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Ben Goertzel

Publications and source records attributed to Ben Goertzel.

At least 19 recordsLinked to original sources
arXiv2026

A Motivational Architecture for Conversational AGI

Motivational architectures in cognitive AI have largely been designed for physical agents regulating bodily needs. Conversational agents operate in a different regime: their sensorimotor loop is linguistic, their environment is a user's evolving mental state, and their consequential actions are speech acts, tool invocations, and strategic silences. This paper proposes a conversational reinterpretation of the OpenPsi motivational lineage, coupled to MetaMo's higher-level motivational scaffold, for agents built on a modular execution substrate. Homeostasis is recast in dialogue-native terms: the agent regulates competence, uncertainty reduction, affiliation, affinity, legitimacy, nurturing, and aesthetic coherence rather than bodily deficits. We propose three contributions: a ten-stage motivational processing pipeline that architecturally separates cognitive modulation from situational appraisal; a dual decision strategy blending urgency-driven fast response with deliberative multi-goal optimization; and an architecturally useful distinction between pre-action feelings and post-action emotions as functionally different forms of affect. We specialize the framework to two example agents -- CompanionAgent and ResearchAgent -- and sketch its extension to social robotics and domain-generic human-level AGI.

cs.AI↗
arXiv2026

Prime Successor Irreducibility: Turing Machine Complexity, Kolmogorov Complexity, and Weakness-Based Formulations

We develop conjectures and theorems expressing the idea that the prime sequence exhibits computational irreducibility in the transition from one prime to its successor. Informally, given a prime pp p, no general algorithm can compute the least prime greater than pp p substantially faster than sequentially testing candidates for primality, except possibly on sparse input sets. Our framework proceeds along complementary lines. First, we formalize Prime Successor Irreducibility in a Turing-machine complexity model (PSI-T), asserting lower bounds on running time relative to a sequential baseline. Second, we propose a Kolmogorov-complexity formulation (PSI-K), asserting that typical prime gaps are algorithmically incompressible at their scale; we prove PSI-K(c, $\delta$) unconditionally for all fixed c<1 using standard sieve bounds. Third, we develop weakness-based formulations: PSI-W (sparse-set anti-concentration) shows no small menu of gap values captures a noticeable fraction of primes, while PSI-W-LE shows collision probabilities decay and logical entropy tends to 1. These extend to prime constellations and consecutive gap vectors. Finally, a sieve-theoretic framework connects local obstruction patterns to Selberg weakness parameters. The PSI-K and weakness formulations connect irreducibility to classical statistical questions about prime gaps. Using the relationship between Kolmogorov complexity and Shannon entropy, we derive rigorous lower bounds on prime gap entropy in dyadic intervals [X,2X]. Together, these formulations provide a unified complexity-theoretic perspective on the apparent local unpredictability of the prime sequence, without asserting randomness or independence.

cs.CC↗
arXiv2025

A Quantale-Weakness Route to $P \neq NP$ via CD Evidence Normalization and Gauge-Buffered Locked Ensembles

We present a proof architecture for \(P \neq NP\) based on an upper--lower clash in polytime-capped conditional description length. We construct an efficiently samplable family of SAT instances \(Y\) such that every satisfying witness for \(Y\) yields the same global message \(M(Y)\). If \(P=NP\), then a standard polynomial-time SAT self-reduction recovers \(M(Y)\) from \(Y\), so \[ K_{\mathrm{poly}}(M(Y)\mid Y)=O(1). \] The lower-bound side shows the opposite. For the same ensemble, no fixed polynomial-time observer can gain substantial predictive advantage on a linear number of selected message coordinates. The argument treats computation as an evidence-producing process: predictive advantage is converted into constructible-dual evidence skew and then into pairwise distinctions between message-opposite worlds. A normalization theorem shows that every target-relevant non-neutral evidence leaf is either a safe-buffer observation or a hidden-gauge observation. Safe-buffer observations have negligible leakage, while hidden-gauge observations are limited by gauge-rank accounting. This yields an atomic evidence budget implying that total message-resolving advantage is \(o(t)\) across \(t\) selected coordinates. Boundary-law mixing gives the near-random baseline for the visible surface. Combining this with the evidence budget gives product small-success and then, by Compression-from-Success, \[ K_{\mathrm{poly}}(M(Y)\mid Y)\ge \Omega(t) \] with high probability. This contradicts the constant upper bound from \(P=NP\). Therefore \(P \neq NP\).

