Rules and Their Logic
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My research on rules and logic was inspired by two sources of influence. The one source was my doctoral dissertation, which emphasized that many facts are reason-based, and supervene on other facts. There are layers of facts where facts in the lower layers are reasons for the existence of facts in the higher layers, and where the latter supervene on the former. The layers are connected by what I then called "nexus", and rules are an important kind of nexus. (Three other kinds of nexus would be causal laws, principles and goals.) The logic of rules is part of the logic of nexus (which, by the way, was never developed as such). This inluence of Feiten en betekenis brought about that the logic of rules was from the very beginning embedded in a logic of reasons.
The second source was traditional AI-research. In that setting it had become commonplace that ordinary (non-mathematical) reasoning is defeasible in the sense that conclusions that were properly drawn from a set of premises might have to be given up in the light of new information. The analysis of defeasible reasoning requires a non-monotonic logic and in the 1990s the search for suitable non-monotonic logics was a hot topic in AI-research. I soon realised that the logic I needed for rules should also be non-monotonic.
These ideas were at that time (the 1990s) still vague, but inspired me to combine insights from ethical theory, the theory of legal reasoning, and the work in AI on non-monotonic logics. As a result I tried to cast the insights from ethical theory and legal argumentation in the formal setting that non-monotonic logics inherited from what I now call classical logic (first-order predicate logic with identity). This "classical" inspiration explains my attempts in the 1990s to describe the logic for reasons and rules by means of a formalism that reminds of classical logic. Some of the main ideas are summarised in the following sections.
Rules have a conditional structure: they have a condition part and a conclusion (consequence) part. Normally, if a case satisfies the conditions, the rule consequence will hold in that case. This makes it seemingly attractive to treat rule application as an argument with the logical form of Modus Ponens (detachment). Take for instance the rule that car drivers must halt for red traffic lights. It is tempting to treat this rule as a conditional statement with as conditions that a person is a car driver and that some traffic light is red. The rule consequence (conclusion) then reads that this person must halt for that traffic light.
There are 'only' four issues:
To solve these isues with regard to the role of rules in rule-applying arguments, I decided to take a bold step. I would treat rules as logical individuals and would use a statement about a rule, namely the statement that the rule exists (is valid), as a premise for a rule-applying argument. To make this work, I also needed to distinguish between the applicability of a rule to a case (when the case satisfies the conditions of the rule) and the application of a rule to the case (when the rule attaches its consequence as a fact to the case).
Take the following argument:
The rule 'Car drivers must halt for red traffic lights' is valid.
Sheila is a car driver.
Sheila approaches a red traffic light.
Therefore: Sheila must halt.
This argument is not valid under classical logic, and to make it valid, it is necessary to adopt a logic that gives statements about the validity of rules a logical role. This different logic was to become Rule Logic.
During the 1990s, Rule Logic was just a part of RBL. Rule Logic as a special logic for rules only appeared in Chapter 3 of Studies in Legal Logic (2005) and even then not under a separate name. As far as I can remember, the name Rule Logic was only introduced in Deontic Logic for Lawyers (2025).
The basic ideas underlying Rule Logic are simple:
It is easy to see that Rule Logic allows exceptions to rules and is non-monotonic. An exception to a rule occurs if a rule is applicable to a case, but nevertheless does not apply to the case. An exception is not a reason why a rule does not apply, but merely shorthand for the situation that an applicable rule does not apply.
Rule Logic allows for rule application by analogy. This occurs if a rule is not applicable to a case, but there are nevertheless reasons why the rule should apply and these reasons outweigh the non-applicability as a reason against application.
Rule application by analogy is discussed in:
Whether a rule applies to a case depends on the balance of reasons for and against application. Balancing reasons is not a process or an act; it is a logical operation on two sets of reasons (the reasons for and against application) on the basis of a premise that states which set of reasons outweighs the other set. The reasons themselves are facts, expressed by true declarative sentences. They are not these sentences themselves; in this respect, RBL differs fundamentally from classical logic where premises and conclusion are all sentences (propositions).
Let us consider an example. Harry unlawfully broke the window of his neighbour's home by shooting a football through it. There is a rule stating that (s)he who unlawfully causes damage to somebody else must compensate the damage. However, Harry is only five years old and does not have the money for compensation. Does the rule apply to Harry's case, making Harry liable for damages?
