Could law be written in formal logic?

Question

I essentially have two questions:

1. Could law be written in formal logic?
2. If that's indeed possible, should it be?

I see possible drawbacks being:

• Difficulty to express certain concepts, I can't exactly point out examples (if you can please do) but I'm guessing that should be the case, even with mechanisms like deontic logic.
• Unappealing and generally inaccessible to the public. But so is current law redaction and that could be avoided by having paired translations in clear natural language.

And possible benefits being:

• Represented in a stricter way, laws would be less prone to wrongful interpretations.
• Usage of computational tools to identify inconsistencies in legislation and trials.

Sorry if I got something wrong, I'm a real layman in logic and English is not my native language. Any contributions are very appreciated.

Answer 1

Yes, it has been done. I believe the first project of this kind was an attempt to render the British Nationality Act 1981 into formal logic, and specifically into the Prolog programming language. It was completed by a team of researchers at Imperial College in the 1980s. Communications of the ACM, May 1986, Volume 29, Number 5, pp. 370-385.

There were a number of difficulties.

• Statutes inevitably rely on background knowledge of legal terminology, principles and practice.
• Statutes can never cover all possible cases that might arise. This is why courts have to interpret the law. Typically within a few years of a new statute being passed a body of supporting case law will arise.
• Some parts of the statute were difficult to interpret, e.g. it contained counterfactual conditionals, which are notoriously difficult to evaluate.
• The law required reasoning about events and times, so it needed a temporal logic.
• Some of the reasoning is of a default nature, which required a logic that is non-monotonic and non-classical.
• The law permits the appropriate authority, the Home Secretary, to waive requirements.
• Under some circumstances, the law can have retroactive effects, which leads to very weird situations in which some proposition is true at a time t, but from a later perspective was not true at time t.

There has also been a fair bit of work within artificial intelligence to create knowledge based systems that can give legal advice, though that is not quite the same as actually writing out a statute in a logical formalism.

I would agree with you that the advantages of using formal logic at the time of drafting would include being able to quickly identify inconsistencies or difficulties in the interpretation. The drawback is that reading formal logic is not easy, and it would place a burden on courts and attorneys in understanding it. It is already not easy to understand 'legalese' and lawyers have to undergo considerable specialist education to grasp it. A formal logic representation of a statute would have to be just a tool, and not have the status of being the law itself. Then you would probably get lawyers arguing about whether the system correctly captures the meaning of the text.

Answer 2

No.

It's a large question, and the shortest coherent answer I can think of is that, while particular laws may be reducible to logical form, law itself cannot, for the simple reason that it must account for human behavior. Real law is riddled with expressions like "due diligence", "reasonable doubt", "appropriate action" that judges will tell you (and did tell me) plainly cannot be reduced to numbers: the classic example, which I heard from three different judges while on jury duty, is the case where forty thieves run into a barn, and when a posse of townspeople finally flushes them out, forty-one emerge, all of them claiming that (s)he had been asleep on the hay when a mob of thieves ran in. Each judge said that whether a 40:1 probability of guilt constituted reasonable doubt, or whether a smaller or larger number was necessary, was up to me, the individual juror.

I stopped sneering at (most) lawyers when I figured this out.

Answer 3

Precedent is going to be a problem

In law, previous decisions made in a case can influence the interpretation and function of a statute. Converting law into formal logic, therefore, involves working back through each relevant decision, piecing together precisely what has been indicated by the written legal code, and by the surrounding cases, and formalizing that as an unambiguous rule.

This might be possible, if, say, each case involved exactly one legal statue that was relied on, and if each previous case had been decided correctly, and if public views, morals and so forth had stayed precisely constant.

But, they don't. Lawyers love "even if" arguments ("my client was nowhere near the river in which the chemicals were poured, and even if he was, you can't prove that he poured the chemicals into it, and even if he did pour them into the river, this action is permitted under x statute, and even if all this is proven there's no way a reasonable person could have thought this action would destroy the local ecosystem") - so a case often hinges on a variety of factors.

