I expect that engineering the automated formation of an explanatory knowledge structure will follow some specific principles. I expect the easiest, and perhaps necessary, way to automate this is by using a high dimensional interrogative knowledge structure (e.g. an LLM). These design principles are derived from the properties of the two categories of knowledge described earlier. These principles also help illustrate the ideas; they can surely be improved upon.
- Intransitivity of inductive constraint:
- Observation (the mapping of a pattern within a knowledge-storing information media to a pattern in input data), when mapped to an assertive knowledge structure (possibly with an interrogative intermediary – a generalization of the data), has accompanying implicit or explicit explanatory context (the circumstance of the observation). The observation only constrains the statements that have causal relationships to it. That is, data can only constrain the statements that can be consistent or inconsistent with an observation in a specific circumstance.
- Assertive knowledge is essentially probing or feeling whether its rigid statements ‘fit’ within the physical world, not adjusting them to the shapes of observed data. The statements cannot have Bayesian credences. If an explanatory structure observes data (e.g. results of a scientific experiment), the results constrain the statements that are causally related (the statements constituting the hypothesis and methodology).
- In the case of an assertive knowledge structure learning from an LLM, the output of an LLM (equivalent to experimental results) constrains the statements causally related to the generation of the prompt (e.g. an assertive knowledge structure that has learned the statements: “microwave ovens heat material” and “styrofoam is a material”, asking an LLM “does a microwave oven heat styrofoam?”; if the answer is “no” one of the assertive statements requires further constraint).
- Assertive knowledge is essentially probing or feeling whether its rigid statements ‘fit’ within the physical world, not adjusting them to the shapes of observed data. The statements cannot have Bayesian credences. If an explanatory structure observes data (e.g. results of a scientific experiment), the results constrain the statements that are causally related (the statements constituting the hypothesis and methodology).
- Observation (the mapping of a pattern within a knowledge-storing information media to a pattern in input data), when mapped to an assertive knowledge structure (possibly with an interrogative intermediary – a generalization of the data), has accompanying implicit or explicit explanatory context (the circumstance of the observation). The observation only constrains the statements that have causal relationships to it. That is, data can only constrain the statements that can be consistent or inconsistent with an observation in a specific circumstance.
- Non-confirmability of knowledge:
- Statements and observations are always fallible; they are only accepted as tentatively true.
- Statements cannot be ‘supported’ and they do not have Bayesian credences; they can only be consistent or not with the observed data.
- When hypotheses do not fit with observations, either the statement is incorrect or component(s) of the explanatory context of the observation are incorrect.
- Observations can be refuted when their explanatory context is refuted.
- Observations can be refuted when their explanatory context is refuted.
- Statements can never be refuted absolutely. Statements removed from the explanatory model may be archived as historical (self-descriptive) knowledge, or archived as heuristics (e.g. Newtonian gravity).
- Statements and observations are always fallible; they are only accepted as tentatively true.
- Data is observed via explanatory structures:
- This principle cannot be applied until the explanatory knowledge structure contains sufficient knowledge to give context to data (e.g. the knowledge structure can understand the methodology of an experiment, or the data sources and algorithms used to train an LLM it is learning from). As the explanatory knowledge structure grows it will be able to understand the meaning (context) of the data it receives. Initially the explanatory knowledge structure must naively believe what it is being told (either by a human or an LLM). Eventually it will evaluate data based on accompanying descriptive statements (e.g. “this data was produced by a the CFX Opus 96 Real-Time PCR System” and “the CFX Opus 96 Real-Time PCR System uses Peltier thermoelectric cooling”), and eventually may be able to deduce the context of data it receives without accompanying descriptive statements.
- Explanatory context of observations or observation sets can be changed, which can change the meaning of the observation data.
- Example: “the primer used in the PCR reaction was inappropriate for the target sequence” or “the temperature in the laboratory was -10° C and outside the operational range of the machine”).
- Example: “the primer used in the PCR reaction was inappropriate for the target sequence” or “the temperature in the laboratory was -10° C and outside the operational range of the machine”).
- Prediction and explanation are symmetric. Compositions of statements can predict (input→output) or explain (output → input) patterns in data.
- This principle cannot be applied until the explanatory knowledge structure contains sufficient knowledge to give context to data (e.g. the knowledge structure can understand the methodology of an experiment, or the data sources and algorithms used to train an LLM it is learning from). As the explanatory knowledge structure grows it will be able to understand the meaning (context) of the data it receives. Initially the explanatory knowledge structure must naively believe what it is being told (either by a human or an LLM). Eventually it will evaluate data based on accompanying descriptive statements (e.g. “this data was produced by a the CFX Opus 96 Real-Time PCR System” and “the CFX Opus 96 Real-Time PCR System uses Peltier thermoelectric cooling”), and eventually may be able to deduce the context of data it receives without accompanying descriptive statements.
