Semantic Analysis of Chisholm's Paradox

Violation handling is a crucial problem in many applications. therefore its paradoxes have been studied in, amongst others, artificial intelligence, agent theory and computer science. The standard way to study these paradoxes is to model them using a formal language, and use formal logic to consider whether the set of sentences is inconsistent, the sentences logically follow from others, or some other anomaly occurs. During the past decades, developments in temporal, action and non-monotonic logics have contributed to a better understanding of the paradoxes and thus of violation handling. In this paper we propose an alternative way to analyze Chisholm’s notorious contrary-to-duty paradox in deontic logic. We model the paradox using semantic models, using insights from conceptual modelling. We aim to gain insight in the open question whether the paradoxes are in some sense logical contradictions, or only apparent contradictions. If a paradox is only an apparent contradiction, then there has to be a model interpreting all sentences.