In this contribution we extend an ontology for modelling agents and their interactions, called Ontology for Agents, Systems, and Integration of Services (in short, OASIS), with conditionals and ontological smart contracts (in short, OSCs). OSCs are ontological representations of smart contracts that allow to establish responsibilities and authorizations among agents and set agreements, whereas conditionals allow one to restrict and limit agent interactions, define activation mechanisms that trigger agent actions, and define constraints and contract terms on OSCs. Conditionals and OSCs, as defined in OASIS, are applied to extend with ontological capabilities digital public ledgers such as the blockchain and smart contracts implemented on it. We will also sketch the architecture of a framework based on the OASIS definition of OSCs that exploits the Ethereum platform and the Interplanetary File System.