1. Pure Theory of Law and Logical Jurisprudence --Focusing on “Basic Norm”--
2002/12/16 at MGU
Workshop on Kelsen’s Basic Norm
Hajime Yoshino
Meiji Gakuin University, Tokyo

2. Contents 1 Introduction 2 What is Logical Jurisprudence (LJ)
3 Theory of Legal Sentence
4 Comparison of the starting points of LJ with Pure Theory of Law (PL)
5 On Theory of Legal System (related to ‘Basic Norm’)
6 Demonstration of the availability of LJ on Systematization of CISG
７ Conclusion

3. 1 Introduction
Hans Kelsen’s final purpose in his “Pure Theory of Law (PL)” is to establish a scientific of law.
This enterprise has --perhaps more-- importance in the present world. We should receive his torch and carry it further. He might, however, have some limitations.
If so, we should overcome them and develop a new, true scientific of law.
I have attempt to make such a scientific theory of law since That is “Logical Jurisprudence (LJ)”.
In this paper, I would like at first to explain what LJ is.
Then, I will compare the starting points of LJ with those of PL.
On these basis, I would like to clarify what are to be “basic norms” from view point of LJ comparing with my concept with Hans Kelsen’s.
I will demonstrate the “basic norms” in the legal system of CISG (United Nations convention on contracts for the international sale of goods).
I conclude this paper suggesting our further discussions.
According to my opinion, Hans Kelsen’s final purpose in his “Pure Theory of Law (PL)” is to establish a scientific of law, whose task is merely to cognize law . He says for example: “It is called a “pure” theory of law, because, because it only describes the law.” (p.1; jp.11)
This enterprise still has--perhaps more-- importance in the present world. We should receive his torch to establish a science of law and carry it further.
PL might, however, have some limitations.
If so, we should overcome them and develop a new, true scientific of law.
I have attempt to make such a scientific theory of law since That is “Logical Jurisprudence (LJ)”.
In this paper I would like at first to explain what LJ is, presenting primitives of the theory and comparing the starting points with that of PL.
I would like to then discuss the theses of LJ in terms of theory of legal sentence, legal reasoning and legal system, occasionally comparing them with those of PL.
I will demonstrate the availability of JL to realize real legal reasoning on the platform of LES-5, which is a legal expert system developed by me..
I conclude this paper suggesting our further discussions.

4. 2. What Is Logical Jurisprudence (LJ)
Logishe Rechtslehre in German
A developed form of “legal logic” (Juristische Logik)
It is not merely an application of logic to law but also a scientific theory of law to establish the true science of law.
Logical Jurisprudence has been developed through the construction of LES-5, a legal reasoning system in the field of CISG (United Nations convention on contracts for the international sale of goods).
Naming LJ is done by Hajime Yoshino.
What is logical jurisprudence.
LJ is: Logishe Rechtslehre in German
A developed form of “legal logic” (It was called as Juristische Logik)
It is not merely an application of logic to law but also a scientific theory of law to establish the true science of law.
Logical Jurisprudence has been developed through the construction of LES-5, a legal reasoning system in the field of CISG (United Nations convention on contracts for the international sale of goods).
Naming LJ is done by Hajime Yoshino.

5. Primitives of LJ
LJ try to explain the whole legal system using minimum elements.
LJ starts form three primitives:
(1) “sentence,”
LJ consider that norm as a meaning does not exist.
LJ starts from sentences.
(2) “validity” of sentence
legal validity as legal truth
“is_valid(sentence1, goal1,time1)”
(3) “inference rule.”
Modus Ponens: （（A ⇒Ｂ）＆Ａ） ⇒Ｂ
LJ try to explain the whole legal system from minimum elements as physics did. It starts from three primitives: “sentence,” “validity” of sentence, and “inference rule.” Logical Jurisprudence attempts to explain the law using these three notions as much as possible.
Logical Jurisprudence starts form “sentence”. LJ does not start form “legal norm” as a meaning like PL. LJ deny the existence of “legal norms as a meaning,” which has traditionally been admitted or presupposed in legal studies and practice. Sentences exist, as a form of written or spoken sign, cognizable or perceptible and therefore communicable. In my opinion, legal norms as a meaning belong to the world of images of interpreter of the sentence. It is what one imagined when legal sentences are thought of. Logical Jurisprudence considers sentences in the field of law as the direct and sound object of legal recognition.[1]
The second basic concept in Logical Jurisprudence is “validity” of a legal sentence. The validity of a legal sentence is viewed by Logical Jurisprudence as a “truth in the logical sense “. That a legal sentence is valid means that the sentence is true in the legal discourse, i.e. legally true. Logical Jurisprudence represents this legal truth by means of a predicate (e.g., this: “is_valid(sentence1, goal1,time1)”. This could be read: “a sentence1 is valid for a goal1 at time1.” The representation of the validity concept by a predicate is characteristic of Logical Jurisprudence that corresponds to the natural language representation of knowledge in the real legal world.
The third basic concept in Logical Jurisprudence is the “inference rule”. The logical correct reasoning is based on inference rules. The main inference rule is
Modus Ponens which is represented in this schema. Here A and B express propositions:
( A ⇒ B ), A ⇒　B
This formula is to be read: If ‘if A then B’ is true and A is true, then follows: B is true. Modus Ponens is the basic reasoning schema legal justification as discussed later.
[1]The difference between conventional and legal sentences and how these differ is discussed in section later.