Jury trial decided cases are even more complex - they hinge on the law, but also on the personal views of jurors. There's often reasonableness tests, (the famous "man on the clapham omnibus") - so in negligence cases, the jury is asked to rule if a "reasonable person" would have foreseen a hazard.

This can't be translated into logic - how would you go about defining a reasonable person? More importantly, a reasonable person would vary over time - a reasonable person of the early 20th century might view the inclusion of radium in face cream as fine, whereas to a 21st century person it'd be a horrifying piece of negligence.

Law is, frankly, a mess. But it's a mess because humans are messy. There are always exceptions, mitigating circumstances, and so forth.

Edit: to add my own "even if" argument - even if we build in precedent, we miss wider social and judicial things. For example, my current home country, the Netherlands. Famously, early legalizer of cannabis. Only, it never legalized it. Cannabis is still illegal. But, there is the "culture of tolerance" - the state has decided to not prosecute possession of weed and certain other drugs. It'd be almost impossible to capture this in a formal logic system that didn't, almost, encode the entire of the society in which the law is happening, but it has a major, profound effect on the legal system.

Answer 4

Most problems associated with the interpretation of law are not problems of logic, but problems of ambiguity. There are countless examples of laws that are drafted in ambiguous terms. For instance:

Planning law in the UK is riddled with terms that are open to interpretation. For example, certain extensions to houses are allowed if they are not 'forward of the principal elevation of the building', yet there are many buildings designed in such a way that none of their elevations can be singled out as being the principal one. Other examples are rules relating to 'material' changes of use, where, of course, the relevant planning act is completely silent about what counts as a 'material' change of use. Another is that 'horse grazing' is allowed on fields whereas 'horse keeping' requires planning permission, and neither grazing nor keeping are defined terms, so there are endless appeals and arguments.

Tax law in the UK specifies different rules for the employed and the self-employed, without defining what employment means. As a consequence, an army of advisers makes a living from arguing about what does and doesn't constitute employment (look up the term 'IR35' to see the length to which the tax authorities have had to go to try to draw a rough dividing line between employment and self-employment without ever achieving the kind of clarity that would be required to program a computer to adjudicate legal cases).

Therefore, even if you were to define laws in formal logic, you would not escape the problem of interpretation, which arises particularly where those drafting laws fail to anticipate all of the circumstances in which the law will apply and all of the ambiguities inherent in the words they use.

Answer 5

While one could codify a system of law using formal logic, I don't think it would be possible to codify a good system that way. No matter how much care is taken when trying to codify laws, situations will arise that were not anticipated. Although laws could be written in a manner that would address such situations unambiguously, that doesn't mean that it would handle such situations well.

Within the laws of the American Contract Bridge Leage (bridge referring to the card game), in addition to provisions that specify penalties for various infractions, is an overarching rule that says that players must not commit deliberate infractions even if the penalty is one they would be willing to accept, and that players who can be shown to have committed infractions deliberately may be subject to additional penalties at the tournament director's discretion. If the rules were to specify a particular means by which deliberate infringements could be demonstrated, and specific penalties to be imposed when they are, that would add additional requirements players would need to follow when committing infractions deliberately so as to avoid any unwanted penalties.

In practice, an important key to preventing people from "gaming" the system centers around the fact that people who might do so can't know the exact criteria by which their actions will be judged. Reducing laws to a formal system would make it possible for people to act in a manner which deliberately violates both the letter of the spirit of the law, but can't be proven to violate either.

Answer 6

See Catala a programming language for tax law based on default logic.

Because Napoleonic legal traditions don't rely on precedent as much as common law traditions and because tax law is limited in scope and you know about adding numbers up sure formal logic can be useful for reasoning about the law.

