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Gerhard Jäger [73]G. Jäger [6]Georg Jäger [3]Gottfried Jäger [2]
Gustav Jäger [1]
  1. Theories for Admissible Sets: A Unifying Approach to Proof Theory.Gerhard Jäger - 1986 - Bibliopolis.
     
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  2.  32
    The Evolution of Convex Categories.Gerhard Jäger - 2007 - Linguistics and Philosophy 30 (5):551-564.
    Gärdenfors (Conceptual spaces, 2000) argues that the semantic domains that natural language deals with have a geometrical structure. He gives evidence that simple natural language adjectives usually denote natural properties, where a natural property is a convex region of such a “conceptual space.” In this paper I will show that this feature of natural categories need not be stipulated as basic. In fact, it can be shown to be the result of evolutionary dynamics of communicative strategies under very general assumptions.
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  3. A Well-Ordering Proof for Feferman's theoryT 0.Gerhard Jäger - 1983 - Archive for Mathematical Logic 23 (1):65-77.
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  4.  33
    Systems of Explicit Mathematics with Non-Constructive Μ-Operator. Part II.Solomon Feferman & Gerhard Jäger - 1996 - Annals of Pure and Applied Logic 79 (1):37-52.
    This paper is mainly concerned with proof-theoretic analysis of some second-order systems of explicit mathematics with a non-constructive minimum operator. By introducing axioms for variable types we extend our first-order theory BON to the elementary explicit type theory EET and add several forms of induction as well as axioms for μ. The principal results then state: EET plus set induction is proof-theoretically equivalent to Peano arithmetic PA <0).
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  5.  67
    Language Structure: Psychological and Social Constraints.Gerhard Jäger & Robert van Rooij - 2007 - Synthese 159 (1):99 - 130.
    In this article we discuss the notion of a linguistic universal, and possible sources of such invariant properties of natural languages. In the first part, we explore the conceptual issues that arise. In the second part of the paper, we focus on the explanatory potential of horizontal evolution. We particularly focus on two case studies, concerning Zipf's Law and universal properties of color terms, respectively. We show how computer simulations can be employed to study the large scale, emergent, consequences of (...)
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  6.  32
    Systems of Explicit Mathematics with Non-Constructive Μ-Operator. Part I.Solomon Feferman & Gerhard Jäger - 1993 - Annals of Pure and Applied Logic 65 (3):243-263.
    Feferman, S. and G. Jäger, Systems of explicit mathematics with non-constructive μ-operator. Part I, Annals of Pure and Applied Logic 65 243-263. This paper is mainly concerned with the proof-theoretic analysis of systems of explicit mathematics with a non-constructive minimum operator. We start off from a basic theory BON of operators and numbers and add some principles of set and formula induction on the natural numbers as well as axioms for μ. The principal results then state: BON plus set induction (...)
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  7.  85
    Rationalizable Signaling.Gerhard Jäger - 2014 - Erkenntnis 79 (S4):1-34.
    An important finding of the game theoretic research on signaling games is the insight that under many circumstances, a signal obtains credibility by incurring costs to the sender. Therefore it seems questionable whether or not cheap talk—signals that are not payoff relevant—can serve to transmit information among rational agents. This issue is non-trivial in strategic interactions where the preferences of the players are not aligned. Researchers like Crawford & Sobel, Rabin, and Farrell demonstrated, however, that even in the case of (...)
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  8.  28
    The Proof-Theoretic Analysis of Transfinitely Iterated Fixed Point Theories.Gerhard JÄger, Reinhard Kahle, Anton Setzer & Thomas Strahm - 1999 - Journal of Symbolic Logic 64 (1):53-67.
    This article provides the proof-theoretic analysis of the transfinitely iterated fixed point theories $\widehat{ID}_\alpha and \widehat{ID}_{ the exact proof-theoretic ordinals of these systems are presented.
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  9.  38
    Bidirectional Optimization From Reasoning and Learning in Games.Michael Franke & Gerhard Jäger - 2012 - Journal of Logic, Language and Information 21 (1):117-139.
