Using Intuitionistic Logic as a basis for Legal Ontologies

Classical Description Logic has been widely used as a basis for ontology creation and reasoning in many knowledge specific domains. These specific domains naturally include Legal Artificial Intelligence. As in any other domain, consistency is an important issue for legal ontologies. However, due to their inherently normative feature, coherence (consistency) in legal ontologies is more subtle than in other domains. Consistency, or absence of logical contradictions, seems more difficult to maintain when more than one law system can judge a case. This is called a conflict of laws. There are some legal mechanisms to solve these conflicts, some of them stating privileged fori, other ruling jurisdiction, etc. In most of the cases, the conflict is solved by admitting a law hierarchy or a law precedence. Even using these mechanisms, coherence is still a major issue in legal systems. Each layer in this legal hierarchy has to be consistent. Since consistency is a direct consequence of how one deals with logical negation, negation is also a main concern of legal systems. Negation and subsumption play a central role in ontology coherence. An adequate intuitionistic semantics for negation in a legal domain comes to the fore when we take legally valid individual statements as the inhabitants of our legal ontology. This allows us to elegantly deal with particular situations of legal coherence, such as a conflict of laws, as those solved by Private International Law analysis. This paper briefly presents our version of Intuitionistic Description Logic, called iALC for Intuitionistic ALC (ALC being the canonical classical description logic system). We also discuss the jurisprudence foundation of our system, and show how we can perform a coherence analysis of “Conflict of Laws in Space” by means of our system iALC. This