Ben Goertzel

Ben Goertzel, Vitaly Bogdanov, Michael Duncan et al.

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.

Sergey Rodionov, Zarathustra Amadeus Goertzel, Ben Goertzel

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.

Ben Goertzel

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.

Ben Goertzel

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

Ben Goertzel

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.

Ben Goertzel, Bill Lauritzen

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, $δ$) 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.

Ben Goertzel

We give a compositional, information-theoretic framework that turns short programs into locality on many independent blocks, and combine it with symmetry and sparsity of masked random Unique-SAT to obtain distributional lower bounds that contradict the self-reduction upper bound under $\mathsf{P}=\mathsf{NP}$. We work in the weakness quantale $w_Q=K_{\mathrm{poly}}(\cdot\mid\cdot)$. For an efficiently samplable ensemble $D_m$ made by masking random $3$-CNFs with fresh $S_m\ltimes(\mathbb{Z}_2)^m$ symmetries and a small-seed Valiant--Vazirani isolation layer, we prove a Switching-by-Weakness normal form: for any polytime decoder $P$ of description length $\le δt$ (with $t=Θ(m)$ blocks), a short wrapper $W$ makes $(P\circ W)$ per-bit local on a $γ$-fraction of blocks. Two ingredients then force near-randomness on $Ω(t)$ blocks for every short decoder: (a) a sign-invariant neutrality lemma giving $\Pr[X_i=1\mid \mathcal{I}]=1/2$ for any sign-invariant view $\mathcal{I}$; and (b) a template sparsification theorem at logarithmic radius showing that any fixed local rule appears with probability $m^{-Ω(1)}$. Combined with single-block bounds for tiny $\mathrm{ACC}^0$/streaming decoders, this yields a success bound $2^{-Ω(t)}$ and, by Compression-from-Success, $K_{\mathrm{poly}}\big((X_1,\ldots,X_t)\mid(Φ_1,\ldots,Φ_t)\big)\ge ηt$. If $\mathsf{P}=\mathsf{NP}$, a uniform constant-length program maps any on-promise instance to its unique witness in polytime (bit fixing via a $\mathrm{USAT}$ decider), so $K_{\mathrm{poly}}(X\midΦ)\le O(1)$ and the tuple complexity is $O(1)$, contradicting the linear bound. The proof is non-relativizing and non-natural; symmetry, sparsification, and switching yield a quantale upper-lower clash, hence $\mathsf{P}\ne\mathsf{NP}$.

Ben Goertzel

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.

Ben Goertzel, Paulos Yibelo

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.

Ben Goertzel

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.

Ben Goertzel

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.

Ben Goertzel

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.

Ben Goertzel

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.

Jonathan Warrell, Alexey Potapov, Adam Vandervorst et al.

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.

Ali Raheman, Anton Kolonin, Ben Goertzel et al.

We present the cognitive architecture of an autonomous agent for active portfolio management in decentralized finance, involving activities such as asset selection, portfolio balancing, liquidity provision, and trading. Partial implementation of the architecture is provided and supplied with preliminary results and conclusions.

Ben Goertzel

A multi-decade exploration into the theoretical foundations of artificial and natural general intelligence, which has been expressed in a series of books and papers and used to guide a series of practical and research-prototype software systems, is reviewed at a moderate level of detail. The review covers underlying philosophies (patternist philosophy of mind, foundational phenomenological and logical ontology), formalizations of the concept of intelligence, and a proposed high level architecture for AGI systems partly driven by these formalizations and philosophies. The implementation of specific cognitive processes such as logical reasoning, program learning, clustering and attention allocation in the context and language of this high level architecture is considered, as is the importance of a common (e.g. typed metagraph based) knowledge representation for enabling "cognitive synergy" between the various processes. The specifics of human-like cognitive architecture are presented as manifestations of these general principles, and key aspects of machine consciousness and machine ethics are also treated in this context. Lessons for practical implementation of advanced AGI in frameworks such as OpenCog Hyperon are briefly considered.

