A Fundamental Duality in the Mathematical and Natural Sciences: From Logic to Biology

Traces an overlooked subset–partition duality—from logic and category theory through entropy and quantum indefiniteness to selectionist and generative mechanisms in biology.

Algebraic Models for Accounting Systems

Develops accounting theory algebraically: balance vectors as modules, transactions as a group, and whole accounting systems as automata with quotients, homomorphisms, and decision algorithms for audit and control.

Economics, Accounting, and Property Theory

Ellerman's vector-accounting monograph: double entry generalized to property vectors ("accounting without valuation"), grounding a property-theoretic account of appropriation, the firm, and goodwill.

On implication and negation in partition logic

Develops implication as a refinement-sensitive operation on set partitions, showing how relative negation yields local Boolean cores within the non-distributive algebra of partitions.

Object-Oriented Representation of Electro-Mechanical Assemblies Using UML

NIST report proposing the Open Assembly Model, a UML-based object-oriented representation for electro-mechanical assembly information exchange.

Ontology and Assembly Joint Topology Representation

Uses mereotopology and SWRL rules to represent assembly joints as ontological relations, illustrated on a fixture assembly case study.

Representing Geometric Structures in d Dimensions: Topology and Order

Formalizes geometric structures in d dimensions via combinatorial topology and order relations, a foundation for cell-complex representations used in assembly/geometric modeling.

Towards an Ontology for Generative Design of Mechanical Assemblies

Proposes a formal ontology of mechanical assembly structure intended to support generative design systems.

Discrete Exterior Calculus

Introduces discrete exterior calculus, a coordinate-free discretization of differential forms on simplicial complexes for computational modeling.

Finite Element Exterior Calculus: From Hodge Theory to Numerical Stability

Surveys finite element exterior calculus, unifying Hodge theory and mixed finite element stability analysis for PDE discretization.

Algebras of Open Dynamical Systems on the Operad of Wiring Diagrams

Develops an operad-algebra formalism for open dynamical systems composed via wiring diagrams, underpinning compositional systems theory.

Graph theoretic foundations of multibody dynamics

Second of a two-part paper deriving O(N) recursive algorithms (Newton-Euler, Lyapunov/Riccati factorizations) for multibody dynamics from the graph-theoretic spatial kernel/operator (SKO/SPO) models built in Part I.

Port-Hamiltonian Systems on Graphs

Builds port-Hamiltonian systems on open directed graphs via Dirac structures, unifying mass-spring-damper networks, spatial mechanisms, hydraulic networks, and consensus dynamics under one compositional geometric framework.

Seven Sketches in Compositionality: An Invitation to Applied Category Theory

A textbook introducing applied category theory (orders, monoidal categories, operads, sheaves, etc.) through seven worked "sketches" connecting math to systems modeling.

Beautimeter: Harnessing GPT for Assessing Architectural and Urban Beauty Based on the 15 Properties of Living Structure

Presents Beautimeter, a GPT-based tool that scores buildings and urban scenes against Christopher Alexander’s 15 properties of living structure to assess their coherence and beauty.

Generative Codes: The Path to Building Welcoming, Beautiful, Sustainable Neighborhoods

Argues that living neighborhoods arise from generative codes: ordered, participatory steps that let buildings and public spaces unfold from local people, land, and context.

Geography as a Science of the Earth’s Surface Founded on the Third View of Space

Recasts geography around an organismic view of space, using scaling and spatial dependence to understand—and deliberately create—places with greater living structure.

Harmony-Seeking Computations: A Science of Non-Classical Dynamics Based on the Progressive Evolution of the Larger Whole

Proposes harmony-seeking computation as a creative process that repeatedly strengthens latent centers in a configuration while preserving and deepening the larger whole.

Living Images: A Recursive Approach to Computing the Structural Beauty of Images or the Livingness of Space

Measures an image’s structural beauty by recursively extracting its nested substructures, revealing a compact hierarchy that also captures visual saliency.

