Interlude I-B: The Hybrids and Their Missing Objects
Aa
This interlude follows several ways of combining generation, retrieval and structured reasoning. Its examples isolate interfaces at which a useful result can lose the grounds or scope needed for its next use. They are schematic constructions, not a survey establishing what every implementation lacks. Volume I, Chapter 6 (Evidence Without Custody) supplies the corresponding question: what can a recipient establish through work performed elsewhere?
The Hybrid Landscape
The preceding chapters diagnosed structural failures in two paradigms. But systems in the wild are rarely pure. Language models call tools. Databases store embeddings. Retrieval pipelines inject evidence into generation. Knowledge graphs provide structure to neural search. The world is full of hybrids.
Combining methods can solve problems that neither method handles alone. The remaining question concerns what their combination preserves. A result can be available to the next component while its source, verification conditions or intended scope are absent from the interface. The examples below make those omissions explicit. An implementation that already preserves and enforces the relevant relation has answered that part of the problem; the book cannot claim the achievement merely by giving it another name.
Knowledge Graphs
Knowledge graphs—Wikidata1, Freebase before its deprecation, enterprise ontologies—represent entities and relations. Their applications support typed queries, constraint checking and explicit reference. A graph can record that Marie Curie was a physicist, that she won the Nobel Prize in Physics, and that the prize was awarded in 1903. Traversal, inference over declared hierarchies and mappings among vocabularies can make such records useful elsewhere.
Adding an edge label is different work from supplying an evaluation method, invariants and an appropriate verification regime for its use. An extensible graph can admit a new predicate immediately. Whether “controversial,” “influential,” “is_sustainable” or “production_ready” becomes checkable across views depends on what accompanies that admission. Maintainer review is one possible arrangement; it is not a necessary property of graph representation.
The A3 / A3b construction concerns that additional obligation. It treats a new predicate as an addition to a language with specified commitments. Existing graph systems can represent definitions, provenance and versions. The schematic interface considered here accepts a new label without requiring those supporting objects; its omission is a choice of interface, not a proof that graphs cannot supply them.
The missing object in that interface is the contract governing the new predicate. Storing the label has not supplied it.
Neurosymbolic AI
Neurosymbolic systems2—DeepProbLog, NeurASP, Logic Tensor Networks, Logical Neural Networks—combine neural perception with symbolic reasoning. A neural component classifies images; a symbolic component reasons over the classifications. The promise is the best of both worlds: pattern recognition at the perceptual boundary, logical inference over structured knowledge.
Consider a boundary that passes a neural classification into symbolic reasoning as a proposition alone. The classifier proposes that an image contains a cat; the next component reasons from that input. If the result is challenged, the recipient needs to recover what was classified, which procedure produced the result and what its output means. The proposition alone does not contain that account.
This is the A2 / A2b / A2c problem under the stipulated interface. A system can retain the image, model identity, confidence and relevant traces; symbolic constraints can also expose disagreement with a neural proposal. What matters here is whether the next stage can inspect and use those grounds, rather than receiving only the proposed answer.
Some systems attach confidence scores or probabilistic weights. This helps with uncertainty quantification, but not with witnessed provenance. Knowing that a proposition has probability 0.7 is not the same as knowing why it has probability 0.7, or what to check if you doubt it.
The missing object at the proposition-only boundary is the account needed to assess the classification. Combining perception and reasoning need not lose it.
Inductive Logic Programming
Inductive Logic Programming3—ILASP, Metagol, Popper—learns logical rules from examples. Given positive and negative instances, an ILP system can invent predicates and Horn clauses that cover the positives and exclude the negatives. This is genuine predicate invention: the system produces new vocabulary that was not in the input.
A learner working over one dataset and one background theory can produce a useful rule without settling how that rule relates to one learned elsewhere. Suppose no relation between the two learning contexts is included in the interface. Agreement within each task then leaves their overlap unexamined.
The A5 question begins at that overlap. “Puffy” can describe different properties in Shopper A’s and Shopper B’s examples. Reconciling their results requires knowing which differences should survive and which comparisons are intended. Learning each predicate successfully has not yet performed that work.
The missing object in this two-context example is the relation governing their comparison. It can be supplied by an extended system; it does not follow from the separate learned rules.
Program Synthesis and Library Learning
Program synthesis systems—DreamCoder4, library learning, neural-guided search—discover reusable abstractions. Given a corpus of tasks, they invent primitives that compress the solution space. DreamCoder provides a canonical example: it can learn concepts like "map," "fold," and domain-specific operations by recognizing recurring structure across tasks. This is a form of predicate invention: the system creates new building blocks that make future problems easier to express.
A compression objective over a task distribution rewards reusable primitives within that distribution. It does not, by itself, require compatibility with an independently developed library. If the two libraries are to be used together, their assumptions and common uses become part of the task.
This brings the A5 problem into the cost account. Search, checking and reconciliation can all consume resources. A primitive that saves work within one library may create work where another library relies on a different interpretation. The relevant comparison includes that later work when the intended use crosses the boundary.
The missing object in the compression-only interface is the obligation to test those shared uses. A synthesis procedure can be designed to include it; success on the original task does not establish that it has.
LLM + Tools (Agents, Chains, Orchestrators)
Tool-augmented language models—LangChain, AutoGPT, OpenAI function calling, agentic workflows—extend generation with action. A model can call a calculator, query a database, browse the web or execute code. Calling a calculator can supply new grounds for an answer. The usefulness of that result still depends on the operation requested and the inputs supplied.
Consider a pipeline that records a tool call but passes only its returned text into generation. Its log may retain the parameters and response, while the later stage omits the reference that would connect an assertion to that work. This is a particular loss of an available relation. Tool orchestration can instead preserve identifiers, carry structured results and require checks before proceeding.
The A2 difficulty occurs when a later assertion requires grounds the pipeline no longer makes available. Two conflicting results may then enter the same answer without their differences being examined. Recovering the records or repeating the relevant operation can restore grounds; repeating the conclusion through another interface cannot do that by itself.
Metadata can represent sources, activities and derivations. Calling it metadata does not disqualify it as evidence. The engineering question is which assertions those records support and what the receiving operation requires before relying on them. A trace left unused may fail that purpose; a checked trace may satisfy it without adopting this book’s particular wrapper.
The missing object in the text-only interface is the usable connection between the later claim and the work supporting it. Keeping a log and making that connection operative are different achievements.
The Pattern
The interfaces separate achievements that a product description can make sound simultaneous. A vocabulary can grow before its new predicates have agreed uses. A classification can enter reasoning before its grounds are available there. A learned primitive can save work before anyone has tested its relations to another library. None of these gaps requires us to deny the achievement that came first.
The missing objects are not random. They form a coherent structure: witnessed assertions (A2, A2b, A2c), certified predicate invention (A3, A3b), context and view structure (A5), gluing discipline (A5), and coherence cost accounting (deferred to Part IV).
The construction must therefore say where each obligation is enforced. Application code, data contracts, existing provenance representations and institutional review may perform parts of that work. A new substrate earns no exemption from the same examination. Its advantage must lie in what it preserves and makes dependable, not in declaring existing implementations incapable by definition.
Consequence
Adding components can provide missing capabilities. It can also multiply boundaries across which their conditions are lost. A construction must specify what crosses each boundary and what makes the recipient entitled to proceed.
Part II develops one proposed arrangement: witnesses travel with claims, predicates carry obligations, contexts remain explicit and overlap is tested where agreement is required. It must show how those relations compose. That is the positive burden the examples have established.
The construction begins with the least glamorous of these tasks: a disciplined notion of “same” with transport obligations.