    We reopen the investigation into the formal and conceptual relationship between bidirectional optimality theory (Blutner in J Semant 15(2):115–162, 1998 , J Semant 17(3):189–216, 2000 ) and game theory. Unlike a likeminded previous endeavor by Dekker and van Rooij (J Semant 17:217–242, 2000 ), we consider signaling games not strategic games, and seek to ground bidirectional optimization once in a model of rational step-by-step reasoning and once in a model of reinforcement learning. We give sufficient conditions for equivalence of bidirectional (...)
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  10.  14
    On Feferman’s Operational Set Theory OST.Gerhard Jäger - 2007 - Annals of Pure and Applied Logic 150 (1-3):19-39.
    We study and some of its most important extensions primarily from a proof-theoretic perspective, determine their consistency strengths by exhibiting equivalent systems in the realm of traditional set theory and introduce a new and interesting extension of which is conservative over.
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  11.  16
    Fixed Points in Peano Arithmetic with Ordinals.Gerhard Jäger - 1993 - Annals of Pure and Applied Logic 60 (2):119-132.
    Jäger, G., Fixed points in Peano arithmetic with ordinals, Annals of Pure and Applied Logic 60 119-132. This paper deals with some proof-theoretic aspects of fixed point theories over Peano arithmetic with ordinals. It studies three such theories which differ in the principles which are available for induction on the natural numbers and ordinals. The main result states that there is a natural theory in this framework which is a conservative extension of Peano arithmeti.
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  12.  23
    Upper Bounds for Metapredicative Mahlo in Explicit Mathematics and Admissible Set Theory.Gerhard Jäger & Thomas Strahm - 2001 - Journal of Symbolic Logic 66 (2):935-958.
    In this article we introduce systems for metapredicative Mahlo in explicit mathematics and admissible set theory. The exact upper proof-theoretic bounds of these systems are established.
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  13.  9
    Pragmatic Processing: An Investigation of the Presuppositions of Determiners Using Mouse-Tracking.Cosima Schneider, Carolin Schonard, Michael Franke, Gerhard Jäger & Markus Janczyk - 2019 - Cognition 193:104024.
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  14.  1
    Zur Beweistheorie Der Kripke-Platek-Mengenlehre Über Den Natürlichen Zahlen.Gerhard Jäger - 1980 - Archive for Mathematical Logic 22 (3-4):121-139.
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  15.  16
    Totality in Applicative Theories.Gerhard Jäger & Thomas Strahm - 1995 - Annals of Pure and Applied Logic 74 (2):105-120.
    In this paper we study applicative theories of operations and numbers with the non-constructive minimum operator in the context of a total application operation. We determine the proof-theoretic strength of such theories by relating them to well-known systems like Peano Arithmetic PA and the system <0 of second order arithmetic. Essential use will be made of so-called fixed-point theories with ordinals, certain infinitary term models and Church-Rosser properties.
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  16.  7
    Language Structure: Psychological and Social Constraints.Gerhard Jäger & Robert Rooij - 2007 - Synthese 159 (1):99-130.
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  17.  31
    About Cut Elimination for Logics of Common Knowledge.Luca Alberucci & Gerhard Jäger - 2005 - Annals of Pure and Applied Logic 133 (1):73-99.
    The notions of common knowledge or common belief play an important role in several areas of computer science , in philosophy, game theory, artificial intelligence, psychology and many other fields which deal with the interaction within a group of “agents”, agreement or coordinated actions. In the following we will present several deductive systems for common knowledge above epistemic logics –such as K, T, S4 and S5 –with a fixed number of agents. We focus on structural and proof-theoretic properties of these (...)
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  18.  10
    Full Operational Set Theory with Unbounded Existential Quantification and Power Set.Gerhard Jäger - 2009 - Annals of Pure and Applied Logic 160 (1):33-52.
    We study the extension of Feferman’s operational set theory provided by adding operational versions of unbounded existential quantification and power set and determine its proof-theoretic strength in terms of a suitable theory of sets and classes.
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  19.  10
    Intuitionistic Common Knowledge or Belief.Gerhard Jäger & Michel Marti - 2016 - Journal of Applied Logic 18:150-163.
  20.  15
    Explicit mathematics and operational set theory: Some ontological comparisons.Gerhard Jäger & Rico Zumbrunnen - 2017 - Association for Symbolic Logic: The Bulletin of Symbolic Logic.