cs.CC↗
arXiv2025

Efficient Quantum-Safe Homomorphic Encryption for Quantum Computer Programs

We present a lattice-based scheme for homomorphic evaluation of quantum programs and proofs that remains secure against quantum adversaries. Classical homomorphic encryption is lifted to the quantum setting by replacing composite-order groups with Module Learning-With-Errors (MLWE) lattices and by generalizing polynomial functors to bounded natural super functors (BNSFs). A secret depolarizing BNSF mask hides amplitudes, while each quantum state is stored as an MLWE ciphertext pair. We formalize security with the qIND-CPA game that allows coherent access to the encryption oracle and give a four-hybrid reduction to decisional MLWE. The design also covers practical issues usually left open. A typed QC-bridge keeps classical bits produced by measurements encrypted yet still usable as controls, with weak-measurement semantics for expectation-value workloads. Encrypted Pauli twirls add circuit privacy. If a fixed knowledge base is needed, its axioms are shipped as MLWE "capsules"; the evaluator can use them but cannot read them. A rho-calculus driver schedules encrypted tasks across several QPUs and records an auditable trace on an RChain-style ledger. Performance analysis shows that the extra lattice arithmetic fits inside today's QPU idle windows: a 100-qubit, depth-10^3 teleportation-based proof runs in about 10 ms, the public key (seed only) is 32 bytes, and even a CCA-level key stays below 300 kB. A photonic Dirac-3 prototype that executes homomorphic teleportation plus knowledge-base-relative amplitude checks appears feasible with current hardware. These results indicate that fully homomorphic, knowledge-base-aware quantum reasoning is compatible with near-term quantum clouds and standard post-quantum security assumptions.

quant-ph↗
arXiv2025

PICO: Secure Transformers via Robust Prompt Isolation and Cybersecurity Oversight

We propose a robust transformer architecture designed to prevent prompt injection attacks and ensure secure, reliable response generation. Our PICO (Prompt Isolation and Cybersecurity Oversight) framework structurally separates trusted system instructions from untrusted user inputs through dual channels that are processed independently and merged only by a controlled, gated fusion mechanism. In addition, we integrate a specialized Security Expert Agent within a Mixture-of-Experts (MoE) framework and incorporate a Cybersecurity Knowledge Graph (CKG) to supply domain-specific reasoning. Our training design further ensures that the system prompt branch remains immutable while the rest of the network learns to handle adversarial inputs safely. This PICO framework is presented via a general mathematical formulation, then elaborated in terms of the specifics of transformer architecture, and fleshed out via hypothetical case studies including Policy Puppetry attacks. While the most effective implementation may involve training transformers in a PICO-based way from scratch, we also present a cost-effective fine-tuning approach.

cs.CR↗
arXiv2025

Homomorphic Encryption of Intuitionistic Logic Proofs and Functional Programs: A Categorical Approach Inspired by Composite-Order Bilinear Groups

We present a conceptual framework for extending homomorphic encryption beyond arithmetic or Boolean operations into the domain of intuitionistic logic proofs and, by the Curry-Howard correspondence, into the domain of typed functional programs. We begin by reviewing well-known homomorphic encryption schemes for arithmetic operations, and then discuss the adaptation of similar concepts to support logical inference steps in intuitionistic logic. Key to our construction are polynomial functors and Bounded Natural Functors (BNFs), which serve as a categorical substrate on which logic formulas and proofs are represented and manipulated. We outline a complexity-theoretic hardness assumption -- the BNF Distinguishing Problem, constructed via a reduction from Subgraph Isomorphism, providing a foundation for cryptographic security. Finally, we describe how these methods can homomorphically encode the execution of total, dependently typed functional programs, and outline strategies for making the approach potentially efficient, including software optimizations and hardware acceleration.