Relatedly France had a peculiar situation with cleaning up horrible legacy code the state used to calculate tax information. Some of the authors worked on cleaning this up a bit A Modern Compiler for the French Tax Code.

Answer 7

Could it? Yes. Would it look anything like what we have now or be practical? No.

It is definitely theoretically possible to write a set of laws using formal logic. As Bumble points out in his excellent answer, some attempts in that direction have even been made in academic circles.

However, such a system would look nothing like what we have now and an attempt to also have a plain language version would do nothing to cure the problem. Either the plain language version would control and no one would even pay attention to the formal version, or the formal version would control and anyone that needed a serious answer to a question for any practical purpose would have to ignore the plain language version.

Also, while Bumble gives an excellent answer, I think he dramatically understates the problems that would arise in practice from such an attempt.

Consider the heap problem. A lot of concepts that people in the real world including in legal situations are simply not well defined. For one example that actually comes up in the law somewhat often, the line between puffery and fraudulent false statements can sometimes be hard to draw. It is very difficult for formal logic to deal with things that are not well defined.

Related to, but separate from the problem of vagueness, the law frequently gives discretion to judges or certain administrative bodies. In fact, under some circumstances, the business judgment rule effectively recognizes discretion for the officers of private corporations. But discretion is difficult to fit into formal logic.

Then there is the difficulty in understanding. Most judges and lawyers do not have backgrounds in formal logic or mathematics. But worse than that, the law presumes that it can be understood by an average laymen. As a lawyer that frequently has to try to explain the law to laymen, I can attest that this is already very much a legal fiction. But despite what many people think, lawyers, judges, and legislatures generally do make an attempt to write in ways meant to be understood. This can be hard because we are dealing with inherently difficult topics, but believe it or not we usually try. While we could presumably build a society where lawyers and judges were educated in formal logic, doing so for the general public is unrealistic presently.

Finally, legislatures sometimes deliberately leave things vague because that is the only way to reach a compromise that can get the votes to pass. You could argue that is already a bug rather than a feature, but it does highlight how much even trying to do this would change the system and some of the practical problems it would create. Legislatures would become even more deadlocked than they are now if they lacked the ability to use vagueness to get things passed. (I realize this is in tension with my last paragraph, but to paraphrase Walt Whitman, "Do legislatures contradict themselves? Very well, they contradict themselves! They are large, they contain multitudes".)

Since I mentioned I'm a lawyer, I should say that I am only licensed in Nevada and nothing I say on Stack Exchange should ever be viewed as legal advice.

Answer 8

Could law be written in formal logic?

No, basically. I call attention to the same problem which most other answers have raised: ambiguity.

Most legal rules create a large statistical bell curve. On one end, the fact patterns produce an easy answer Yes. On the other, the fact patterns produce an easy No.

As one approaches the median, cases become harder. More people are likely to disagree. These cases are the judgment calls, and they are the reason we have judges and juries.

Take the example of murder. On the Yes side of the curve are the cases where someone kills an innocent person. On the No side are deaths occurring without significant intervention by a second person, notably accidents.

Then there is the difficult middle. Suppose the armed victim was burglarizing a house? Suppose the burglar was unarmed? Suppose the homeowner thought the victim was a burglar, but the decedent was just there to ask directions? Suppose the armed decedent ran from the yard, and the homeowner gave chase? Suppose the homeowner stopped the chase, but the decedent ran into the street and was hit by a car?

Murder? These are all questions on which reasonable people can and do disagree. I do not see the myriad nuances of human life being expressed in a formal logic.

Answer 9

I am neither a lawyer, judge nor philosopher. However, I have read the opinions of several people who were all three who would disagree with your reasoning as to benefits.

Specifically, is there such a thing as a wrong[ful] interpretation? I would assume that, "correct," (the opposite of wrong), to you, means, "that which makes sense to me as the interpretation of the law as written that I believe is the best."