    We discuss several ontological properties of explicit mathematics and operational set theory: global choice, decidable classes, totality and extensionality of operations, function spaces, class and set formation via formulas that contain the definedness predicate and applications.
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  21.  8
    Extending the System T0 of Explicit Mathematics: The Limit and Mahlo Axioms.Gerhard Jäger & Thomas Studer - 2002 - Annals of Pure and Applied Logic 114 (1-3):79-101.
    In this paper we discuss extensions of Feferman's theory T 0 for explicit mathematics by the so-called limit and Mahlo axioms and present a novel approach to constructing natural recursion-theoretic models for systems of explicit mathematics which is based on nonmonotone inductive definitions.
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  22. First Order Theories for Nonmonotone Inductive Definitions: Recursively Inaccessible and Mahlo.Gerhard Jäger - 2001 - Journal of Symbolic Logic 66 (3):1073-1089.
    In this paper first order theories for nonmonotone inductive definitions are introduced, and a proof-theoretic analysis for such theories based on combined operator forms a la Richter with recursively inaccessible and Mahlo closure ordinals is given.
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  23.  11
    Cut-Free Common Knowledge.Gerhard Jäger, Mathis Kretz & Thomas Studer - 2007 - Journal of Applied Logic 5 (4):681-689.
  24.  20
    Some Notes on the Formal Properties of Bidirectional Optimality Theory.Gerhard Jäger - 2002 - Journal of Logic, Language and Information 11 (4):427-451.
    In this paper, we discuss some formal properties of the model ofbidirectional Optimality Theory that was developed inBlutner (2000). We investigate the conditions under whichbidirectional optimization is a well-defined notion, and we give aconceptually simpler reformulation of Blutner's definition. In thesecond part of the paper, we show that bidirectional optimization can bemodeled by means of finite state techniques. There we rely heavily onthe related work of Frank and Satta (1998) about unidirectionaloptimization.
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  25. Beweistheorie vonKPN.Gerhard Jäger - 1980 - Archive for Mathematical Logic 20 (1-2):53-63.
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  26.  16
    Fixed Point Theories and Dependent Choice.Gerhard Jäger & Thomas Strahm - 2000 - Archive for Mathematical Logic 39 (7):493-508.
    In this paper we establish the proof-theoretic equivalence of (i) $\hbox {\sf ATR}$ and $\widehat{\hbox{\sf ID}}_{\omega}$ , (ii) $\hbox{\sf ATR}_0+ (\Sigma^1_1-\hbox{\sf DC})$ and $\widehat{\hbox {\sf ID}}_{<\omega^\omega} , and (iii) $\hbox {\sf ATR}+(\Sigma^1_1-\hbox{\sf DC})$ and $\widehat{\hbox {\sf ID}}_{<\varepsilon_0} $.
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  27.  11
    Universes in Explicit Mathematics.Gerhard Jäger, Reinhard Kahle & Thomas Studer - 2001 - Annals of Pure and Applied Logic 109 (3):141-162.
    This paper deals with universes in explicit mathematics. After introducing some basic definitions, the limit axiom and possible ordering principles for universes are discussed. Later, we turn to least universes, strictness and name induction. Special emphasis is put on theories for explicit mathematics with universes which are proof-theoretically equivalent to Feferman's.
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  28.  7
    The Proof-Theoretic Analysis of Transfinitely Iterated Fixed Point Theories.Gerhard Jager, Reinhard Kahle, Anton Setzer & Thomas Strahm - 1999 - Journal of Symbolic Logic 64 (1):53-67.
    This article provides the proof-theoretic analysis of the transfinitely iterated fixed point theories $\widehat{ID}_\alpha and \widehat{ID}_{<\alpha};$ the exact proof-theoretic ordinals of these systems are presented.
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  29.  40
    Operational Closure and Stability.Gerhard Jäger - 2013 - Annals of Pure and Applied Logic 164 (7-8):813-821.
    In this article we introduce and study the notion of operational closure: a transitive set d is called operationally closed iff it contains all constants of OST and any operation f∈d applied to an element a∈d yields an element fa∈d, provided that f applied to a has a value at all. We will show that there is a direct relationship between operational closure and stability in the sense that operationally closed sets behave like Σ1 substructures of the universe. This leads (...)
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  30.  32
    Residuation, Structural Rules and Context Freeness.Gerhard Jäger - 2004 - Journal of Logic, Language and Information 13 (1):47-59.
