A logical reasoning with preference

In a decision making context, multiple choices of actions are usually ooered to solve a particular problem. Consequently, the question of preferences among the actions will occur. The ordering of recommended actions by preference is made by taking into account the states of the universe of discourse. We develop here a logic L p for reasoning about preferences in such circumstances. The language of the logic is propositional extended with a special binary relation of preference among formulae. The model theory of the logic is studied and the soundness and completeness theorem is established. 1 L p informally The study of concepts in which moral philosophers take an interest is categorized by von Wright 4] into three groups: deontological, value-concepts and anthropological. The notion of preference or betterness belongs to the group of value-concepts and holds a prominent place in decision making context. There are several application domains where preference need to be represented, for example, medicine and economics. In particular, in oncology there are preferences which if contravened may rise hazardous situation, for example, there is a preference to administer the drug taxol before cisplatin than after in the treatment of cancer 3]. Therefore, a formal study of preference is recognised as an important goal yet to be attempted. To achieve this we construct a formal logic of preference in this paper. There are several types of preferences that are relative to state or circumstances. For example, in the treatment of deep-vein thrombosis, preferring subcutaneous administration of heparin to intravenous administration is a preference between two diierent kinds of action. On the other hand, preferring health to illness is a preference between two properties. Considering the importance of actions and properties in the context of preference, we study them rst 1