- Separation of explanatory assertive knowledge (mechanistic statements) from descriptive assertive knowledge (statements about the state of the world):
- Both explanatory and descriptive assertive knowledge are constrained by inductive knowledge; however, separation formalizes the “theory-laden” structure of observation, may help prevent overfitting of the the explanatory world model to a specific learning environment, and may potentiate the re-interpretation of observations via new explanations.
- Example:
- Explanatory memory structure: “A capital city is the municipality holding the seat of government of a country.”
- Descriptive memory structure: “Tegucigalpa is the capital city of Honduras.”
- Explanatory memory structure: “A capital city is the municipality holding the seat of government of a country.”
- Both explanatory and descriptive assertive knowledge are constrained by inductive knowledge; however, separation formalizes the “theory-laden” structure of observation, may help prevent overfitting of the the explanatory world model to a specific learning environment, and may potentiate the re-interpretation of observations via new explanations.
- New assertive statements must contain some unambiguous explanatory content (context):
- Statements which lack connection to the world model cannot be added unless context can be found. Disconnected statements are incompatable with the explanatory world model and cannot be computed by it. Excluding disconnected statements like “the sun rises every day because the sun rises every day” may be necessary to prevent overfitting or model collapse during training.
- Example 1:
- Disconnected statement: “All flums are squirbly.”
- Contextualized statement: “There exist logical statements that do not describe the physical world. First-order logic consists of the following rules... This input data is a statement of first-order logic that does not describe the physical world: “All flums are squirbly.”
- Disconnected statement: “All flums are squirbly.”
- Example 2: when Van Leeuwenhoek first observed microbes he may have generated a statement like “The microbe is the smallest living structure”, where the term “microbe” had never been used before in science; however, other components of the statement connect it with the greater explanatory structure. Additional explanations can then be connected to the new term, “microbe”.
- Example 1:
- Statements which lack connection to the world model cannot be added unless context can be found. Disconnected statements are incompatable with the explanatory world model and cannot be computed by it. Excluding disconnected statements like “the sun rises every day because the sun rises every day” may be necessary to prevent overfitting or model collapse during training.
- New assertive statements must be observable:
- Observations occur when a statement or statement composition in an assertive knowledge structure maps (or fails to map) to a pattern in data (either from a measuring device or induced from measurement).
- Example: If building an assertive world model using an LLM, adding a new statement to the knowledge of chemical reactions should increase mapping of the assertive knowledge structure to the interrogative knowledge structure (e.g. if the statement “acid + base → salt + water” is generated by the LLM and incorporated into an assertive knowledge structure containing other basic statements about chemistry, like balancing equations, the new statement can be used to generate the chemical equation “HCl + NaOH → NaCl + H2O”, an output that can then be compared to knowledge contained in the LLM).
- Example: If building an assertive world model using an LLM, adding a new statement to the knowledge of chemical reactions should increase mapping of the assertive knowledge structure to the interrogative knowledge structure (e.g. if the statement “acid + base → salt + water” is generated by the LLM and incorporated into an assertive knowledge structure containing other basic statements about chemistry, like balancing equations, the new statement can be used to generate the chemical equation “HCl + NaOH → NaCl + H2O”, an output that can then be compared to knowledge contained in the LLM).
- Not every consequence of a new statement needs to be observed in data but the statement must be observable within data we have.
- Example: when Einstein conjectured the general theory of relativity, the theory was observable via its consistency with other knowledge and data, and its explanatory power (see below). Specific consequences of the theory, like the existence of black holes, were not observed until much later.
- Example: when Einstein conjectured the general theory of relativity, the theory was observable via its consistency with other knowledge and data, and its explanatory power (see below). Specific consequences of the theory, like the existence of black holes, were not observed until much later.
- Inconsistency indicates error in a statement and opportunity for statement addition or substitution.
- Observations occur when a statement or statement composition in an assertive knowledge structure maps (or fails to map) to a pattern in data (either from a measuring device or induced from measurement).
- Assertive statements may include error terms representing stochastic variables:
- Error terms may represent entropy inherent in observations. Entropy is predictive or explanatory imprecision with respect to data. Entropy is caused by deficiencies in descriptive and explanatory knowledge (except in the case of quantum mechanical uncertainty). Entropy is practically unavoidable when generating explanations or predictions. The presence of entropy in an observation indicates that additional context can be added or existing explanatory statements may be improved.
- Error terms are distinct from the other content of explanatory statements because they are fixed to specific explanatory perspectives (context of observations).
