The instance, property, and instance-property copula mark the end of transitivity in one or both directions in an inheritance chain, and represent "individual", "attribute", or both, respectively.
The instance and property copulas correspond to two ways to specify a set. Some, but not all, terms are sets.
Valid syllogistic rules of NAL-2 are variants of the transitivity of inheritance, including resemblance, analogy, and comparison.
The inference rules of IL-3 come from the definitions of the related compound term, and may take one or two premises. The conclusion may contain new terms not included in the system's vocabulary.
In a term logic, the compositional and structural rules can be seen as variants of the syllogistic rules.
Intersection and union are dual operators, as in set theory, with respect to the extension and intension of a term.
The inference rules of NAL-3 include compositional, decompositional, and structural rules, as well as a choice rule that takes simplicity into account. The rules defined in lower layers remain valid when a compound is used as a whole.
The same idea is used in set theory, except here it is not limited to sets defined extensionally.
The inference rules of IL-4 come from the definitions of the related compound term. Each of them only takes one premise.
The inference rules of NAL-4 only take one premise, and produce conclusions with the same truth-value, since the premise and the conclusion express the same content, though in different form.
The meaning of a concept is determined by its relations with the other concepts. Some relations are syntactic (component-compound), and the others are semantic (subject-predicate).
A semantic relation can be extensional, intensional, or both. The extension and intension of a concept mutually determines each other in IL, and their sizes change in the opposite direction. In NARS, they are defined differently from the conventional definition (which presumes model-theoretic semantics), while still keep the same intuitive meaning.
The meaning of a compound term is semi-compositional: it is determined partly by the syntactic relations, and partly by the semantic relations with the compound as a whole, which usually cannot be fully derived from the former. The meaning of a compound term is initially determined fully by the syntactic relations, but later more and more by the semantic relations, which usually cannot be derived from the former.
Restricted by available resources, when processing a given task, each involved concept normally is used with partial meaning. Which part will be used is influenced by the priority distribution among beliefs, which depends on experience and context. Related topics: essence and definition, analogy and metaphor.
A useful concept usually have relatively sharp and balanced extension and intension, such as basic level categories and natural kinds.
A term (or concept) in NARS is not a "symbol" as in traditional "symbolic AI" in that it does not directly represent an external "object", but an internal "pattern", which include operations and perceptions (more on that later).
Recognition, perception, and categorization: answering "T → ?" for a given term T. There are often multiple answers that are not mutual exclusive, but form an inheritance hierarchy. The choice rule in NAL: expectation and simplicity. Control factors: familiarity and relevance.
In NARS, all forms of empirical knowledge is producible and modifiable by experience (though can be implanted, too). At this level, learning is complete.
On the other hand, the grammar rules, inference rules, and control mechanisms are defined at the meta-level, which are not acquired, but built-in.
In NARS, learning and reasoning are basically two aspects of the same process. Learning is an open-ended process that does not follow any predetermined algorithm, as studied in "machine learning".
New concepts appears in the system in three ways: accepted, composed, altered. The "original meaning" of a concept is not necessarily its "current" meaning. In general, there is no "correct", "true", or "ultimate" meaning for a concept, though concepts with stable and clear meaning are preferred.
The leaning process self-organizes the system's knowledge, according to the system's experience, to improve the system's performance.