Counter Turing Test

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Proofs Without Nominals: Gödel's Ontological Argument, its Shallow Embedding, and the Open Questions of the Monatshefte Notes
Sep 28, 2026Christoph BenzmüllerFirst-Order Logic Axiom
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Cultural Competence in Context: A Large Language Model Passes the Turing Test in Finland
Sep 16, 2026Otto Segersven, Pentti HenttonenLinguistics Counter Turing Test
Department of Computer Science, University of Helsinki · Faculty of Social Sciences, University of Tampere
Gödel's and Scott's Variants of the Ontological Argument in Lean 4 and TPTP THF
Sep 14, 2026Christoph BenzmüllerTheorem Proving Proof
AI Systems Engineering, Otto-Friedrich-Universität Bamberg, Germany · Faculty of Mathematics and Computer Science, Freie Universität Berlin, Germany
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University of Electronic Science and Technology of China · Ludwig Maximilian University of Munich · Munich Center for Machine Learning
Turing's First Imitation Game: Design Concepts and a Human-Approximates-Machine Reading
Aug 6, 2026Sharon Temtsin, Christoph BartneckCounter Turing Test Imitation
University of Canterbury Christchurch, New Zealand
Measuring in-context algorithmic reasoning in language models against an exact Bayes-optimal standard
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Oxford Immune Algorithmics, Oxford University Innovation & London Institute for Healthcare Engineering, U.K · Department of Biomedical Computing, School of Biomedical Engineering and Imaging Sciences & King’s Institute for AI, King’s College London, U.K
Auditing Discovery Claims: A Two-Sided Criterion for Agentic Science, with the Negative Side Decidable
Aug 2, 2026Wenhui Chen, Jianlin Chen, Ziyao Lin +1Independent-Pool Single-Draw Oracle Model Auditing
University of Macau · 2South China University of Technology
Chess_db: A framework for working with large chess game datasets
Jul 23, 2026Nicos Angelopoulos, Jan WielemakerChess Large Databases
University College & Imperial College, London UK · University College & Imperial College London, UK · SWI-Prolog solutions +1
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Institute of Innovation Research, Hitotsubashi University (Professor Emeritus) · Meisei University (Professor Emeritus) · Shuhari System
Optimization Is Not All You Need
Jul 13, 2026Minh Hua, Rita RaleyPrompt Optimization Counter Turing Test
Scale AI · San Francisco, California · Department of English +1
Computing with Stochastic Oracles in AI-Augmented Computation
Jul 8, 2026Jie WangFirst Order Oracle Complexity Counter Turing Test
Richard A. Miner School of Computing and Information Sciences, University of Massachusetts, Lowell, MA 01854, USA.
Statistically Indistinguishable, Operationally Distinct: A Formal Barrier for Tabular Foundation Models
Jun 27, 2026Tassilo Klein, Johannes HoffartTabular Foundation Models Counter Turing Test
SAP SE
The Red Queen Gödel Machine: Co-Evolving Agents and Their Evaluators
Jun 24, 2026Alex Iacob, Andrej Jovanović, William F. Shen +10Self-Improving Agents Self-Evolving Agents
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Jun 2, 2026Fabio CuzzolinTheory-Of-Mind Reasoning Cognitive Science
Institure for AI, Data Analysis and Systems (AIDAS) School of Engineering, Computing and Mathematics Oxford Brookes University
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May 20, 2026Rajarshi Roy, Nasrin Imanpour, Ashhar Aziz +16Ai-Generated Image Detection Generative Artificial Intelligence
Kalyani Government Engineering College, India. · University of South Carolina, USA. · IIIT Delhi, India. +10
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May 20, 2026Rajarshi Roy, Gurpreet Singh, Ashhar Aziz +16Machine-Generated Text Detection Attacker Large Language Model
Kalyani Government Engineering College, India. · IIIT Guwahati, India. · IIIT Delhi, India. +10
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May 16, 2026Weiyi Kong, Shiyang Lai, Jinghua Piao +1Multi-Agent Large Language Model Systems Collapse
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Institute of Innovation Research, Hitotsubashi University, Kunitachi, Tokyo 186-8603, Japan · Meisei University, Hino, Tokyo, Japan · Shuhari System, Tokyo, Japan
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May 13, 2026Sungwoo Goo, Hwi-yeol Yun, Sangkeun JungBackpropagation Language Modeling
College of Pharmacy Chungnam National University Daejeon, South Korea · Department of Computer Science & Engineering Chungnam National University Daejeon, South Korea
Generalizing the Turing Test to Interactive Agents
May 11, 2026Daniel Mitropolsky, Riccardo Neumarker, Emanuele Rimoldi +2Counter Turing Test Intelligence
MIT · ETH Zurich · EPFL
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Manipal University Jaipur, Jaipur, Rajasthan, 303007, India · Indian Institute of Science Education and Research (IISER) Kolkata, Mohanpur, 741246, India · The West Bengal National University of Juridical Sciences, Kolkata, 700098, India
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Apr 30, 2026Haofei Yu, Yining Zhao, Lenore Blum +2Artificial Intelligence Systems Counter Turing Test
University of Illinois Urbana–Champaign · Carnegie Mellon University · Massachusetts Institute of Technol
Human or Machine? A Preliminary Turing Test for Speech-to-Speech Interaction
Feb 27, 2026Xiang Li, Jiabao Gao, Sipei Lin +5Seed-Tts-Eval Benchmark Paralinguistic Cues
State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications · Shenzhen Research Institute of Big Data · The Chinese University of Hong Kong, Shenzhen +2
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Oct 30, 2025Adam WinchellCounter Turing Test Efficiency
SGM: A Statistical Godel Machine for Risk-Controlled Recursive Self-Modification
Oct 11, 2025Xuening Wu, Shenqin Yin, Yanlan Kang +4Modifications Counter Turing Test
Fudan University · University of California, San Diego · Tongji University
Inverse Turing Bench: Evaluating Language Models as Judges of Human vs. AI Dialogue
Date pendingWilliam Hager, Ishika Rathi, Masum Hasan +1Human-Ai Interaction Conversational Artificial Intelligence
University of Rochester · Independent Researcher · Stony Brook University