Ben Goertzel

It is argued that a broad class of AGI-relevant algorithms can be expressed in a common formal framework, via specifying Galois connections linking search and optimization processes on directed metagraphs whose edge targets are labeled with probabilistic dependent types, and then showing these connections are fulfilled by processes involving metagraph chronomorphisms. Examples are drawn from the core cognitive algorithms used in the OpenCog AGI framework: Probabilistic logical inference, evolutionary program learning, pattern mining, agglomerative clustering, pattern mining and nonlinear-dynamical attention allocation. The analysis presented involves representing these cognitive algorithms as recursive discrete decision processes involving optimizing functions defined over metagraphs, in which the key decisions involve sampling from probability distributions over metagraphs and enacting sets of combinatory operations on selected sub-metagraphs. The mutual associativity of the combinatory operations involved in a cognitive process is shown to often play a key role in enabling the decomposition of the process into folding and unfolding operations; a conclusion that has some practical implications for the particulars of cognitive processes, e.g. militating toward use of reversible logic and reversible program execution. It is also observed that where this mutual associativity holds, there is an alignment between the hierarchy of subgoals used in recursive decision process execution and a hierarchy of subpatterns definable in terms of formal pattern theory.

Ben Goertzel

A novel optimization strategy, Info-Evo, is described, in which natural gradient search using nonparametric Fisher information is used to provide ongoing guidance to an evolutionary learning algorithm, so that the evolutionary process preferentially moves in the directions identified as "shortest paths" according to the natural gradient. Some specifics regarding the application of this approach to automated program learning are reviewed, including a strategy for integrating Info-Evo into the MOSES program learning framework.

Ben Goertzel

It is argued that a fuzzy version of 4-truth-valued paraconsistent logic (with truth values corresponding to True, False, Both and Neither) can be approximately isomorphically mapped into the complex-number algebra of quantum probabilities. I.e., p-bits (paraconsistent bits) can be transformed into close approximations of qubits. The approximation error can be made arbitrarily small, at least in a formal sense, and can be related to the degree of irreducible "evidential error" assumed to plague an observer's observations. This logical correspondence manifests itself in program space via an approximate mapping between probabilistic and quantum types in programming languages.

Ben Goertzel

It is argued that 4-valued paraconsistent truth values (called here "p-bits") can serve as a conceptual, mathematical and practical foundation for highly AI-relevant forms of probabilistic logic and probabilistic programming and concept formation. First it is shown that appropriate averaging-across-situations and renormalization of 4-valued p-bits operating in accordance with Constructible Duality (CD) logic yields PLN (Probabilistic Logic Networks) strength-and-confidence truth values. Then variations on the Curry-Howard correspondence are used to map these paraconsistent and probabilistic logics into probabilistic types suitable for use within dependent type based programming languages. Zach Weber's paraconsistent analysis of the sorites paradox is extended to form a paraconsistent / probabilistic / fuzzy analysis of concept boundaries; and a paraconsistent version of concept formation via Formal Concept Analysis is presented, building on a definition of fuzzy property-value degrees in terms of relative entropy on paraconsistent probability distributions. These general points are fleshed out via reference to the realization of probabilistic reasoning and programming and concept formation in the OpenCog AGI framework which is centered on collaborative multi-algorithm updating of a common knowledge metagraph.

Ben Goertzel

Typed metagraphs are defined as hypergraphs with types assigned to hyperedges and their targets, and the potential to have targets of hyperedges connect to whole links as well as targets. Directed typed metagraphs (DTMGs) are introduced via partitioning the targets of each edge in a typed metagraph into input, output and lateral sets; one can then look at "metapaths" in which edges' output-sets are linked to other edges' input-sets. An initial algebra approach to DTMGs is presented, including introduction of constructors for building up DTMGs and laws regarding relationships among multiple ways of using these constructors. A menagerie of useful morphism types is then defined on DTMGs (catamorphisms, anamorphisms, histomorphisms, futumorphisms, hylomorphisms, chronomorphisms, metamorphisms and metachronomorphisms), providing a general abstract framework for formulating a broad variety of metagraph operations. Deterministic and stochastic processes on typed metagraphs are represented in terms of forests of DTMGs defined over a common TMG, where the various morphisms can be straightforwardly extended to these forests. A variation of the approach to undirected typed metagraphs is presented; and it is indicated how the framework outlined can applied to realistic metagraphs involving complexities like dependent and probabilistic types, multidimensional values and dynamic processing including insertion and deletion of edges.