Structural Beauty: A Structure-Based Computational Approach to Quantifying the Beauty of an Image

Proposes a quantitative measure of structural beauty based on how many substructures an image contains and how strongly they form a hierarchy across scales.

Structure-Preserving Transformations

Explains structure-preserving transformations: incremental changes that extend the centers and relationships already present in a place rather than weakening its wholeness.

The Nature of Poetic Order

Gabriel's slide essay relating poetry's formal order to Christopher Alexander's ideas of generative structure, exploring how constraint and pattern produce living order in creative work.

Wholeness as a Hierarchical Graph to Capture the Nature of Space

Models spatial wholeness as a hierarchical graph of mutually reinforcing centers, using PageRank and scaling depth to quantify the life of parts and wholes.

A Taxonomy of Granular Partitions

Formalizes partitions as tree-structured cognitive devices projected onto reality, then classifies how accurately, structurally, and completely their cells recognize objects, with applications to cadastral and geographic data.

A Theory of Granular Partitions

Formalizes granular partitions as hierarchical cell systems projected onto reality, combining cognitive selectivity with mereological structure for naming, classifying, mapping, and representation.

About the Unreal

Models fiction, blueprints, simulations, and other information about unreal entities through logical combinations of actual classes, avoiding commitments to nonexistent dummy instances.

Against Fantology

Critiques the idea that first-order logic reveals reality’s ontology, tracing its atomism, timelessness, Booleanism, and reductionism before proposing a six-category ontology and an enhanced Davidsonian formal language.

Against Fantology Again

Extends the critique of fantology through default ontologization, arguing that Quine’s canonical notation is incoherent about classes and excludes intentional phenomena and distinct modes of existence.

Agglomerations

Defines agglomerations as geographically dispersed yet unified aggregates—populations, cultures, organizations, and diasporas—and develops a realist mereotopology for their boundaries, identity, and change.

Bodily Systems and the Spatial-Functional Structure of the Human Body

Integrates anatomy and physiology by modeling the body as a nested spatial-functional hierarchy whose parts are demarcated as system elements through the functions they bear and realize.

Boundaries: An Essay in Mereotopology

Reconstructs and extends the Brentano–Chisholm mereotopology in which dependent, coincident boundaries account for contact and the continuum across points, lines, surfaces, and bodies.

Capabilities: An Ontology

Defines a capability as a disposition in whose realization an organism or group has or had an interest, placing capabilities between dispositions and functions in Basic Formal Ontology.

Carving Up Reality

Explains how context-sensitive, coarse-grained partitions guide reference and perception while preserving transitive parthood and distinguishing fiat demarcations from boundaries grounded in reality.

Categories in Top-Level Ontologies: Revisiting the Aristotelian Background

Reconstructs Aristotle’s categories as the philosophical basis of BFO, extending the ontological square with processes into a six-category framework for continuants, occurrents, dependence, and multiple scientific granularities.

CLASSIFYING PROCESSES: AN ESSAY IN APPLIED ONTOLOGY

Extends Basic Formal Ontology to scientific process data through process profiles—quality, rate, and cyclical aspects that ground measurements, time-series graphs, and representations of dynamic systems.

Diagrams, Documents, and the Meshing of Plans

Shows how diagrams and evolving networks of documents mesh plans, obligations, and specialized labor to enable coordinated collective action beyond the limits of linear text.

Do Mountains Exist? Towards an Ontology of Landforms

Argues that mountains are object-like in everyday thought but elevation fields in environmental science, motivating a geospatial ontology that supports both perspectives.

Drawing Boundaries

Updates the distinction between human-demarcated fiat boundaries and physically grounded bona fide boundaries, tracing its uses in geography, property, ecology, and Basic Formal Ontology.

Environmental Metaphysics

Develops an ontology of token niches as tenant–medium–retainer structures, using physical and fiat boundaries to explain environmental fit, protection, movement, and niche construction.

