Interesting question. "Ontology" is often used in confusing and polyvalent ways, so let's start by clearing up the terminology very quickly for those who aren't intimate with the various different meanings.

What does "ontology" mean?

Broadly, ontology the field is the philosophical study of being. An ontology is a method for establishing what beings or entities may exist (cf. epistemology's whether we should believe they exist), how they may be grouped, and the relations they may have.

In information and computer science, "ontology" is used in a related, but not identical sense to refer to formally defined sets of types, properties and the relationships between them. To answer your question, then, relations compose part of an ontology, but ontologies do not comprise sets of relations and nothing but sets of relations. From the Wikipedia page:

An ontology is a description (like a formal specification of a program) of the concepts and relationships that can formally exist for an agent or a community of agents. This definition is consistent with the usage of ontology as set of concept definitions, but more general. And it is a different sense of the word than its use in philosophy. -- Tom Gruber, Toward Principles for the Design of Ontologies Used for Knowledge Sharing.

_{(Gruber updated the definition in 2007, but it is not so much different as an extension.)}

Ontologies and ACT-R

ACT-R defines a basic ontology with the entities modules, buffers and pattern-matchers, ways to group entities within their type (e.g., perceptual-motor vs. memory modules), and the relations between them.

We use ontologies to abstract away from particular data structures. The ACT-R cognitive architecture both implies and specifies an ontology, and we can use that ontology to extend ACT-R, or make ACT-R talk to other architectures which may not have any data structure overlap with ACT-R. Oltramari et al. (2014) provides an apt concrete example. They coupled ACT-R to the SCOPE knowledge management system, where they use concrete information science ontologies in order to extend ACT-R to use abstract philosophical ontologies.

In general, ACT-R models only employ as much knowledge as required to perform well-defined cognitive tasks. By and large, they can be seen as “monadic” agents, whose knowledge bases are limited, partially reusable and sporadically portable across experimental conditions. On the contrary, in order to replicate high-level contextual reasoning and pattern recognition in humans, large amount of common-sense knowledge should be available to ACTR: to overcome these limitations, we propose to equip ACT-R with a specific module for processing ontologies [philosophical sense], i.e. semantic specifications of a given domain or application (Guarino, 1998) [information science sense], which are generally used in combination with inference engines for deductive reasoning. Since the ACT-R declarative module supports a relatively coarse-grained semantics based on slot-value pairs, and the procedural system is not optimal to effectively manage complex logical constructs, a specific extension is needed to make ACT-R suitable to fulfill knowledge-intensive cognitive tasks like context-driven spatial reasoning. Accordingly, we engineered an extra module as a bridging component between the cognitive architecture and an external knowledge-base system KBS, SCONE (Fahlman, 2006).

References

• Oltramari, A., Vinokurov, Y., Lebiere, C., Oh, J., & Stentz, A. (2014, March). Ontology-Based Cognitive System for Contextual Reasoning in Robot Architectures. In 2014 AAAI Spring Symposium Series.