In some legal systems, this is far from universal. Ambiguity, and sometimes even logical inconsistency, may be a desired trait in some laws. In other systems, the added inconsistency may be a product of negotiation between parties who aren't of exactly like mind.

Can it be done? Yes, this is answered widely and (please excuse the pun) beyond a reasonable doubt. Perhaps it is not something that is done frequently because the result does not provide much added value to the people writing the laws.

Answer 10

Oliver Wendell Holmes (1881):

The life of the law has not been logic: it has been experience. The felt necessities of the time, the prevalent moral and political theories, intuitions of public policy, avowed or unconscious, even the prejudices which judges share with their fellow-men, have had a good deal more to do than the syllogism in determining the rules by which men should be governed. The law embodies the story of a nation’s development through many centuries, and it cannot be dealt with as if it contained only the axioms and corollaries of a book of mathematics. In order to know what it is, we must know what it has been, and what it tends to become. We must alternately consult history and existing theories of legislation. But the most difficult labor will be to understand the combination of the two into new products at every stage. The substance of the law at any given time pretty nearly corresponds, so far as it goes, with what is then understood to be convenient; but its form and machinery, and the degree to which it is able to work out desired results, depend very much upon its past.

Answer 11

With all due respect, @Bumble (and all your voters), I find your answer radically wrong by multiple reasons.

From here on, I use the term formalism meaning formal expression, not as in QM, where the term implies a theoretical and philosophical account. From here on, I address the OP.

To start, logic is already expressed as a formal system (formal means founded on axioms/concepts with inferred theorems, using a formal language). The system of legal rules in books has not funny symbols like /forall or /iif, but it has exactly the same --and perhaps more appropriate-- relational elements between objects.

Perhaps you assume logic will provide a formality to law if it is expressed with FOL: wrong. Logic is already a formalism. A formalism is essentially something written with logical consistency. The informal expression of law is morals. You might think morals and laws are different in content, yes, that's true, but that is for pragmatic reasons. Laws tend to be equivalent to morals, but the process of formalizing morals is quite complex and subject to human errors and interests. Morals are the informal rules, law is the formal expression of morals.

Following, the legal formalism is not founded on logic (the formalism) but on the reason (the actual tool, the dynamics of thinking):

F(Law) ⊆ Reason

Switching to an alternative formalism, which depends on ANOTHER formalism (logic) implies introducing multiple complexities that I will discuss at the end, on my answer:

F(Law) ⊆ F(Logic) ⊆ Reason

Following, the obstacle is far from being what is presented as problematic in the answer:

Statutes inevitably rely on background knowledge of legal terminology, principles and practice.

That is not a problem. All language is based on "background knowledge of [legal LIFE] terminology, principles and practice". The application of propositional logic already implies a dependency on such background. This is not a problem of expressing law with logic, this is a problem of semantics.

My company once bought 70 printers that powered on at the tenth click of the ON button, and the contract didn't mentioned that, which is normal, nobody expects a statement about the "ON" button. Our lawyer said "sorry, contracts can't and don't describe all default facts" (yes, they tried to sell us refurbished material as new). We've got the money back, but not due to the contract: because it is a default fact of life: having a button implies pressing ONCE, not ten times. That's not a legal issue. That's a pure semantics problem, which was solved not by the lawyer, but by an IT guy.

Statutes can never cover all possible cases that might arise. This is why courts have to interpret the law. Typically within a few years of a new statute being passed a body of supporting case law will arise.

This is the same case, for a similar issue: all laws having the form forall x, x is A (e.g. all people having an income is subject to pay taxes). The problem is not logic, it is semantics.

Some parts of the statute were difficult to interpret, e.g. it contained counterfactual conditionals, which are notoriously difficult to evaluate.

Again, a problem of semantics. And if the statement is difficult to interpret, the problem is hermeneutics, not the use of logic.

The law required reasoning about events and times, so it needed a temporal logic.

This is not a problem of the application of logic to law. It is the natural consequence of any formalism: expressing empirical facts with a formal notation implies introducing dimensional resources that propagate to all result.