- Example: heighti = b0 + b1agei + εi , where b0 is the intercept, b1 is a parameter that age is multiplied by to obtain a prediction of height, εi is the error term, and i identifies a child. This implies that height is predicted by age, with some error. The error term is derived from the distribution of data that constitute observation from a specific explanatory perspective. Adding additional connections between observation data and explanatory statements (e.g. heighti = (b0 + b1agei) (b2sexi) (b3∑genotypei) … + εi) changes the error. Shifting the explanatory context of data also changes the error (e.g. heighti = length of Procrustes bed + εi).
- Error terms may represent entropy inherent in observations. Entropy is predictive or explanatory imprecision with respect to data. Entropy is caused by deficiencies in descriptive and explanatory knowledge (except in the case of quantum mechanical uncertainty). Entropy is practically unavoidable when generating explanations or predictions. The presence of entropy in an observation indicates that additional context can be added or existing explanatory statements may be improved.
- Optimize toward better explanations:
- Better explanations increase explanatory power of the model. This is different from optimizing for predictive success, as in training of LLMs, because better explanations are determined by comparing a world model to the world, not to an environment (context). Incorporating a better explanation may decrease predictive success of the model relative to a specific environment.
- Replace an old statement with a new statement when the new statement can correct inconsistencies (e.g. if new data causes a statement to conflict with its observation), can resolve a conflict between statements, or substitute the predictions of an old statement while increasing explanatory power .
- Example: The statement “maggots are generated spontaneously from inanimate matter” is observable in some data (e.g. “day 0: no flys seen in garbage can; day 3: 6 flys seen in garbage can”). The statement can be replaced by other statements with greater explanatory power that also reproduce observations (e.g. explanatory statements such as “arthropods lay eggs” “flys are arthropods” “flys develop through sequential stages: egg, larva, pupa and adult” and a descriptive statement “the lid of the garbage can is not sealed”). The new statements constitute a better explanation for the data if the new statements are also consistent with other measured or inferred data)
- Example: The statement “maggots are generated spontaneously from inanimate matter” is observable in some data (e.g. “day 0: no flys seen in garbage can; day 3: 6 flys seen in garbage can”). The statement can be replaced by other statements with greater explanatory power that also reproduce observations (e.g. explanatory statements such as “arthropods lay eggs” “flys are arthropods” “flys develop through sequential stages: egg, larva, pupa and adult” and a descriptive statement “the lid of the garbage can is not sealed”). The new statements constitute a better explanation for the data if the new statements are also consistent with other measured or inferred data)
- Explanatory power is equivalent to predictive or explanatory resolution. When a statement can describe (allow observation of) some previously unknown mechanic of the world, it increases explanatory power of the knowledge structure.
- Example: the addition of the statements constituting Einstein's field equations enables prediction and explanation of new phenomena, like gravitational lensing and black holes, and finer prediction of previously described phenomena, like the perihelion precession of Mercury.
- Explanatory power is analogous to the term “reach” as defined by David Deutsch as “the ability of some explanations to solve problems beyond those that they were created to solve”. Interrogative knowledge does not have reach in the absolute sense that assertive knowledge does.
- A traditional metric of relative information loss (e.g. Akaike information criterion
) may be useful for evaluating explanatory power. The method should avoid estimation via Bayesian statistics or using absolute probabilities, neither of which would be compatible with assertive learning.
- Some metric of how fundamental a statement is with respect to the global knowledge structure may also be useful (e.g. betweenness centrality
); more fundamental statements are harder to vary.
- Example: the addition of the statements constituting Einstein's field equations enables prediction and explanation of new phenomena, like gravitational lensing and black holes, and finer prediction of previously described phenomena, like the perihelion precession of Mercury.
- Good explanations tend to be concise.
- Because assertive statements are composable and they predict via statement structures, more concise statements generally have greater reach. Thus, parsimony should tend to optimize explanatory power of the model.
- Effective statement generation using an LLM would likely be a process of accreting simple patterns rather than generating complex patterns in a single shot.
- Effective statement generation using an LLM would likely be a process of accreting simple patterns rather than generating complex patterns in a single shot.
- Conciseness also enables more focused observations and refutations.
- Example 1: a single point mutation is more likely to be adaptive than many simultaneous point mutations
- Example 2: Pythagorean theory
is more likely to consistent with observations than the set of theories in Pythagoreanism
.
- Because assertive statements are composable and they predict via statement structures, more concise statements generally have greater reach. Thus, parsimony should tend to optimize explanatory power of the model.
- Better explanations increase explanatory power of the model. This is different from optimizing for predictive success, as in training of LLMs, because better explanations are determined by comparing a world model to the world, not to an environment (context). Incorporating a better explanation may decrease predictive success of the model relative to a specific environment.
