Semantic compounds and higher-order concept construction

Composition is a powerful tool in word formation: Two or more words are joined to form a new word. However, it is not merely a linguistic phenomenon but a conceptual process as has been made clear in both cognitive semantics [Jackendoff1983] and generative lexical theory [Pustejovsky1995]. In accordance, the A-LLM allows two concepts to be joined to form a new concept. The formal structure of A-LLM‘s compounding is grounded in the interpretation of concepts as unary functions. In this view, a concept a is not merely a static semantic unit but also an operator capable of taking another concept b as an argument. The resulting compound a(b) is a new node in A-LLM’s semantic graph whose definitional edges connect it to both a and b. This functional interpretation is consistent with theories of lexical decomposition that treat semantic roles as argument structures [ChierchiaMcConnellGinet2000], yet A-LLM extends this by applying the mechanism uniformly to all concepts, not only to those derived from verbs or predicates.

Compounds of the form a(b) allow concepts to operate as functions over other concepts, enabling recursive and hierarchical conceptual construction; both a and b may be atoms or compounds (e.g. \mathit{highest}(\mathit{mountain})(\mathit{Moon})). The transformation calculus governs how transformations propagate through compounds, ensuring that semantic identity is preserved even in complex constructions. For example, with \mathit{air_pressure} = \mathit{pressure}(\mathit{air}), the concept \mathit{instrument}(\mathit{air_pressure}) = \mathit{instrument}(\mathit{pressure}(\mathit{air})), verbalized in English by the word barometer, arises through a sequence of transformations applied to both concepts air and pressure, followed by functional compounding. The calculus guarantees that such composite structures maintain full interpretive transparency and remain reducible to LDV primitives.

The interaction between compounding and the transformation calculus is governed by propagation rules. Vertical transformations applied to compounds affect the functional component. For example, verbalizing a compound such as \mathit{smallness} = \mathit{opposite}(\mathit{largeness}) yields \mathit{decrease_(to)} = \mathit{verb}(\mathit{smallness}) = \mathit{verb}(\mathit{opposite}(\mathit{largeness})), preserving the functional identity of the concept. Horizontal transformations propagate according to the relational structure of the compound: if pressure is horizontally linked to vacuum_pressure through complementarity, then \mathit{instrument}(\mathit{pressure}(\mathit{air})) stands in a corresponding horizontal relation to \mathit{instrument}(\mathit{vacuum_pressure}(\mathit{air})). These propagation rules reflect the structured nature of conceptual relations described in cognitive and lexical semantics [Cruse1986], [Lehrer1990] but are formalized with greater precision.

Compounding also provides the conceptual infrastructure for modeling domain-specific ontologies. Scientific and technical vocabularies frequently rely on conceptual combinations rather than atomic terms. Complex concepts such as thermal_conductivity, genetic_mutation, atmospheric_turbulence, or cellular_respiration can all be represented through nested compounds derived from atomic primitives. For example, atmospheric_turbulence is represented as \mathit{turbulence}(\mathit{air}(\mathit{Earth})). These kinds of representations enable A-LLM to encode complex knowledge through a uniform conceptual calculus rather than through manually constructed hierarchies.

The expressive power of compounding becomes apparent when considered in the context of inference. Because compounds encode functional relationships, they naturally support inferential chains. Kinship reasoning, for example, can be expressed entirely through repeated functional application: \mathit{grandmother}(x) = \mathit{mother}(\mathit{parent}(x)). Such inferential representations align with classical work in formal semantics on definitional and relational dependencies [KampReyle1993]. A-LLM provides a graph-based mechanism that renders these structures computationally accessible and conceptually explicit.

The functional view of concepts as unary functions aligns with type-theoretic approaches in lexical semantics. Löbner [Lobner2011] introduces functional nouns as concepts whose meaning takes the possessor or bearer as argument. These concepts correspond exactly to A-LLM's handling of compounds: role terms such as \mathit{father}(\mathit{Rosi}), \mathit{president}(\mathit{France}), unique parts such as \mathit{cover}(\mathit{computer}), abstract aspects such as \mathit{name}(\mathit{Pope}), \mathit{age}(\mathit{Picasso}) or \mathit{meaning}(\mathit{meaning}). Prepositional concepts can also be represented as compounds, e.g. \mathit{under}(\mathit{water}), snorkeling = \mathit{sport}(\mathit{under}(\mathit{water})), \mathit{behind}(\mathit{Moon}), \mathit{inside}(\mathit{house}). Possessive and property chains (“my father‘s wife’s mother's car”) become nested applications, e.g. \mathit{car}(\mathit{mother}(\mathit{wife}(\mathit{father}(\mathit{my}))))). Inferences arise by substitution: With \mathit{Rosi} = \mathit{mother}(\mathit{Mary}) and \mathit{Tom} = \mathit{father}(\mathit{Rosi}) it follows that \mathit{Tom} = \mathit{father}(\mathit{mother}(\mathit{Mary})); with \mathit{grandfather_maternal} = \mathit{father}(\mathit{mother}) we can reduce the chain \mathit{father}(\mathit{mother}(\mathit{Mary})) and get \mathit{Tom} = \mathit{grandfather_maternal}(\mathit{Mary}). Such chains can be stored as assertions in the semantic graph and used for inference. The following section discusses how A-LLM helps to draw inferences.