Some of the reasoning is of a default nature, which required a logic that is non-monotonic and non-classical.

This occurs not only in the case of laws, not even in any discipline, but in any possible rational judgement. All words in a dictionary are circular definitions. Their meaning comes from life experience. So, ALL terms used in traditional law or law expressed in FOL involve a lot of by default meaning.

The law permits the appropriate authority, the Home Secretary, to waive requirements.

In addition to by default hermeneutics, all logic, not only legal logic, is always applied in a context of conditions which include culture, tradition, morals, religion, beliefs, etc. This is not a problem of logic, but a problem of law.

Under some circumstances, the law can have retroactive effects, which leads to very weird situations in which some proposition is true at a time t, but from a later perspective was not true at time t.

This is exactly the previous case.

Now, my answer

Since law is already a formal system without funny symbols, I assume the question goes in the direction of expressing law using some sectorial formalism as first order logic.

Let's start with the problem of deepness, using simple FOL: to what extent of depth should law be expressed? In order to express the rule "all (P)eople getting an (I)ncome and is not payin(G) taxes should pay (T) them" we can use:

• T(x)
• ∀x(T(x))
• ∀x(I(x) → T(x))
• ∀x(P(x) ∧ ∃y(I(x, y) ∧ ¬G(x) → T(x)))
• ...

Sorry if any mistakes. Consider that:

• Case-1: the lesser the depth, the simplest the logical understanding and the heavier the semantics loads associated to each object, which implies an open and subjective interpretation.
• Case-2: the deeper the target, the lighter the semantic load associated with each term, while there is the need of a more strict and rigid / precise definition of the object.

The actual case, I mean, how law is expressed currently, corresponds to Case-1. Almost all laws can be expressed as A(x), which leaves to the legal domain the hermeneutics about the objects and properties, A and x.

In addition, such case, actually being applied, is another proof that law is already a formal system.

Your question suggests to switch to Case-2, which would imply (1) a huge effort (decades, probably) on finding precise object definitions and properties, and all such effort for what? Just (2) to express laws as extremely complex equations, only machines and experts would understand. This raises a new issue (3), which could be positive: in the process, such analysis and definition of rules would allow finding logical inconsistencies, and fixing them... implies changing the actual laws!

The marks (1) and (2) show the two NEGATIVE key points that emerge if legal rules are expressed using some type of logical formalism which is not the current one. The point (6) marks a POSITIVE aspect, while there are more.

So, my direct answer to can law be expressed using some sectorial formalism of logic? is yes, considering this pros and cons:

Disadvantages

1. A gigantic measure of complexity and effort to find precise definitions about objects and relations. Some terms that are generic and subject to open interpretation should be replaced by subclasses, according to strict taxonomies.
2. A lot of complexity in writing/expressing and reading/interpreting the rules. Now, lawyers should not only need years to study laws, but years to study the actual discipline that allows using the rules in court.
3. Applying law would not really be a matter of invoking rules, but to accept and verify that empirical facts correspond to legal objects (e.g. do you fulfill the conditions to be accepted as a (P)erson? who is not (D)educing your (T)axes? Are the 72 proofs provided valid?)
4. While perhaps more precise, legal services would be extremely costly to the citizen.
5. Such actual implementation would not prevent skipping the law, just by not marking a checkbox in a filling form, and perhaps would simplify finding and exploiting legal holes.

Advantages

6. Detecting inconsistencies in actual laws, which implies noticing and fixing them (changing current laws).
7. Trials would be simpler, online, lawyers would just introduce the facts as standard objects, and would invoke a law by its identifier. The judge application, equivalent to a PROLOG prompt, would just accept the objects and instantly compute the result and the sentence. Perhaps trials will disappear as such to become mobile phone applications where we just receive punishments sent by some computer server, which might replace the Judicial Power of the State.