6. 3 Theory of Legal Sentence in LJ
LJ starts from legal sentences.
What kind of legal sentences are there?
A legal system is to be analyzed and constructed in terms of three types of alternative fundamental concepts of legal sentence:
1) (Legal) rule sentence and (Legal) fact sentence
2) object sentence and meta sentence
3) element sentence and complex sentence
Existence of an obligation and the validity of the legal object sentence (Fig.2)
LJ starts from legal sentences. A legal sentence is a sentence used in law.
What kind of legal sentences are there?
In LJ, a legal system is to be analyzed and constructed in terms of three types of alternative of fundamental concepts of legal sentence.
1) (Legal) rule sentence and (Legal) fact sentence
2) object sentence and meta sentence
3) element sentence and complex sentence
LJ explains the existence of an obligation in terms of the validity of the legal object sentence.
I would like to make these more clear below.

7. Legal rule and fact sentences
Legal rule sentences:
“∀X{a(X) ← b(X)}”.
legal consequence ←legal requirement
“∀X{become_effective(offer(X,A),T) ← reach(offer(X,A),offeree(B,X),T)}”
Legal fact sentences:
“b(x1)”.
reach(offer(o1,anzai),offeree(bernard,o1),4_05).
First, it is important to distinguish between legal rule and fact sentences.
Legal rule sentences have the these syntactic form: “∀X{a(X) ← b(X)}”. This formula is read: “For all X, X is a, if X is b”. The consequence of the sentence, which is the formula at left in the implication, is called a “legal consequence” and the antecedent, which is the formula at right, is called a “legal requirement.” For example: “if an offer reaches to offeree, then the offer becomes effective.” Here it is to be noted that the connection between a legal requirement and a legal consequence is expressed merely by means of material implication. To this connection, LJ considers, it is not necessary to give a special philosophical meaning like Kelsen’s imputation (Zurechnung)
Legal fact sentences have the following syntactic form: “b(x1)”, read: “x1 is b”. For example: “Anzai’s offer reached offeree Barnard on April 5th.
It is to be noted that the difference between legal rule sentence and legal fact sentences is, in Logical Jurisprudence, purely syntactic, as mentioned above. The difference has no philosophical meaning.
LJ does not agree with methodological dualism in terms of norm and fact or ought and is, what Kelsen stand for.

8. Legal elementary and complex sentences
Elementary legal sentence
the smallest unit of legal sentences.
“One must drive a car under 100 km /hour on a highway”
Complex legal sentence
A group of legal sentences, which has an unique name
“The United Nations Convention on Contracts of the International Sale of Goods”
a code, parts or sections or an article of the statute
The concept of a complex legal sentence enables us to treat the validity of legal sentence at once.
Secondly, legal sentences are to be classified in terms of elementary sentences and complex legal sentences.
A elementary sentence is the smallest unit of legal sentences.
Statutes or contracts are composed of elementary legal sentences,
e.g., "one must drive a car under 100 km /hour on a highway” or
A complex legal sentence is a group of legal sentences, e.g.,
“the United Nations Convention on Contracts for the International Sale of Goods,” or
“a contract for sale of a farming machine between A and B on October ”
Not only a code, but also parts or sections or an article of a statute can be a complex legal sentence.. In most cases, the fact that a certain legal sentence belongs to a complex legal sentence is represented by the place and the space where they are printed. The relationship is represented in Logical Jurisprudence by a sentence describing the united relationship of grouped sentences.
The concept of a complex legal sentence enables us to treat the validity of legal sentences at once. Namely, if one has described the validity of a complex legal sentence then all legal sentences that belong to it have been regulated at once in that they are valid. The advantage of the complex legal sentence is that it contributes to producing economical description.

