325 - 346.
    This paper developes a relational---as opposed to a functional---theory of types. The theory is based on Hilbert and Bernays' eta operator plus the identity symbol, from which Church's lambda and the other usual operators are then defined. The logic is intended for use in the semantics of natural language.
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  • Herbrand complexity and the epsilon calculus with equality.Kenji Miyamoto & Georg Moser - 2023 - Archive for Mathematical Logic 63 (1):89-118.
    The $$\varepsilon $$ -elimination method of Hilbert’s $$\varepsilon $$ -calculus yields the up-to-date most direct algorithm for computing the Herbrand disjunction of an extensional formula. A central advantage is that the upper bound on the Herbrand complexity obtained is independent of the propositional structure of the proof. Prior (modern) work on Hilbert’s $$\varepsilon $$ -calculus focused mainly on the pure calculus, without equality. We clarify that this independence also holds for first-order logic with equality. Further, we provide upper bounds analyses (...)
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  • Günter Asser (1926–2015).Armin Hemmerling - 2015 - Mathematical Logic Quarterly 61 (3):127-131.
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  • The Epsilon-Reconstruction of Theories and Scientific Structuralism.Georg Schiemer & Norbert Gratzl - 2016 - Erkenntnis 81 (2):407-432.
    Rudolf Carnap’s mature work on the logical reconstruction of scientific theories consists of two components. The first is the elimination of the theoretical vocabulary of a theory in terms of its Ramsification. The second is the reintroduction of the theoretical terms through explicit definitions in a language containing an epsilon operator. This paper investigates Carnap’s epsilon-reconstruction of theories in the context of pure mathematics. The main objective here is twofold: first, to specify the epsilon logic underlying his suggested definition of (...)
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  • Ultraprodukte in der Theorie der logischen Auswahlfunktionen.Dietrich Schwartz - 1975 - Mathematical Logic Quarterly 21 (1):385-394.
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  • Choice and descriptions in enriched intensional languages — I.R. Routley, R. K. Meyer & L. Goddard - 1974 - Journal of Philosophical Logic 3 (3):291 - 316.
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  • Dynamic Tractable Reasoning: A Modular Approach to Belief Revision.Holger Andreas - 2020 - Cham, Schweiz: Springer.
    This book aims to lay bare the logical foundations of tractable reasoning. It draws on Marvin Minsky's seminal work on frames, which has been highly influential in computer science and, to a lesser extent, in cognitive science. Only very few people have explored ideas about frames in logic, which is why the investigation in this book breaks new ground. The apparent intractability of dynamic, inferential reasoning is an unsolved problem in both cognitive science and logic-oriented artificial intelligence. By means of (...)
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  • Counterfactuals and Arbitrariness.Moritz Schulz - 2014 - Mind 123 (492):1021-1055.
    The pattern of credences we are inclined to assign to counterfactuals challenges standard accounts of counterfactuals. In response to this problem, the paper develops a semantics of counterfactuals in terms of the epsilon-operator. The proposed semantics stays close to the standard account: the epsilon-operator substitutes the universal quantifier present in standard semantics by arbitrarily binding the open world-variable. Various applications of the suggested semantics are explored including, in particular, an explanation of how the puzzling credences in counterfactuals come about.
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  • Epsilon-invariant substitutions and indefinite descriptions.Zoltán Molnár - 2013 - Logic Journal of the IGPL 21 (5):812-829.
    It is known that an epsilon-invariant sentence has a first-order reformulation, although it is not in an explicit form, since, the proof uses the non-constructive interpolation theorem. We make an attempt to describe the explicit meaning of sentences containing epsilon-terms, adopting the strong assumption of their first-order reformulability. We will prove that, if a monadic predicate is syntactically independent from an epsilon-term and if the sentence obtained by substituting the variable of the predicate with the epsilon-term is epsilon-invariant, then the (...)
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  • On rewriting sentences into formulas.Pavel Křížek - 1978 - Studia Logica 37 (1):115 - 128.
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  • Notes on the theory of variable binding term operators.Newton C. A. da Costa & Chris Mortensen - 1983 - History and Philosophy of Logic 4 (1-2):63-72.
    The general theory of variable binding term operators is an interesting recent development in logic. It opens up a rich class of semantic and model-theoretic problems. In this paper we survey the recent literature on the topic, and offer some remarks on its significances and on its connections with other branches of mathematical logic.
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  • Certains aspects syntactiques d'une notion de modele: Relativisation d'une fonction logique de choix.Marcel Guillaume - 1960 - Synthese 12 (2-3):236 - 248.
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