All of this, considering that I've never been in court, don't know many lawyers, and spend my time walking without direction. Lawyers would surely find many more issues when introducing an additional formalism to law. Perhaps you should ask this in https://law.stackexchange.com/ including the link of this discussion, in order to find more legal perspectives, which might be quite interesting.

Answer 12

No, law cannot be written in formal logic.

You can read the rest if you wish to, because data is data, but i think this simple explanation that i have written after writing all that may just be it.

One thing to clarify, I am talking about formal logic specifically in terms of computer transferable, so maybe first order logic, as I am not up to know with my terms.

Formal Logic, as to my understanding, is the atom of the linguistic world. Because, it uses barely any linguistic inputs, it uses the simplest of terms that have from absolutely no to negligible ambiguities about them. And Law and language itself, are the cell, as they are made up of so many of these different words, which are not in the least standardised, for in our vain pursuit for simplicity, we try to fit as many nuancedly distinct spectral expressions as we can into one word.

Now, you cannot make the cell exist at the atomic level, because the cell is made of atoms, some along the vein of formal logic and others maybe not but, only atoms can exist at the atomic level, the cells are a product, not the basic raw material. This is an interesting concept that i believe as simple as it is a lot of humanity just does not use it as much. Comparatively, simplicity came first, jsut like numbers, it is clealry distinguishable. But we have not held language to the same standards as we have held mathematics to, and today even though the words joy and happy and feeling good are different things, the average human does not care to place them in their spetral order on the scale of happiness and according to my knowledge there are no active bodies trying to formalise words and their intensities of expression, in fact in todays society we are just moving further away from specificity of things.

I hope that answers your question.

This is the first answer below this paragraph. Coming from an interdisciplinary view, psychology has taught me that a single word could sometimes unlock the thread of understanding and that word varies for different people, so i like to make map my whole thinking process in words, even though i am aware of that not being an acceptable behaviour on these sites, i believe data is data and it can always help to just have more of it.

Formal logic at it's essence is linguistic simplicity. Words that have either no ambiguity about them and/or are just connectional are the ones used. Or the use of symbols to eliminate ambiguity, which means you are eliminating as many factors as you can so you can get the absolutely simplest form.

Real Language is a soup. A form of communication started by beings extremely disparate to us in knowledge. and thus the words have jsut come out so, an extreme mess. Language itself is undefined, if you look at English, it just does not have any rules that ground it, even for the grammar used. How can you capture a chaotic and complex system that is undefined into a production, a creation. Computers are not humans, and they need everything to be taught to them, unlike human kids, who just copy what they see, because they already have the framework to do so, and we have yet to cognize all these frameworks.

Once we do so, we can then complicate the systemic nature of the computer to go from absolute simplicity to being a complicated one, and then, it could start distinguishing between certain things, but even then, we would need to ground language into chains or rules, and we would need to introduce millions of new words, each specific to a scenario, so as to grant it the ability to distinguish. The more words we have in that manner, the better. As you can see these principles are the same as in the development of computer encoding, we went from ASCII to Unicode to UTF-8 and as we progressed we just made room for more information to be processed. While I cannot at the moment cognize the exact similarities between these analogies of the computer character encoding development and how the human language needs to develop too, as i studied that a long time ago and it is not fresh, i just think that it is absolute vanity to even try to do such a thing at the most basic level.

And to continue the atom cell analogy, we are creating a cell out of the computer world, artificial intelligence and specifically OpenAI and these recent developments, are just steps in that direction. So it is possible to computerise law, it is absolutely possible, at first we will face problems, but each problem would only need to be solved once, like case law. But this would be better than case law.

P.S:

The trouble with the ''British Nationality Act 1981'' is that the pursuers failed to cognise the simple differences in terms of levels of complexity between the two things, which i believe, is a fault of the excitement of the purusit which may have overpowered their reason to forego basic observations, or limited their powers on basic observations. A true shame.