cs.LO↗
arXiv2025

Intensional Inheritance Between Concepts: An Information-Theoretic Interpretation

This paper addresses the problem of formalizing and quantifying the concept of "intensional inheritance" between two concepts. We begin by conceiving the intensional inheritance of $W$ from $F$ as the amount of information the proposition "x is $F$ " provides about the proposition "x is $W$. To flesh this out, we consider concepts $F$ and $W$ defined by sets of properties $\left\{F_{1}, F_{2}, \ldots, F_{n}\right\}$ and $\left\{W_{1}, W_{2}, \ldots, W_{m}\right\}$ with associated degrees $\left\{d_{1}, d_{2}, \ldots, d_{n}\right\}$ and $\left\{e_{1}, e_{2}, \ldots, e_{m}\right\}$, respectively, where the properties may overlap. We then derive formulas for the intensional inheritance using both Shannon information theory and algorithmic information theory, incorporating interaction information among properties. We examine a special case where all properties are mutually exclusive and calculate the intensional inheritance in this case in both frameworks. We also derive expressions for $P(W \mid F)$ based on the mutual information formula. Finally we consider the relationship between intensional inheritance and conventional set-theoretic "extensional" inheritance, concluding that in our information-theoretic framework, extensional inheritance emerges as a special case of intensional inheritance.

cs.AI↗
arXiv2025

ActPC-Geom: Towards Scalable Online Neural-Symbolic Learning via Accelerating Active Predictive Coding with Information Geometry & Diverse Cognitive Mechanisms

This paper introduces ActPC-Geom, an approach to accelerate Active Predictive Coding (ActPC) in neural networks by integrating information geometry, specifically using Wasserstein-metric-based methods for measure-dependent gradient flows. We propose replacing KL-divergence in ActPC's predictive error assessment with the Wasserstein metric, suggesting this may enhance network robustness. To make this computationally feasible, we present strategies including: (1) neural approximators for inverse measure-dependent Laplacians, (2) approximate kernel PCA embeddings for low-rank approximations feeding into these approximators, and (3) compositional hypervector embeddings derived from kPCA outputs, with algebra optimized for fuzzy FCA lattices learned through neural architectures analyzing network states. This results in an ActPC architecture capable of real-time online learning and integrating continuous (e.g., transformer-like or Hopfield-net-like) and discrete symbolic ActPC networks, including frameworks like OpenCog Hyperon or ActPC-Chem for algorithmic chemistry evolution. Shared probabilistic, concept-lattice, and hypervector models enable symbolic-subsymbolic integration. Key features include (1) compositional reasoning via hypervector embeddings in transformer-like architectures for tasks like commonsense reasoning, and (2) Hopfield-net dynamics enabling associative long-term memory and attractor-driven cognitive features. We outline how ActPC-Geom combines few-shot learning with online weight updates, enabling deliberative thinking and seamless symbolic-subsymbolic reasoning. Ideas from Galois connections are explored for efficient hybrid ActPC/ActPC-Chem processing. Finally, we propose a specialized HPC design optimized for real-time focused attention and deliberative reasoning tailored to ActPC-Geom's demands.

cs.AI↗
arXiv2024

PLN and NARS Often Yield Similar strength $\times$ confidence Given Highly Uncertain Term Probabilities

We provide a comparative analysis of the deduction, induction, and abduction formulas used in Probabilistic Logic Networks (PLN) and the Non-Axiomatic Reasoning System (NARS), two uncertain reasoning frameworks aimed at AGI. One difference between the two systems is that, at the level of individual inference rules, PLN directly leverages both term and relationship probabilities, whereas NARS only leverages relationship frequencies and has no simple analogue of term probabilities. Thus we focus here on scenarios where there is high uncertainty about term probabilities, and explore how this uncertainty influences the comparative inferential conclusions of the two systems. We compare the product of strength and confidence ($s\times c$) in PLN against the product of frequency and confidence ($f\times c$) in NARS (quantities we refer to as measuring the "power" of an uncertain statement) in cases of high term probability uncertainty, using heuristic analyses and elementary numerical computations. We find that in many practical situations with high term probability uncertainty, PLN and NARS formulas give very similar results for the power of an inference conclusion, even though they sometimes come to these similar numbers in quite different ways.