Layers: A New Approach to Locating Objects in Space

Extends mereotopology with layers that distinguish material objects, holes, and processes from the spatial and spatiotemporal regions they occupy, supporting dynamic geospatial reasoning beyond static map overlays.

Making space: the natural, cultural, cognitive and social niches of human activity

Shows how legal decisions, plans, historical reasoning, and language create fiat spatial and spatiotemporal entities, then draws limits and practical lessons for ontology-supported AI.

More Things in Heaven and Earth

Develops an ontology of spatial regions and boundaries, arguing that political territories are historically created fiat objects through performative maps while also recognizing vague, overlapping, and incomplete geographic objects.

Naïve Physics: An Essay in Ontology

Reconstructs naïve physics as a realist ontology of the common-sense world—objects, processes, stuffs, boundaries, media, and values—drawing on Gestalt psychology and phenomenology to broaden AI’s set-theoretic models.

New Foundations for Qualitative Physics

Argues for a scientific ontology of the qualitative common-sense world, using morphological discontinuities to connect physical substrates, sensible qualities, Aristotelian categories, and ecologically constrained cognition.

Objects and Their Environments: From Aristotle to Ecological Ontology

Extends Aristotelian substance–accident ontology into a realist theory of behavioral settings and ecological niches as nested, bounded wholes in which organisms, objects, and activities mutually fit.

On Classifying Material Entities in Basic Formal Ontology

Clarifies BFO’s material entities by distinguishing objects, aggregates, and fiat object parts, and analyzes objects through causal unity by covering, physical forces, or engineered assembly without claiming exhaustivity.

On Credentials

Provides a social ontology of credentials as portable, inspectable institutional documents that certify identity or status and give bearers the practical deontic power to exercise rights, with a typology of their forms and functions.

On Drawing Lines on a Map

Builds a typology of spatial boundaries around the fiat–bona fide distinction, applying it to maps, political and property divisions, scattered objects, linguistic framing, and truthmakers.

Ontological Foundations for Geographic Information Science

Sets a research agenda for geospatial ontology, linking formal accounts of geographic objects, processes, scale, and vagueness to human concepts, interoperable data, and ontology-driven GIS.

Ontologies of Common Sense, Physics and Mathematics

Proposes linked upper ontologies for common sense, physics, and mathematics, arguing that classical models connect real magnitudes to mathematics whereas modern physics relates measurements to entities lacking commonsense universals.

Ontology and Geographic Kinds

Argues that geographic kinds are intrinsically spatial and boundary-centered, requiring mereology and topology to connect physical reality, cultural categorization, cognition, and GIS representation.

SNAP and SPAN: Towards Dynamic Spatial Ontology

BFO's bicategorial framework: SNAP snapshot ontologies of continuants and a SPAN ontology of processes in spacetime, linked by trans-ontological relations to capture change — demonstrated on the ontology of geodynamics.

Surrounding Space: The Ontology of Organism-Environment Relations

Develops a formal ontology of token niches as tenant–medium–retainer structures, extending static organism–environment fit into a dynamic account of vacant niches, movement, interaction, and niche construction.

The Cognitive Geometry of War

Argues that modern ideals of compact, contiguous national territory help drive conflict, and proposes perforated, non-contiguous, and geometrically flexible borders as alternatives to displacement and ethnic cleansing.

The Logic of Systems of Granular Partitions

Builds a sound S4-style modal logic for labeled, typed granular partitions, modeling refinement and cross-partition counterparts so differently selective views can reason about the same mereologically structured reality.

Toward a Realistic Science of Environments

Defends Gibsonian ecological realism: organisms directly perceive affordances in physically real niches, while granular partitions show how different species inhabit perspectives on one world, not separate constructed worlds.

True Grid

Generalizes Alberti’s perspectival grid into a realist theory of projection: pictures, maps, names, concepts, and databases are “true grids” when their cells preserve relevant structure and refer transparently to reality.

