Count-As Conditionals, Classification and Context

Searle represents constitutive norms as count-as conditionals, written as ‘X counts as Y in context C’. Grossi et al. study a class of these conditionals as ‘in context C, X is classified as Y ’. In this paper we propose a generalization of this relation among count-as conditionals, classification and context, by defining a class of count-as conditionals as ‘X in context C0 is classified as Y in context C’. We show that if context C0 can be different from context C, then we can represent a larger class of examples, and we have a weaker logic of count-as conditionals. 1 Count-as conditionals, classification and context Searle [7] argues that there is a distinction between two types of rules. “Some rules regulate antecedently existing forms of behaviour. For example, the rules of polite table behaviour regulate eating, but eating exists independently of these rules. Some rules, on the other hand, do not merely regulate an antecedently existing activity called playing chess; they, as it were, create the possibility of or define that activity. The activity of playing chess is constituted by action in accordance with these rules. The institutions of marriage, money, and promising are like the institutions of baseball and chess in that they are systems of such constitutive rules or conventions” ([7], p. 131). For Searle, regulative and constitutive norms are related via institutional facts like marriage, money and private property. They emerge from an independent ontology of “brute” physical facts through constitutive rules of the form “such and such an X counts as Y in context C” where X is any object satisfying certain conditions and Y is a label that qualifies X as being something of an entirely new sort. E.g., “X counts as a presiding official in a wedding ceremony”, “this bit of paper counts as a five euro bill” and “this piece of land counts as somebody’s private property”. Regulative norms refer to these institutional facts. E.g., consider a society which believes that a field fenced by an agent counts as the fact that the field is the agent’s property. The fence is a physical “brute” fact, while being a property is an institutional fact. Regulative norms forbidding trespassing refer to the abstract concept of property rather than to fenced fields. Grossi et al. [4] study the relation between on the one hand countas conditionals and on the other hand classification and context. They formalize a class of count-as conditionals as contextual classifications, and thus do not claim that all count-as conditionals can be represented in this way. Roughly, as we understand it, their idea of classification is that X and Y are interpreted as sets (of facts, objects, 1 Dipartimento di Informatica Università di Torino Italy. E-mail: [email protected] 2 Department of Computer Science, University of Luxembourg. E-mail: [email protected] events, actions, etc) and that ‘X is classified as Y ’, or ‘X is-a Y ’ for short, is interpreted as ‘the set of interpretations of X is a subset of the set of interpretations of Y ’. Thus, classification is the is-a relation frequently studied in conceptual modeling, for example as a subsumption relation in type theory, or as a T-Box expression in description logics. Moreover, Grossi et al. use modal logic to represent their count-as conditionals as contextual classifications. They represent X and Y as propositions, and the context as a modal operator (to be precise, as a particular kind of KD45 modality). Roughly, representing the classification relation as a material implication ‘X → Y , they propose the following definition. ‘X counts as Y in context C’ is represented by [C](X → Y ). For example, consider a regulative norm stating that vehicles are forbidden in the park, and the constitutive norm ‘bicycles count as vehicles in the park’. This count-as conditional classifies bicycles as vehicles in the context of being in the park, and can be formalized as [park](bicycles → vehicles). The logic of Grossi et al. turns out to be much stronger than other logics of count-as conditionals, such as the one of Jones and Sergot [5]. In Jones and Sergot’s study of count-as conditionals, the logic of count-as conditionals is very weak. It just satisfies replacements of logical equivalents, left disjunction and right conjunction. Moreover, they are inclined to accept transitivity. In addition, the logic of Grossi et al. satisfies, for example, reflexivity and contraposition. We believe that there are two important advantages in representing count-as conditionals as contextual classifications. The first advantage is that it may help to better understand constitutive norms. Defining count-as conditionals as contextual classifications might lead to a more precise characterization of count-as conditionals – though it will not cover the whole class of count-as conditionals. The second advantage of defining count-as conditionals as contextual classifications is that it may help us to understand how countas conditionals are related to regulative norms like obligations and permissions, which is one of the main open questions in normative systems. Since regulative norms can be defined as classifications of behaviors in obligatory, permitted and unnormed ones, count-as conditionals as contextual classifications may explain this relation. Given these two advantages, we are interested in generalizing the class of count-as conditionals that can be considered as contextual classifications. One reason to look for generalizations is that the formalization does not seem to take Searle’s distinction between brute and institutional facts into account. For example, since X are brute facts and Y are institutional facts, this distinction may suggest that X and Y themselves refer to distinct contexts. Another reason is that it does not seem straightforward to represent examples. For example, what is the context in “this bit of paper counts as a five euro bill” or in “this piece of land counts as somebody’s private property”?