Ben Goertzel

Beginning with a simple semantics for propositions, based on counting observations, it is shown that probabilistic and fuzzy logic correspond to two different heuristic assumptions regarding the combination of propositions whose evidence bases are not currently available. These two different heuristic assumptions lead to two different sets of formulas for propagating quantitative truth values through lattice operations. It is shown that these two sets of formulas provide a natural grounding for the multiplicative and additive operator-sets in linear logic. The standard rules of linear logic then emerge as consequences of the underlying semantics. The concept of linear logic as a ``logic of resources" is manifested here via the principle of ``conservation of evidence" -- the restrictions to weakening and contraction in linear logic serve to avoid double-counting of evidence (beyond any double-counting incurred via use of heuristic truth value functions).

Ben Goertzel, Mike Duncan, Debbie Duong et al.

The DeepWalk algorithm is used to assign embedding vectors to nodes in the Atomspace weighted, labeled hypergraph that is used to represent knowledge in the OpenCog AGI system, in the context of an application to probabilistic inference regarding the causes of longevity based on data from biological ontologies and genomic analyses. It is shown that vector difference operations between embedding vectors are, in appropriate conditions, approximately alignable with "intensional difference" operations between the hypergraph nodes corresponding to the embedding vectors. This relationship hints at a broader functorial mapping between uncertain intensional logic and vector arithmetic, and opens the door for using embedding vector algebra to guide intensional inference control.

Ben Goertzel, Andres Suarez Madrigal, Gino Yu

A novel approach to automated learning of syntactic rules governing natural languages is proposed, based on using probabilities assigned to sentences (and potentially longer word sequences) by transformer neural network language models to guide symbolic learning processes like clustering and rule induction. This method exploits the learned linguistic knowledge in transformers, without any reference to their inner representations; hence, the technique is readily adaptable to the continuous appearance of more powerful language models. We show a proof-of-concept example of our proposed technique, using it to guide unsupervised symbolic link-grammar induction methods drawn from our prior research.

Ben Goertzel

Ideas and formalisms from far-from-equilibrium thermodynamics are ported to the context of stochastic computational processes, via following and extending Tadaki's algorithmic thermodynamics. A Principle of Maximum Algorithmic Caliber is proposed, providing guidance as to what computational processes one should hypothesize if one is provided constraints to work within. It is conjectured that, under suitable assumptions, computational processes obeying algorithmic Markov conditions will maximize algorithmic caliber. It is proposed that in accordance with this, real-world cognitive systems may operate in substantial part by modeling their environments and choosing their actions to be (approximate and compactly represented) algorithmic Markov networks. These ideas are suggested as potential early steps toward a general theory of the operation of pragmatic generally intelligent systems.

Ben Goertzel

A formal theory of simplicity is introduced, in the context of a "combinational" computation model that views computation as comprising the iterated transformational and compositional activity of a population of agents upon each other. Conventional measures of simplicity in terms of algorithmic information etc. are shown to be special cases of a broader understanding of the core "symmetry" properties constituting what is defined here as a Compositional Simplicity Measure (CoSM). This theory of CoSMs is extended to a theory of CoSMOS (Combinational Simplicity Measure Operating Sets) which involve multiple simplicity measures utilized together. Given a vector of simplicity measures, an entity is associated not with an individual simplicity value but with a "simplicity bundles" of Pareto-optimal simplicity-value vectors. CoSMs and CoSMOS are then used as a foundation for a theory of pattern and multipattern, and a theory of hierarchy and heterarchy in systems of patterns. A formalization of the cognitive-systems notion of a "coherent dual network" interweaving hierarchy and heterarchy in a consistent way is presented. The high level end result of this investigation is to re-envision Occam's Razor as something like: When in doubt, prefer hypotheses whose simplicity bundles are Pareto optimal, partly because doing so both permits and benefits from the construction of coherent dual networks comprising coordinated and consistent multipattern hierarchies and heterarchies.

Ben Goertzel

A novel computational model (CoDD) utilizing combinatory logic to create higher-order decision trees is presented. A theoretical analysis of general intelligence in terms of the formal theory of pattern recognition and pattern formation is outlined, and shown to take especially natural form in the case where patterns are expressed in CoDD language. Relationships between logical entropy and algorithmic information, and Shannon entropy and runtime complexity, are shown to be elucidated by this approach. Extension to the quantum computing case is also briefly discussed.

