SEMANTIC ANALYSIS OF CHISHOLM’S PARADOX Jan Broersen a Leendert van der Torre b a Universiteit Utecht, P.O. Box 80.089, 3508 TB, Utrecht b CWI, P.O. Box 94079, 1090 GB, Amsterdam Abstract 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. 1 Introduction Violation handling is a crucial problem in many applications, and its paradoxes have therefore 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, some sentence follows from another one, or some other anomaly occurs. Chisholm’s paradox [6] consists of the following four sentences. it ought to be that a certain man go to the assistence of his neighbours (1) it ought to be that if he does go he tell them he is comming (2) if he does not go then he ought not to tell them he is comming (3) he does not go (4) In traditional approaches to formalizing this example, see [15] for an overview, each sentence is repre- sented by a logical formula, and then either the set of sentences is inconsistent, one sentence follows from another one, or some other anomaly occurs. Therefore it is traditionally called a paradox. During the past decades, developments in temporal, action or non-monotonic logics have contributed to a better understand- ing of the paradoxes and thus of violation handling (we take violation handling here to be interpreted in a broad sense, encompassing conflict handling, exception handling, recovery from anomalous states, etc.). A disadvantage of starting with a logic to tackle the problem is that one cannot know beforehand whether the formalization of the example is going to be consistent. Another problem with the logical approach is that we cannot use modeling methodologies developed in conceptual modeling. Therefore, we propose to start by looking for a model on which all sentences can be interpreted. If it is possible to interpret the sentences of the scenario consistently, in the sense that we deal with an apparent paradox, then it should be possible to find such models. Then, if we study the meaning of the sentences in terms of logics interpreted on these models, we never end up in the situation in which our formalization is inconsistent. However, capturing the meaning of the sentences in an intuitive way is not the only criterion for a satisfactory formalization in terms of logical formulas. In addition we have to face the following two problems: on the one hand, we have to avoid unwanted consequences, and on the other hand, we