Truth and the Visual Field

Uses mereotopology and Gibsonian ecology to treat perception and language as carving transient fiat boundaries in reality, defining a judgment field as the truth-making portion of the world selected by a true sentence.

Vague Reference and Approximating Judgments

Formalizes vague reference as multiple crisp candidate referents within granular partitions, then explains approximation as using familiar spatial or temporal reference grids to constrain vagueness without truth-value indeterminacy.

A pretty but not greedy printer (functional pearl)

Derives a non-greedy pretty printer that optimizes for the shortest valid layout, supports arbitrary subdocument alignment, and runs linearly in the size of its output.

A Pretty Expressive Printer

Introduces an expressive pretty-printing language and a formally verified, practical printer that selects optimal layouts using customizable cost objectives while remaining efficient on real-world formatters.

Between Tech and Art: The Vegetation of Horizon Zero Dawn

A production breakdown of Horizon Zero Dawn’s vegetation pipeline, covering global wind simulation, layered foliage motion, coverage-preserving alpha mipmaps, shading, asset LODs, placement, and cascaded shadows.

Explainable AI for Designers: A Human-Centered Perspective on Mixed-Initiative Co-Creation

Defines explainable AI for game designers, mapping co-creative systems by their explainability, initiative, and domain overlap so explanations serve concrete design tasks.

Extracting Physics from Blended Platformer Game Levels

Infers playable jump physics from generated platformer levels, including hybrid physics models for levels that blend the geometry and style of multiple games.

Ghost of Tsushima: Procedural Grass

Explains Ghost of Tsushima’s compute-driven grass pipeline, from tiled placement and culling to indirect drawing, cubic Bézier blade geometry, variable LOD, wind animation, and material shading.

Improved Alpha Testing Using Hashed Sampling

Develops hashed alpha testing, a stable quasi-random thresholding method that preserves distant alpha-mapped foliage and hair while controlling flicker, anisotropy, and interactions with TAA and alpha-to-coverage.

Procedural Content Generation through Quality Diversity

Argues for quality-diversity algorithms in procedural generation, producing broad collections of varied, playable content while exposing the design space for exploration and co-creation.

Procedural Content Generation via Machine Learning (PCGML)

Defines and surveys PCGML: generating functional game content directly from models trained on existing examples, with uses spanning creation, completion, repair, critique, and compression.

Procedural Generation of Villages on Arbitrary Terrains

Presents a three-stage procedural model that grows terrain-responsive village roads and settlements, partitions land into plausible parcels, and generates slope-adapted buildings with open shape grammars.

Real-Time GPU Tree Generation

Introduces a GPU work-graph pipeline that generates, animates, edits, and continuously LODs detailed seasonal trees every frame, replacing gigabytes of baked geometry with kilobytes of parameters.

Realistic Modeling and Rendering of Plant Ecosystems

Presents a foundational pipeline for authoring plant ecosystems through terrain design, ecological simulation, procedural plant models, approximate instancing, and efficient rendering of billion-primitive scenes.

Real‐time Realistic Rendering and Lighting of Forests

Combines detailed z-field trees with terrain shader-maps to render immense forests in real time, preserving sun, sky, canopy, and ground-lighting effects through seamless, scale-consistent transitions.

Responsive Real-Time Grass Rendering for General 3D Scenes

Renders every grass blade as responsive tessellated geometry on arbitrary 3D surfaces, with per-blade wind, gravity, and collision physics plus aggressive culling that retains dense fields in real time.

Runtime Evaluation of Procedural Content Generation in an Endless Runner Game Using Autonomous Agents

Integrates procedural generation and validation in an endless runner, using aerial and ground agents to detect blocked or unnavigable content before the player reaches it.

Towards Friendly Mixed Initiative Procedural Content Generation: Three Pillars of Industry

Distills three requirements for industry-friendly co-creative PCG tools: preserve designer control, keep feedback loops short, and fit into existing production pipelines.