Ben Goertzel

What kind of programming language would be most appropriate to serve the needs of integrative, multi-paradigm, multi-software-system approaches to AGI? This question is broached via exploring the more particular question of how to create a more scalable and usable version of the "Atomese" programming language that forms a key component of the OpenCog AGI design (an "Atomese 2.0") . It is tentatively proposed that the core of Atomese 2.0 should be a very flexible framework of rewriting rules for rewriting a metagraph (where the rules themselves are represented within the same metagraph, and some of the intermediate data created and used during the rule-interpretation process may be represented in the same metagraph). This framework should support concurrent rewriting of the metagraph according to rules that are labeled with various sorts of uncertainty-quantifications, and that are labeled with various sorts of types associated with various type systems. A gradual typing approach should be used to enable mixture of rules and other metagraph nodes/links associated with various type systems, and untyped metagraph nodes/links not associated with any type system. This must be done in a way that allows reasonable efficiency and scalability, including in concurrent and distributed processing contexts, in the case where a large percentage of of processing time is occupied with evaluating static pattern-matching queries on specific subgraphs of a large metagraph (including a rich variety of queries such as matches against nodes representing variables, and matches against whole subgraphs, etc.).

Ben Goertzel

A new conceptual foundation for the notion of "information" is proposed, based on the concept of a "distinction graph": a graph in which two nodes are connected iff they cannot be distinguished by a particular observer. The "graphtropy" of a distinction graph is defined as the average connection probability of two nodes; in the case where the distinction graph is a composed of disconnected components that are fully connected subgraphs, this is equivalent to Ellerman's logical entropy, which has straightforward relationships to Shannon entropy. Probabilistic distinction graphs and probabilistic graphtropy are also considered, as well as connections between graphtropy and thermodynamic and quantum entropy. The semantics of the Second Law of Thermodynamics and the Maximum Entropy Production Principle are unfolded in a novel way, via analysis of the cognitive processes underlying the making of distinction graphs This evokes an interpretation in which complex intelligence is seen to correspond to states of consciousness with intermediate graphtropy, which are associated with memory imperfections that violate the assumptions leading to derivation of the Second Law. In the case where nodes of a distinction graph are labeled by computable entities, graphtropy is shown to be monotonically related to the average algorithmic information of the nodes (relative to to the algorithmic information of the observer). A quantum-mechanical version of distinction graphs is considered, in which distinctions can exist in a superposed state; this yields to graphtropy as a measure of the impurity of a mixed state, and to a concept of "quangraphtropy." Finally, a novel computational model called Dynamic Distinction Graphs (DDGs) is formulated, via enhancing distinction graphs with additional links expressing causal implications, enabling a distinction-based model of "observers."

Anton Kolonin, Ben Goertzel, Deborah Duong et al.

One approach to achieving artificial general intelligence (AGI) is through the emergence of complex structures and dynamic properties arising from decentralized networks of interacting artificial intelligence (AI) agents. Understanding the principles of consensus in societies and finding ways to make consensus more reliable becomes critically important as connectivity and interaction speed increase in modern distributed systems of hybrid collective intelligences, which include both humans and computer systems. We propose a new form of reputation-based consensus with greater resistance to reputation gaming than current systems have. We discuss options for its implementation, and provide initial practical results.

Ben Goertzel, Julia Mossbridge, Eddie Monroe et al.

The "Loving AI" project involves developing software enabling humanoid robots to interact with people in loving and compassionate ways, and to promote people' self-understanding and self-transcendence. Currently the project centers on the Hanson Robotics robot "Sophia" -- specifically, on supplying Sophia with personality content and cognitive, linguistic, perceptual and behavioral content aimed at enabling loving interactions supportive of human self-transcendence. In September 2017 a small pilot study was conducted, involving the Sophia robot leading human subjects through dialogues and exercises focused on meditation, visualization and relaxation. The pilot was an apparent success, qualitatively demonstrating the viability of the approach and the ability of appropriate human-robot interaction to increase human well-being and advance human consciousness.