Harry's case satisfies the conditions of the rule. (I ignore all interpretation issues to keep the example simple.) Because Harry's case satisfies the rule conditions, the rule is applicable to the case. The applicability of the rule is a contributory reason why the rule applies. However, Harry's young age is a reason why the rule does not apply to the case. Moreover, Harry's parents are liable and a double liability for both Harry and Harry's parents would be against the rule's purpose. The age and the rule's purpose give two reasons why the rule does not apply. These two reasons need to be balanced against the applicability of the rule as a reason for application.
It is not automatically so that two reasons outweigh a single reason, or that the applicability of a rule outweighs all reasons against application. It is necessary to take a decision on which set of reasons outweighs the other set. This decision takes the shape of an additional premise stating which set of reasons wins. If the applicability of the rule wins, the rule applies and Harry becomes liable. If Harry's age and the liability of his parents together win, the rule does not apply and there are no legal consequences from this rule.
Arguments in RBL do not necessarily deal with rule application. There can also be reasons for and against a conclusion that is not based on a rule. Take for instance a debate on whether a particular football match was a good one. There can be good-making reasons, as well as bad-making reasons, and the relative weight of these reasons determines whther the match was good or bad. Also here it holds that the determination of the reason set with the bigger weight takes the shape of a premises that answers precisely that question.
The determination of which set of reasons outweighs the other set finds its logical representation in a premise that answers the question. This premise can tself be the outcome of another argument. One case in point is that any non-empty set of reasons outweighs the empty set. For example, if there are reasons why this was a good football match, and no reasons why it was a bad match, it is easy to draw the conclusion that the former set outweighs the latter set, and then the follow-up conclusion that the football match was good.
Another example of reasoning about the relative weight of reasons is that, if it is given that the set of reasons {a, b, c} outweighs the set {p, q, r}, this is a reason why the set {a,b,c,d} outweighs the set {p, q, r}.
Sometimes it is possible to use a precedent to determine which is the stronger set of reasons. Suppose that, in some case, the court had to balance reasons. If we assume that court decisions have authority for future cases, the assignment of relative weights by the court is a reason to assign the same relative weight in future cases.
Reasoning about the relative weights of sets of reasons is discussed in:
After Dworkin made a fundamental distinction between rules and principles, legal theorists started to debate the distinction. According to Dworkin, rules and principles would have a similar structure, namely with a condition part and a consequence (conclusion) part. Their difference would be logical: rules would apply in an all-or-nothing fashion, meaning that their consequence would set in if their conditions are satisfied. On this view legal debates on the outcome of a cases are typically debates on how statutory and case law should be interpreted. With the interpretation the content of a rule is fixed, and given the logic of legal rules, as Dworkin saw it, the rest would be a simple Modus Ponens-style argument.
Dworkin was not very clear on whether rules really have this all-or-nothing logic. If they have, many things that are ususally called rules would not be rules after all because these would-be rules lack the logic of rules. Or, the idea that rules have an all-or-nothing logic is mistaken. Then there can be more rules than Dworkin might admit in first instance, but these rules would lack a clear logic. One way to interpret Rule Logic is as a way to provide Dworkin with the logic for rules that he needed (but never specified).
Principles would have a different logic. They also have a condition-consequence structure, but if the conditions of a principle are satisfied by the facts of a case, these facts would merely be a reason for the principle consequence to set in. If necessary, this reason should be balanced against reasons against the conseqence.
Alexy disagreed with Dworkin that legal principles have a condition-consequence struture. According Alexy, legal principles would be a kind of values or goals - he called them Optimierungsgebote - which should be realised to an extent as large as possible. However in determining what is possible. other factors may also play a role, and the interaction with these other factors involves balancing.
It does not matter very much who was correct in the debate on the structure of principles. The important point about which Dworkin and Alexy agreed is that the application of legal rules can be set aside by legal principles (and perhaps also other factors).
In his early work on practical reason, Raz introduced the notion of an exclusionary reason. In my, not so modest, opinion, the details of Raz's account were wrong, but the main idea was correct: there can be reasons that somehow set other reasons aside. Following Raz's terminology, these reasons may be called exclusionary reasons.
Rule Logic gives these exclusionary reasons a place as reasons against the application of an applicable rule. A reason against the application of a rule can be based on a Dworkin-style legal principle, but also on an Alexy-style principle, goal, value or even a human or fundamental right.
There were several publications that discussed the relation between rules, principles, goals, values, and fundamental or human rights:
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