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Proofs Without Nominals: Gödel's Ontological Argument, its Shallow Embedding, and the Open Questions of the Monatshefte Notes

Christoph Benzmüller

AI Systems Engineering, Otto-Friedrich-Universität Bamberg, Germany · Faculty of Mathematics and Computer Science, Freie Universität Berlin, Germany

First-Order Logic Axiom Proof Ontology Counter Turing Test Modalities

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The shallow embedding of higher-order modal logic in classical higher-order logic, used in Benzmüller and Scott's Notes on Gödel's and Scott's variants of the ontological argument (2025), reaches beyond the modal object language of the arguments: its property quantifiers range over terms that may also express nominals and satisfaction operators of hybrid logic, and a proof using one proves a theorem of the embedding that need not be one of the modal logic. That the framework affords this is not new, and whether a result is one of the modal logic can be settled in two ways: by replaying it in an explicit proof calculus, done by hand for chosen theorems, or by analysing the proofs the embedding itself produces, done here mechanically, for every result at once. Every statement the Notes prove has a proof inside the object language: 294 written out by hand and machine-checked, none using a nominal. The proofs the Notes themselves give instantiate no nominal either; what the detector flags there are terms a prover substituted. The three questions the Notes leave open are settled too, without nominals, but the conjunction axiom has to be emended: generalised in the Notes to Gödel's "any number of summands", it covers the conjunction of no properties, and of one; the empty one alone settles all three, and the two together yield what a separate axiom of Gödel's is for. This article restricts the conjunction axiom to at least two different conjuncts, the reading Gödel's footnote suggests, and the questions are settled again, by proofs that turn on the argument rather than a degenerate instance. The restriction holds of the object language only: with a nominal the axioms make the accessibility relation the identity and the readings coincide. Every theorem is verified in Isabelle/HOL and independently in Lean 4; the countermodels are Nitpick's, certified by the build.

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