cs.AI↗
arXiv2024

ActPC-Chem: Discrete Active Predictive Coding for Goal-Guided Algorithmic Chemistry as a Potential Cognitive Kernel for Hyperon & PRIMUS-Based AGI

We explore a novel paradigm (labeled ActPC-Chem) for biologically inspired, goal-guided artificial intelligence (AI) centered on a form of Discrete Active Predictive Coding (ActPC) operating within an algorithmic chemistry of rewrite rules. ActPC-Chem is envisioned as a foundational "cognitive kernel" for advanced cognitive architectures, such as the OpenCog Hyperon system, incorporating essential elements of the PRIMUS cognitive architecture. The central thesis is that general-intelligence-capable cognitive structures and dynamics can emerge in a system where both data and models are represented as evolving patterns of metagraph rewrite rules, and where prediction errors, intrinsic and extrinsic rewards, and semantic constraints guide the continual reorganization and refinement of these rules. Using a virtual "robot bug" thought experiment, we illustrate how such a system might self-organize to handle challenging tasks involving delayed and context-dependent rewards, integrating causal rule inference (AIRIS) and probabilistic logical abstraction (PLN) to discover and exploit conceptual patterns and causal constraints. Next, we describe how continuous predictive coding neural networks, which excel at handling noisy sensory data and motor control signals, can be coherently merged with the discrete ActPC substrate. Finally, we outline how these ideas might be extended to create a transformer-like architecture that foregoes traditional backpropagation in favor of rule-based transformations guided by ActPC. This layered architecture, supplemented with AIRIS and PLN, promises structured, multi-modal, and logically consistent next-token predictions and narrative sequences.

cs.AI↗
arXiv2024

Metagoals Endowing Self-Modifying AGI Systems with Goal Stability or Moderated Goal Evolution: Toward a Formally Sound and Practical Approach

We articulate here a series of specific metagoals designed to address the challenge of creating AGI systems that possess the ability to flexibly self-modify yet also have the propensity to maintain key invariant properties of their goal systems 1) a series of goal-stability metagoals aimed to guide a system to a condition in which goal-stability is compatible with reasonably flexible self-modification 2) a series of moderated-goal-evolution metagoals aimed to guide a system to a condition in which control of the pace of goal evolution is compatible with reasonably flexible self-modification The formulation of the metagoals is founded on fixed-point theorems from functional analysis, e.g. the Contraction Mapping Theorem and constructive approximations to Schauder's Theorem, applied to probabilistic models of system behavior We present an argument that the balancing of self-modification with maintenance of goal invariants will often have other interesting cognitive side-effects such as a high degree of self understanding Finally we argue for the practical value of a hybrid metagoal combining moderated-goal-evolution with pursuit of goal-stability -- along with potentially other metagoals relating to goal-satisfaction, survival and ongoing development -- in a flexible fashion depending on the situation

cs.AI↗
arXiv2023

Generative AI vs. AGI: The Cognitive Strengths and Weaknesses of Modern LLMs

A moderately detailed consideration of interactive LLMs as cognitive systems is given, focusing on LLMs circa mid-2023 such as ChatGPT, GPT-4, Bard, Llama, etc.. Cognitive strengths of these systems are reviewed, and then careful attention is paid to the substantial differences between the sort of cognitive system these LLMs are, and the sort of cognitive systems human beings are. It is found that many of the practical weaknesses of these AI systems can be tied specifically to lacks in the basic cognitive architectures according to which these systems are built. It is argued that incremental improvement of such LLMs is not a viable approach to working toward human-level AGI, in practical terms given realizable amounts of compute resources. This does not imply there is nothing to learn about human-level AGI from studying and experimenting with LLMs, nor that LLMs cannot form significant parts of human-level AGI architectures that also incorporate other ideas. Social and ethical matters regarding LLMs are very briefly touched from this perspective, which implies that while care should be taken regarding misinformation and other issues, and economic upheavals will need their own social remedies based on their unpredictable course as with any powerfully impactful technology, overall the sort of policy needed as regards modern LLMs is quite different than would be the case if a more credible approximation to human-level AGI were at hand.