- Three strategies to guide the creation of new explanatory statements (creativity):
- Mapping an assertive knowledge structure to a high dimensional interrogative knowledge structure:
- When the explanatory structure has not recreated regions of the interrogative knowledge structure, that indicates remaining unexplained and learnable patterns in the world. The spaces where the two structures do not overlap indicates where deficiencies in knowledge exist.
- Example: within a human mind (containing both assertive and interrogative knowledge) we can notice when an intuition about the world lacks explanation, then seek to explain the intuition. An analagous process can conceivably work in an AI.
- When the explanatory structure has not recreated regions of the interrogative knowledge structure, that indicates remaining unexplained and learnable patterns in the world. The spaces where the two structures do not overlap indicates where deficiencies in knowledge exist.
- Highlighting internal explanatory deficiencies or conflicts:
- An explanatory deficiency exists when some explanation is observable in the data but the explanation is poorly connected to the rest of the explanatory world model (e.g. observing that the sun periodically rises and falls while lacking an explanation for why it does so, or lacking an explanation of what the sun is with respect to the earth).
- When a conflict between explanatory statements is discovered (or emerges once a better explanation is introduced) new explanations can be created specifically for resolving the conflict.
- Because inductive constraint is intransitive and because observations have explanatory context, conflicts between patterns in data and patterns in the assertive world model should be tentatively attributed multiple statements. Possible explanations refuted by the data should be labeled as possibly incorrect, then inspected individually (from different directions in the network) until the source of the error can be identified or a better explanation can be substituted.
- Example 1: New data from the Michelson-Morley experiment
were inconsistent with the theory of a luminiferous aether. The theory of the luminiferous aether was later replaced the better theories of special relativity.
- Example 2: The famous internal explanatory conflict of Achilles and the tortoise
. I think this is caused by the mistaken assumption that velocity is not discrete.
- Example 3: The Algol paradox
caused by the mistaken assumption that the masses of binary stars are fixed.
- Because inductive constraint is intransitive and because observations have explanatory context, conflicts between patterns in data and patterns in the assertive world model should be tentatively attributed multiple statements. Possible explanations refuted by the data should be labeled as possibly incorrect, then inspected individually (from different directions in the network) until the source of the error can be identified or a better explanation can be substituted.
- Notably, sometimes conflicts between statements will only exist between extrapolations or compositions of explanations which are not present in existing (training) data. In this case investigating the conflict may require collection of new data (experimentation); the world model should become capable of generating methods for such experiments.
- Automated conflict identification may be similar to automated sanity checking
of software.
- An explanatory deficiency exists when some explanation is observable in the data but the explanation is poorly connected to the rest of the explanatory world model (e.g. observing that the sun periodically rises and falls while lacking an explanation for why it does so, or lacking an explanation of what the sun is with respect to the earth).
- Identifying and relating common explanatory statements or statement structures:
- When explanations for multiple phenomena have identical “shapes”, that may indicate that the phenomena and the explanations for them can be unified.
- This process may be able to utilize some existing methods of automated code refactoring
.
- When explanations for multiple phenomena have identical “shapes”, that may indicate that the phenomena and the explanations for them can be unified.
- Mapping an assertive knowledge structure to a high dimensional interrogative knowledge structure:
- Assertive knowledge creation using low dimensional versus high dimensional induction.
- Low dimensional interrogative knowledge can be used as constrained sensory inputs to an assertive structure (e.g. biological senses). When explanatory knowledge exists, low dimensional interrogative knowledge can be used for experiment (focused data collection and statement testing).
- High dimensional interrogative knowledge can be used for these same purposes. A high dimensional interrogative structure (especially, and perhaps exclusively, one that is trained on assertive statements) can be used for kickstarting an assertive structure. Patterns of the environment are translated into features within the interrogative structure. The features map to discrete symbols in a natural language that can be used to compose formal assertive statements. The high dimensional interrogative structure has enough encoded patterns to rapidly test/refute many statements without the need to receive new sensory or experimental data.
- Kickstarting may not be complete until the model has an assertive world model sufficient to simulate the mechanics of its environment, including itself, and begin generating new (targeted) experiments to improve it’s knowledge (by referencing data outside the interrogative knowledge structure).
- Kickstarting may not be complete until the model has an assertive world model sufficient to simulate the mechanics of its environment, including itself, and begin generating new (targeted) experiments to improve it’s knowledge (by referencing data outside the interrogative knowledge structure).
- Progress in independent assertive knowledge creation beyond learning from an interrogative knowledge structure and from available data will require a versatile physical vehicle for interacting with the world (either a mechanical body or a proxy like a human body).