Collaborator login
New collaborator registration
Forgot password

Welcome to Representing Knowledge with Primitives

Computers should help people deal with everyday problems from making decisions to playing games. To offer more help, computers need more complete representations of knowledge, defined as useful incorporated information. This web site provides tools to collaborate on creating more complete representations, starting with textual natural language.


This research web site explores a hypothesis about representing knowledge:

Conditional probabilities
Conditional probabilities deal with uncertainty in information, ambiguity, vagueness, and approximation. Probabilities factor in utilities, which principled Decision-Analytics may use to choose the best among an exponential quantity of processing alternatives. Probabilities subsume other uncertainty measures and include higher-order probabilities about the measures themselves.
with closure logic expressions
To get an expressive and fine-grained enough representation, conditional probabilities, which are statements about events, can use complex logic expressions, including closure logic. Closure logic can express negation and the stop words that other approaches ignore. Providing a unified methodology, closure logic can express intent, including subjunctive hypotheticals, along with other moods without using modal logic; processes; and contexts like frames.
with predicates from a limited set of primitives
Predicates in closure logic expressions can come from a limited set of templates, called primitives, which parameterize values, e.g., numbers and strings. Specific to generic hierarchies among conditions can derive taxonomies. Expressions can be compared and manipulated to handle analogies.
can tractably represent common sense knowledge.
This combination should lead to new processing capabilities, despite the unbounded nature of ideas, the complexity of ideas, and the uncertainty of the ideas communicated with natural language.

Tractable means easily managed or controlled (probabilistic) rather than running in polynomial time (deterministic).


Knowledge Representations drive the implementations of general purpose computing, called Artificial Intelligence as it approaches human capabilities. An implementation of the hypothesis can satisfy goals for Knowledge Representation of being: helpful, understandable, principled, parsimonious, small, and secure. Many classes of use cases could employ this implementation:

An implementation of the hypotheses could support several requirements that can be derived from these use cases: capability, access, context, uncertainty, judgment, adaptability, efficiency, and possibly scale. The comparison of methods page gives more details.

Describing applications that go well beyond what is currently possible using a developing technology that mostly correctly recognizes text and provides a representation of its meaning that may be reasoned about, including uncertainties, is a challenge. With such applications in mind, collaborators or other help could develop the technology more quickly.


The development approach includes:

The approach provides several implementation benefits.

Only a few kinds of components produce the entire Knowledge Representation: conditional probabilities containing closure logic expressions have predicates with unbounded parameters (numbers, strings) from limited set of primitives (predicate patterns), combined in closures only with conjunctions (AND) and classical negation (NOT). Other commonly used logic components such as functions, constants, disjunctions (OR), implications, or modals (possibility, deontic logic) may be constructed from the few. A common representation allows diverse items, such as meanings, syntax, and processing actions, to be combined, which has been a long-standing issue for natural language understanding. Few components also simplifies implementation, nonetheless allowing specializations and heuristics to optimize processing.
A few, well-chosen components can represent much. Taxonomies of ontologies derive from combining components. Contexts are the closures of closure logic. Conditional probabilities can potentially multiple meanings simultaneously, such as the connotations and denotations of words, the meat of logic. Closures that subtract predicates can represent metaphors. Closures may explicitly represent paradoxes even though they are inconsistent in traditional logic. Closures also easily attach metadata to statements. Rare events, counterfactuals, and fiction need nothing special.
The few declarative components provide clarity. Information coming from the approach has a straightforward explanation with logic, which may be resistant to bias or misinformation. The conditional probabilities and their expressions have graphical representations providing alternates to pure, linear symbols. There is not even a Rete algorithm to complicate explanation.
The approach allows optimizing representation. Among uncertainty measures, probabilities permit great accuracy allowing modeling of phenomena from measurements like frequencies to subjective judgments. Secondary probabilities, as I. J. Good discussed, allow the explicit representation of precision. Probabilities provide a rich collection of manipulations including conditional probabilities. With probabilities and value judgments, Decision Theoretic techniques can both justify external judgments and provide a rational for internal processing decisions. The fine-grained components may attach specializations and heuristics for more efficient processing. The processing cycles used should be orders of magnitude less than current popular approaches.
The approach is flexible both in how it is used and how it is implemented. The conditions of conditional probabilities linked into a generic and specific hierarchy provides defaults. Each situation can override the defaults, allowing custom handling, for instance, for different users. These defaults allow defeasible non-monotonic reasoning providing real-time knowledge maintenance. The set of suggested primitives in use is not gospel. Although some primitives are unlikely to change, in particular, those that John F. Sowa suggests, many of the suggested primitives may easily be substituted, at least initially.
The approach includes capabilities for extensions. The implementation being developed includes algorithms for the maintenance of conditional probabilities organized by condition. Conditions may be created with their conditionees (outcomes), replaced as conditions or with their conditionees, updated, and deleted (CRUD), the standard for database operations. A heuristic merging algorithm will suggest combined closure logic expressions for either the conditions or conditionees. These algorithms form the basis for other extensions such as rules engines, which may be implemented with theorem provers. Since the approach does not implement arithmetic and statistics, such capabilities could be implemented as added layers. Handling of natural language, possibly including tokenization; stemming or lemmatization; parsing, which could look up appropriate syntax, including suffixes; and generation, which could weigh and select attributes arranged for output could also be capabilities that would access the representation. Other capabilities, for instance creating computer programs, might also have an implementation that accessed the representation.

Getting started

Collaborators are welcome to add their thoughts about how anything may be described. Such philosophical insights may be given without specific consideration of the logic, probability, or algorithms that handle them.

Register to read more. Then make an edition to collaborate. As desired, add primitives or condition groups with outcomes.

This introduction, comparison of methods, glossary, references, and site implementation pages are openly available. However, most pages are only available to registered collaborators.

Collaborators register with the site providing at least postal codes, such as a U.S. ZIP code, which provides a locality, and E-mail addresses so that a site administrator may authenticate them. Since authentication is manual, new potential collaborators may gain full access slowly, particularly if the information provided is minimal.

Except for a self-assigned identifier string, all collaborator information is only available to administrators, unless collaborators choose to share their information with other authenticated collaborators.

Site navigation

Only a few pages are visible without logging in.

Copyright © 2022 Robert L. Kirby.  All rights reserved.