cs.AI↗
arXiv2023

An Evaluation of GPT-4 on the ETHICS Dataset

This report summarizes a short study of the performance of GPT-4 on the ETHICS dataset. The ETHICS dataset consists of five sub-datasets covering different fields of ethics: Justice, Deontology, Virtue Ethics, Utilitarianism, and Commonsense Ethics. The moral judgments were curated so as to have a high degree of agreement with the aim of representing shared human values rather than moral dilemmas. GPT-4's performance is much better than that of previous models and suggests that learning to work with common human values is not the hard problem for AI ethics.

cs.CL↗
arXiv2023

OpenCog Hyperon: A Framework for AGI at the Human Level and Beyond

An introduction to the OpenCog Hyperon framework for Artificiai General Intelligence is presented. Hyperon is a new, mostly from-the-ground-up rewrite/redesign of the OpenCog AGI framework, based on similar conceptual and cognitive principles to the previous OpenCog version, but incorporating a variety of new ideas at the mathematical, software architecture and AI-algorithm level. This review lightly summarizes: 1) some of the history behind OpenCog and Hyperon, 2) the core structures and processes underlying Hyperon as a software system, 3) the integration of this software system with the SingularityNET ecosystem's decentralized infrastructure, 4) the cognitive model(s) being experimentally pursued within Hyperon on the hopeful path to advanced AGI, 5) the prospects seen for advanced aspects like reflective self-modification and self-improvement of the codebase, 6) the tentative development roadmap and various challenges expected to be faced, 7) the thinking of the Hyperon team regarding how to guide this sort of work in a beneficial direction ... and gives links and references for readers who wish to delve further into any of these aspects.

cs.AI↗
arXiv2022

A Liquid Democracy System for Human-Computer Societies

Problem of reliable democratic governance is critical for survival of any community, and it will be critical for communities powered with Artificial Intelligence (AI) systems upon developments of the latter. Apparently, it will be getting more and more critical because of increasing speeds and scales of electronic communications and decreasing latencies in system responses. In order to address this need, we present design and implementation of a reputation system supporting "liquid democracy" principle. The system is based on "weighted liquid rank" algorithm employing different sorts of explicit and implicit ratings being exchanged by members of the society as well as implicit assessments of of the members based on measures of their activity in the society. The system is evaluated against live social network data with help of simulation modelling for an online marketplace case.

cs.MA↗
arXiv2022

A Reputation System for Market Security and Equity

We simulate a reputation system in a market to optimise the balance between market security and market equity. We introduce a method of using a reputation system that will stabilise the distribution of wealth in a market in a fair manner. We also introduce metrics of a modified Gini that takes production quality into account, a way to use a weighted Pearson as a tool to optimise balance.

cs.MA↗
arXiv2022

A meta-probabilistic-programming language for bisimulation of probabilistic and non-well-founded type systems

We introduce a formal meta-language for probabilistic programming, capable of expressing both programs and the type systems in which they are embedded. We are motivated here by the desire to allow an AGI to learn not only relevant knowledge (programs/proofs), but also appropriate ways of reasoning (logics/type systems). We draw on the frameworks of cubical type theory and dependent typed metagraphs to formalize our approach. In doing so, we show that specific constructions within the meta-language can be related via bisimulation (implying path equivalence) to the type systems they correspond. This allows our approach to provide a convenient means of deriving synthetic denotational semantics for various type systems. Particularly, we derive bisimulations for pure type systems (PTS), and probabilistic dependent type systems (PDTS). We discuss further the relationship of PTS to non-well-founded set theory, and demonstrate the feasibility of our approach with an implementation of a bisimulation proof in a Guarded Cubical Type Theory type checker.

cs.AI↗