Ben Goertzel, Nil Geisweiller, Chris Poulin

A general formulation of optimization problems in which various candidate solutions may use different feature-sets is presented, encompassing supervised classification, automated program learning and other cases. A novel characterization of the concept of a "good quality feature" for such an optimization problem is provided; and a proposal regarding the integration of quality based feature selection into metalearning is suggested, wherein the quality of a feature for a problem is estimated using knowledge about related features in the context of related problems. Results are presented regarding extensive testing of this "feature metalearning" approach on supervised text classification problems; it is demonstrated that, in this context, feature metalearning can provide significant and sometimes dramatic speedup over standard feature selection heuristics.

Ben Goertzel

A novel partial order is defined on the space of digraphs or hypergraphs, based on assessing the cost of producing a graph via a sequence of elementary transformations. Leveraging work by Knuth and Skilling on the foundations of inference, and the structure of Heyting algebras on graph space, this partial order is used to construct an intuitionistic probability measure that applies to either digraphs or hypergraphs. As logical inference steps can be represented as transformations on hypergraphs representing logical statements, this also yields an intuitionistic probability measure on spaces of theorems. The central result is also extended to yield intuitionistic probabilities based on more general weighted rule systems defined over bicartesian closed categories.

Ruiting Lian, Ben Goertzel, Linas Vepstas et al.

A new model of symbol grounding is presented, in which the structures of natural language, logical semantics, perception and action are represented categorically, and symbol grounding is modeled via the composition of morphisms between the relevant categories. This model gives conceptual insight into the fundamentally systematic nature of symbol grounding, and also connects naturally to practical real-world AI systems in current research and commercial use. Specifically, it is argued that the structure of linguistic syntax can be modeled as a certain asymmetric monoidal category, as e.g. implicit in the link grammar formalism; the structure of spatiotemporal relationships and action plans can be modeled similarly using "image grammars" and "action grammars"; and common-sense logical semantic structure can be modeled using dependently-typed lambda calculus with uncertain truth values. Given these formalisms, the grounding of linguistic descriptions in spatiotemporal perceptions and coordinated actions consists of following morphisms from language to logic through to spacetime and body (for comprehension), and vice versa (for generation). The mapping is indicated between the spatial relationships in the Region Connection Calculus and Allen Interval Algebra and corresponding entries in the link grammar syntax parsing dictionary. Further, the abstractions introduced here are shown to naturally model the structures and systems currently being deployed in the context of using the OpenCog cognitive architecture to control Hanson Robotics humanoid robots.

Ben Goertzel

"Cognitive synergy" refers to a dynamic in which multiple cognitive processes, cooperating to control the same cognitive system, assist each other in overcoming bottlenecks encountered during their internal processing. Cognitive synergy has been posited as a key feature of real-world general intelligence, and has been used explicitly in the design of the OpenCog cognitive architecture. Here category theory and related concepts are used to give a formalization of the cognitive synergy concept. A series of formal models of intelligent agents is proposed, with increasing specificity and complexity: simple reinforcement learning agents; "cognit" agents with an abstract memory and processing model; hypergraph-based agents (in which "cognit" operations are carried out via hypergraphs); hypergraph agents with a rich language of nodes and hyperlinks (such as the OpenCog framework provides); "PGMC" agents whose rich hypergraphs are endowed with cognitive processes guided via Probabilistic Growth and Mining of Combinations; and finally variations of the PrimeAGI design, which is currently being built on top of OpenCog. A notion of cognitive synergy is developed for cognitive processes acting within PGMC agents, based on developing a formal notion of "stuckness," and defining synergy as a relationship between cognitive processes in which they can help each other out when they get stuck. It is proposed that cognitive processes relating to each other synergetically, associate in a certain way with functors that map into each other via natural transformations. Cognitive synergy is proposed to correspond to a certain inequality regarding the relative costs of different paths through certain commutation diagrams. Applications of this notion of cognitive synergy to particular cognitive phenomena, and specific cognitive processes in the PrimeAGI design, are discussed.

Linas Vepstas, Ben Goertzel

A novel approach to the fully automated, unsupervised extraction of dependency grammars and associated syntax-to-semantic-relationship mappings from large text corpora is described. The suggested approach builds on the authors' prior work with the Link Grammar, RelEx and OpenCog systems, as well as on a number of prior papers and approaches from the statistical language learning literature. If successful, this approach would enable the mining of all the information needed to power a natural language comprehension and generation system, directly from a large, unannotated corpus.