    The article presents proofs of the context freeness of a family of typelogical grammars, namely all grammars that are based on a uni- ormultimodal logic of pure residuation, possibly enriched with thestructural rules of Permutation and Expansion for binary modes.
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  31.  14
    Second Order Theories with Ordinals and Elementary Comprehension.Gerhard Jäger & Thomas Strahm - 1995 - Archive for Mathematical Logic 34 (6):345-375.
    We study elementary second order extensions of the theoryID 1 of non-iterated inductive definitions and the theoryPA Ω of Peano arithmetic with ordinals. We determine the exact proof-theoretic strength of those extensions and their natural subsystems, and we relate them to subsystems of analysis with arithmetic comprehension plusΠ 1 1 comprehension and bar induction without set parameters.
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  32.  48
    A Buchholz Rule for Modal Fixed Point Logics.Gerhard Jäger & Thomas Studer - 2011 - Logica Universalis 5 (1):1-19.
    Buchholz’s Ω μ+1-rules provide a major tool for the proof-theoretic analysis of arithmetical inductive definitions. The aim of this paper is to put this approach into the new context of modal fixed point logic. We introduce a deductive system based on an Ω-rule tailored for modal fixed point logic and develop the basic techniques for establishing soundness and completeness of the corresponding system. In the concluding section we prove a cut elimination and collapsing result similar to that of Buchholz (Iterated (...)
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  33.  16
    Some Theories with Positive Induction of Ordinal Strength Φω.Gerhard Jäger & Thomas Strahm - 1996 - Journal of Symbolic Logic 61 (3):818-842.
    This paper deals with: (i) the theory ID # 1 which results from $\widehat{\mathrm{ID}}_1$ by restricting induction on the natural numbers to formulas which are positive in the fixed point constants, (ii) the theory BON(μ) plus various forms of positive induction, and (iii) a subtheory of Peano arithmetic with ordinals in which induction on the natural numbers is restricted to formulas which are Σ in the ordinals. We show that these systems have proof-theoretic strength φω 0.
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  34.  36
    About Some Symmetries of Negation.Brigitte Hösli & Gerhard Jäger - 1994 - Journal of Symbolic Logic 59 (2):473-485.
    This paper deals with some structural properties of the sequent calculus and describes strong symmetries between cut-free derivations and derivations, which do not make use of identity axioms. Both of them are discussed from a semantic and syntactic point of view. Identity axioms and cuts are closely related to the treatment of negation in the sequent calculus, so the results of this article explain some nice symmetries of negation.
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  35.  3
    Short note: Least fixed points versus least closed points.Gerhard Jäger - 2021 - Archive for Mathematical Logic 60 (7):831-835.
    This short note is on the question whether the intersection of all fixed points of a positive arithmetic operator and the intersection of all its closed points can proved to be equivalent in a weak fragment of second order arithmetic.
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  36.  11
    The Strength of Admissibility Without Foundation.Gerhard Jäger - 1984 - Journal of Symbolic Logic 49 (3):867-879.
  37. About the Proof-Theoretic Ordinals of Weak Fixed Point Theories.Gerhard Jäger & Barbara Primo - 1992 - Journal of Symbolic Logic 57 (3):1108-1119.
    This paper presents several proof-theoretic results concerning weak fixed point theories over second order number theory with arithmetic comprehension and full or restricted induction on the natural numbers. It is also shown that there are natural second order theories which are proof-theoretically equivalent but have different proof-theoretic ordinals.
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  38. Ρ-Inaccessible Ordinals, Collapsing Functions and a Recursive Notation System.Gerhard Jäger - 1984 - Archive for Mathematical Logic 24 (1):49-62.
     
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  39.  5
    Reflections on Reflections in Explicit Mathematics.Gerhard Jäger & Thomas Strahm - 2005 - Annals of Pure and Applied Logic 136 (1-2):116-133.
    We give a broad discussion of reflection principles in explicit mathematics, thereby addressing various kinds of universe existence principles. The proof-theoretic strength of the relevant systems of explicit mathematics is couched in terms of suitable extensions of Kripke–Platek set theory.
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  40.  17
    Power Types in Explicit Mathematics?Gerhard Jäger - 1997 - Journal of Symbolic Logic 62 (4):1142-1146.
