arXiv subjects

Ben Goertzel

Publications and source records attributed to Ben Goertzel.

At least 37 records · Page 2Linked to original sources

arXiv2021

Reflective Metagraph Rewriting as a Foundation for an AGI "Language of Thought"

MeTTa (Meta Type Talk) is a novel programming language created for use in the OpenCog Hyperon AGI system. It is designed as a meta-language with very basic and general facilities for handling symbols, groundings, variables, types, substitutions and pattern matching. Primitives exist for creating new type systems and associated DSLs. IInformally, MeTTa is Hyperon's lowest-level "language of thought" -- the meta-language in which algorithms for learning more particular knowledge representations, will operate, and in which these algorithms themselves may be represented. Here we explain how one might go about formalizing the MeTTa language as a system of metagraph rewrite rules, an approach that fits in naturally to the Hyperon framework given that the latter's core component is a distributed metagraph knowledge store (the Atomspace). The metagraph rewrite rules constituting MeTTa programs can also be represented as metagraphs, giving a natural model for MeTTa reflection and self-modifying code. Considering MeTTa programs that compute equivalences between execution traces of other MeTTa programs allows us to model spaces of MeTTa execution traces using Homotopy Type Theory. Considering the limit of MeTTa programs mapping between execution traces of MeTTa programs that map between execution traces of MeTTa programs that ..., we find that a given MeTTa codebase is effectively modeled as an infinity-groupoid, and the space of all MeTTa codebases as an (infinity,1)-topis This topos is basically the same as the so-called "Ruliad" previously derived from rewrite rules on hypergraphs, in a discrete physics context. The formalization of MeTTA as metagraph rewrite rules may also provide a useful framework for structuring the implementation of efficient methods for pattern matching and equality inference within the MeTTa interpreter.

cs.PL↗

arXiv2021

Architecture of Automated Crypto-Finance Agent

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.

cs.AI↗

arXiv2021

The General Theory of General Intelligence: A Pragmatic Patternist Perspective

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.

cs.AI↗

arXiv2021

Patterns of Cognition: Cognitive Algorithms as Galois Connections Fulfilled by Chronomorphisms On Probabilistically Typed Metagraphs

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.

cs.AI↗

arXiv2021

Info-Evo: Using Information Geometry to Guide Evolutionary Program Learning

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.

cs.NE↗

arXiv2021

Paraconsistent Foundations for Quantum Probability

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.

cs.AI↗

arXiv2021

Paraconsistent Foundations for Probabilistic Reasoning, Programming and Concept Formation

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.

cs.AI↗

arXiv2020

Folding and Unfolding on Metagraphs

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.

cs.AI↗

arXiv2020

Uncertain Linear Logic via Fibring of Probabilistic and Fuzzy Logic

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).

cs.AI↗

arXiv2020

Grounding Occam's Razor in a Formal Theory of Simplicity

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.

cs.AI↗

arXiv2020

Guiding Symbolic Natural Language Grammar Induction via Transformer-Based Sequence Probabilities

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.

cs.CL↗

arXiv2020

Embedding Vector Differences Can Be Aligned With Uncertain Intensional Logic Differences

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.

cs.AI↗

arXiv2020

Maximal Algorithmic Caliber and Algorithmic Causal Network Inference: General Principles of Real-World General Intelligence?

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.

cs.AI↗

arXiv2020

What Kind of Programming Language Best Suits Integrative AGI?

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.).

cs.AI↗

arXiv2020

Combinatorial Decision Dags: A Natural Computational Model for General Intelligence

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.

cs.AI↗

arXiv2019

A Reputation System for Multi-Agent Marketplaces

We present an exploration of a reputation system based on explicit ratings weighted by the values of corresponding financial transactions from the perspective of its ability to grant "security" to market participants by protecting them from scam and "equity" in terms of having real qualities of the participants correctly assessed. We present a simulation modeling approach based on the selected reputation system and discuss the results of the simulation.

cs.MA↗

arXiv2019

A Reputation System for Marketplaces - Viability Assessment

In this work we explore the implementation of the reputation system for a generic marketplace, describe details of the algorithm and parameters driving its operation, justify an approach to simulation modeling, and explore how various kinds of reputation systems with different parameters impact the economic security of the marketplace. Our emphasis here is on the protection of consumers by means of an ability to distinguish between cheating participants and honest participants, as well as the ability to minimize losses of honest participants due to scam.

cs.SI↗

arXiv2019

Distinction Graphs and Graphtropy: A Formalized Phenomenological Layer Underlying Classical and Quantum Entropy, Observational Semantics and Cognitive Computation

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."

cs.AI↗