A Sequential Two-Step Algorithm for Fast Generation of Vehicle Racing Trajectories

Generates near-optimal racing trajectories quickly by alternating between a minimum-time speed profile and a convex path update that reduces curvature.

Active walker model for the formation of human and animal trail systems

Models trail systems as self-organization: walkers reinforce attractive routes while unused traces fade, producing dendritic ant trails and low-detour pedestrian networks.

Interactive procedural street modeling

Lets designers generate and edit large street networks through tensor fields, combining procedural speed with brush-like global and local control over street patterns.

Modelling the Evolution of Human Trail Systems

Shows how pedestrian trails emerge through feedback between destination-seeking walkers, existing paths, and vegetation recovery, yielding a compromise between directness and shared infrastructure.

Mountain Trail Formation and the Active Walker Model

Extends the active-walker model to steep terrain, explaining zigzag mountain trails through slope avoidance, directional persistence, and mutual reinforcement by ascending and descending walkers.

Principles of Trail Layout and Design

A field-oriented guide to durable trail design, emphasizing curvilinear alignment, natural drainage, sustainable grades, control points, and close reading of landform and soils.

Procedural Generation of Roads

Automatically routes and constructs roads with an anisotropic shortest-path method that weighs slope and obstacles while treating surface segments, bridges, and tunnels consistently.

The Topography of Minoan Peak Sanctuaries

Argues that Minoan peak sanctuaries were chosen for visibility and proximity to local settlements, forming a beacon-like sacred network whose contraction tracked settlement abandonment rather than cultic collapse.

Adaptive Behavioral Programming

Adds reinforcements to live sequence charts and BPJ so scenario-based programs can learn from their environment, specifying goals to pursue and scenarios to avoid, with modular learning decompositions.

Challenges in Modeling and Unmodeling Emergence, Rule Composition, and Networked Interactions in Complex Reactive Systems

Position paper on modeling emergence, rule composition, and networked interactions in complex reactive systems, introducing "unmodeling"—explicitly excluding entities and behaviors from model execution.

Distributing Scenario-Based Models: A Replicate-and-Project Approach

Distributes scenario-based models by replicating the full specification on every component and projecting it per component, mimicking centralized behavior while sharply reducing synchronization.

Enhancing Scenario-Based Modeling Using Large Language Models

Extended methodology for combining LLM chatbots with scenario-based modeling: iterative generation of stand-alone scenarios checked by analysis and human review, framed as a step toward Wise Computing.

On Augmenting Scenario-Based Modeling with Generative AI

Outlines a structured method for using generative-AI chatbots in modeling: iteratively generate scenario-based model fragments, then analyze and inspect them to converge on an accurate system model.

On tracing reactive systems

Introduces model-based trace visualization and exploration for reactive systems, using scenario-based (LSC) abstractions and the Tracer prototype, demonstrated on a PacMan game.

Relaxing Synchronization Constraints in Behavioral Programs

Proposes eager execution for behavioral programs: fast b-threads run ahead when synchronization outcomes are predictable, improving performance, modularity, and distributability, shown in a C++ BP framework.

Towards Behavioral Programming in Distributed Architectures

Extends behavioral programming to distributed architectures: b-threads as Erlang processes, eager execution to relax synchronization, and modular distributed execution, demonstrated on simulations and a quadrotor.

The City as Convivial Centre

Kohr's essay arguing that cities exist for convivial life rather than economic function, and that human-scale size is what lets a city serve as a centre of leisure, culture, and encounter.

The Question Concerning Technology

Heidegger's essay on the essence of technology as Enframing (Gestell), a mode of revealing that reduces the world to standing-reserve, and on art as a possible saving power.

Arches: A Framework for Modeling Complex Terrains

Introduces a hybrid volumetric–implicit framework for interactively modeling terrains with overhangs, arches, caves, sand, and rocks, plus efficient tools for erosion and automated rock-pile generation.

FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation

A GPU framework for routing surface flow through terrain and its depressions fast enough to make erosion, river, lake, and ecosystem simulations interactive.

From features to fingerprints: A general diagnostic framework for anthropogenic geomorphology

Integrates geomorphology, archaeology, and high-resolution remote sensing into a framework for reading anthropogenic landforms as landscape-scale sociocultural fingerprints.

Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion

Generates large, controllable mountain terrains by coupling user-painted tectonic uplift with fluvial erosion, then turning the resulting stream graph into detailed landforms.

Legacy sediment: Definitions and processes of episodically produced anthropogenic sediment

Broadens legacy sediment to episodically produced anthropogenic alluvium and colluvium, and explains its deposition, storage, and remobilization through sediment delivery–transport capacity dynamics.

Physically-based analytical erosion for fast terrain generation

Turns the stream power law into an interactive terrain tool, replacing thousands of erosion time steps with analytical solutions and a direct control for landscape age.

Priority-Flood: An Optimal Depression-Filling and Watershed-Labeling Algorithm for Digital Elevation Models

Introduces Priority-Flood, a simple, optimal algorithm that removes drainage-blocking depressions from elevation models and can also derive watersheds and flow directions.

Procedural Riverscapes

Builds editable, animated riverscapes from bare terrain by carving hydrologically plausible channels and blending real-time procedural water primitives instead of simulating fluids.

Terrain Generation Using Procedural Models Based on Hydrology

Generates controllable, multiscale terrain from a sketched drainage network, representing rivers and landforms as an editable hierarchy of continuous procedural primitives.

A Layered Particle-Based Fluid Model for Real-Time Rendering of Water

Renders particle-based water and volumetric foam in real time using perspective-aware surface smoothing, physically guided foam formation, and layered depth compositing.

A Survey of Ocean Simulation and Rendering Techniques in Computer Graphics

Surveys ocean graphics from spectral deep-water models to near-shore fluid simulation, then covers the foam, spray, and light transport needed for convincing rendering.

Advected river textures

Combines a 2D Navier–Stokes solver, hydrostatic pressure columns, and advected procedural textures to render detailed, terrain-responsive rivers at real-time frame rates.

Lagrangian Texture Advection: Preserving both Spectrum and Velocity Field

Advects fluid textures with deformable particle grids, preserving both the input texture’s visual spectrum and exact motion along the velocity field without cumulative stretching.

Real-time Breaking Waves for Shallow Water Simulations

Adds real-time overturning waves to shallow-water heightfields by detecting steep fronts and spawning connected particle sheets that collapse into splashes and foam.

Real-time Rendering of Enhanced Shallow Water Fluid Simulations

Builds a real-time rendering pipeline for shallow-water simulations, adding fine surface detail, advected foam, photon-based caustics, and screen-space reflection and refraction.

Real-time Rendering of River Networks

Renders branching river networks efficiently with quadratic Bézier curves, GPU distance fields, and streaming normal maps instead of dense geometry or particle simulation.

Real-time River Representation by Dynamic Control of Data on Waves

Dynamically switches river-wave models by viewing distance, preserving nearby reflection and wave detail while retaining wind-driven motion across the full landscape.

Scalable real‐time animation of rivers

Animates rivers across vast terrains by computing steady flow locally and advecting fine surface detail only where visible, at a screen-space sampling density.

Very Fast Real-Time Ocean Wave Foam Rendering Using Halftoning

Uses a spectrally controlled halftone mask to make texture-based ocean foam dissipate as clumped bubbles that pop, rather than merely fading transparently.

Water Flow in Portal 2

Explains Portal 2’s production-friendly water shader: artist-painted flow maps advect layered normal maps, while offsets and noise suppress repetition and pulsing on limited hardware.

Water surface wavelets

Represents water waves as spatially varying directional amplitudes, enabling vast interactive simulations with fine detail, moving obstacles, solid coupling, and direct artistic control.

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