    In this note it is shown that in explicit mathematics the strong power type axiom is inconsistent with (uniform) elementary comprehension and discuss some general aspects of power types in explicit mathematics.
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  41.  7
    Truncation and Semi-Decidability Notions in Applicative Theories.Gerhard Jäger, Timotej Rosebrock & Sato Kentaro - 2018 - Journal of Symbolic Logic 83 (3):967-990.
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  42.  9
    Explicit Mathematics and Operational Set Theory: Some Ontological Comparisons.Gerhard Jäger & Rico Zumbrunnen - 2014 - Bulletin of Symbolic Logic 20 (3):275-292.
    We discuss several ontological properties of explicit mathematics and operational set theory: global choice, decidable classes, totality and extensionality of operations, function spaces, class and set formation via formulas that contain the definedness predicate and applications.
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  43.  18
    Alexander Koller, Ralph Debusmann, Malte Gabsdil, and Kristina Striegnitz/Put My Galakmid Coin Into the Dispenser and Kick It: Computational Linguistics and Theorem Proving in a Computer Game 187–206.Gerhard Jager & Structural Rules Residuation - 2004 - Journal of Logic, Language and Information 13 (1):537-539.
    The article presents proofs of the context freeness of a family of typelogical grammars, namely all grammars that are based on a uni- ormultimodal logic of pure residuation, possibly enriched with thestructural rules of Permutation and Expansion for binary modes.
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  44.  8
    Choice Principles, the Bar Rule and Autonomously Iterated Comprehension Schemes in Analysis.S. Feferman & G. Jäger - 1983 - Journal of Symbolic Logic 48 (1):63-70.
    In [10] Friedman showed that is a conservative extension of <ε0for-sentences wherei= min, i.e.,i= 2, 3, 4 forn= 0, 1, 2 +m. Feferman [5], [7] and Tait [11], [12] reobtained this result forn= 0, 1 and even with instead of. Feferman and Sieg established in [9] the conservativeness of over <ε0for-sentences for alln. In each paper, different methods of proof have been used. In particular, Feferman and Sieg showed how to apply familiar proof-theoretical techniques by passing through languages with Skolem (...)
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  45.  18
    Variation on a Theme of Schutte.D. Probst & G. Jager - 2004 - Mathematical Logic Quarterly 50 (3):258.
    Let ≺ be a primitive recursive well-ordering on the natural numbers and assume that its order-type is greater than or equal to the proof-theoretic ordinal of the theory T. We show that the proof-theoretic strength of T is not increased if we add the negation of the statement which formalizes transfinite induction along ≺.
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  46.  7
    Bar Induction and Ω Model Reflection.Gerhard Jäger & Thomas Strahm - 1999 - Annals of Pure and Applied Logic 97 (1-3):221-230.
    We show that the principle of ω model reflection for Π1n − 1 formulas is equivalent over ACA0 to the scheme of Π1n bar induction. This extends and refines previous results of Friedman and Simpson.
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  47.  7
    Beweistheorie von KPN.Kurt Schutte & Gerhard Jager - 1983 - Journal of Symbolic Logic 48 (3):879.
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  48.  78
    Towards an Explanation of Copula Effects.Gerhard Jäger - 2003 - Linguistics and Philosophy 26 (5):557-593.
    This paper deals with a series of semantic contrasts between the copula be and the preposition as, two functional elements that both head elementary predication structures. It will be argued that the meaning of as is a type lowering device shifting the meaning of its complement NP from the type of generalized quantifiers to the type of properties (where properties are conceived as relations between individuals and situations), while the copula be induces a type coercion from (partial) situations to (total) (...)
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  49.  6
    Upper Bounds for Metapredicative Mahlo in Explicit Mathematics and Admissible Set Theory.Gerhard Jager & Thomas Strahm - 2001 - Journal of Symbolic Logic 66 (2):935-958.
    In this article we introduce systems for metapredicative Mahlo in explicit mathematics and admissible set theory. The exact upper proof-theoretic bounds of these systems are established.
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  50.  22
    A Version of Kripke-Platek Set Theory Which is Conservative Over Peano Arithmetic.Gerhard Jäger - 1984 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 30 (1-6):3-9.
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