9. Legal object and meta sentences
A legal object sentence describes an object.
The object in law is the obligation of a person
“B must pay A the price of $10000”
A legal meta sentence describes about a legal sentence
It describes the validity of a legal sentence.
“”B must pay A the price of $10000” is valid”.
“(1) This Convention applies to contracts of sale of goods between parties whose places of business are in different States : (a) when the States are Contracting States; or … ”
It is also important to distinguish between legal object sentences and legal meta sentences.
A legal object sentence describes the object itself. In the legal domain, the object is an “obligation”. Legal object sentences prescribe the obligations of a person.
Sentences such as “one must drive a car under 100 km /hour on a highway” and “B must pay A the price of $10000” are legal object sentences.
The obligation is described in object sentences using a normative predicate such as, “must”, “ought”, “obligatory”, “have obligation”, and so on.
A legal meta sentence describes a legal sentence. More precisely, it describes the validity of a legal sentence. Some legal meta sentences describe the validity of legal meta sentences. An example of a legal meta sentence is: “(1) This Convention applies to contracts of the sale of goods between parties whose places of business are in different states: (a) when states are contracting states; or … ” (Article 1 of the CISG).
There is also a legal meta sentence which describes about the validity of a legal meta sentence.

10. 4 Comparison of the starting points of LJ with Pure Theory of Law (PL)
Norm as a Meaning
Legal Norm[1]
Fact as an entity
Norm as special meaning
Imputation (Zurechnung)
Legal Positivism
Primary Norm and Secondary Norm
Basis of Validity: Issued on the basis of Upper Norm
Theory of Hierarchical Structure of Law
Basic Norm LJ
Sentence as a sign
Law Sentence
Fact as a form of sentences
Rule as a form of sentences
Material Implication
Scientific Positivism
Object sentence and meta sentence
Basis of Validity: Logical Proof through Legal Meta Inference
Theory of Legal Meta Rules and meta inference
????
Pure Theory of Law (PL) starts for a norm as a meaning, while LJ starts from a sentence as a sign .
In PL, “legal norm” is kernel concept, while in LJ “law sentence” or “Legal Norm Sentence”.
[1] Kelsen says: “By “norm” we mean that something ought to be or ought to happen, especially that a human being ought to behave in a specific way.” The legal norms, which make certain acts legal or illegal are the objects of the science of law. (p.4; jp.19)
According to LJ legal norm as a meaning does not exist as an entity, but belongs to image world of the interpreter as described above.
The “imputation (Zurechnung)”, which connect a legal requirement with a legal effect, an essential concept of PL, while in LJ the connection is expressed by means of “material implication” in logic.
PL stands for Legal Positivism, while LJ scientific positivism.
The systematization of law in PL is based on hi alternative concepts of legal norm: primary norm and secondary norm. (In PL, the former is norm of compulsion and the later is norm of action.). The systematization of law in LJ is based on my alternative concepts of object sentence and meta sentence, which will be explained just later.
In PL, the basis of the validity of legal norm is that it is issued on the basis of upper norm, while the basis of the validity of a legal sentence is that it is proved through legal (meta) inference.
PL developed the theory of hierarchical structure of law, while LJ developed the theory of Legal Meta Rules.

11. 5 Theory of Legal System in LJ
The law requires a legal system as a deductive system so that a judgment is justified from the legal system together with the relevant facts of a event.
How legal order is to be systematized as a deductive system, that has been a target of legal philosophical studies.
LJ analyze and construct a legal system in terms of above three primitives including three types of alternative legal sentence.
LJ succeeded in demonstrating the legal system as a deductive system on those basis.
Thereby, the concept of validity of legal sentences and legal meta inference play a important role.
The final target of legal reasoning is to prove the validity of object sentences, to identify what kind of sentences describing obligation are valid.
On the way, sentences expressing various legal state of affairs are to be proved valid as well.

12. 5.1 Legal meta inference
Legal sentence, which is applied to solve a problem, is to be valid. In other words:
Only valid legal sentence can be applied as the premises of the legal inference.
The inference, which decide whether the legal sentence applied is valid, is called legal meta inference.
In the legal meta inference, legal meta rule sentences are applied.

13. 5.2 The validity relationship between legal sentences
The validity of a legal object sentence is based on the description of the validity in the legal meta sentence.
The validity of this legal meta sentences is prescribed by other legal meta sentences.
A legal meta sentence that prescribes the validity of a legal meta sentence can be called a higher or upper level legal meta sentence.
The highest, final level of legal meta sentence can be called a “basic” legal meta sentence.
The validity of the final, highest legal meta sentence is to be set as fact.[1]
In the statistic aspect of law, PL clarified, the validity relationship between legal norms. It reached to the theory of hierarchical structure of law. Then, how LJ can analyze and explain validity relationship between legal sentences.
LJ analyzes and explains the validity relationship in term of legal meta sentences.
The validity of legal sentences is prescribed by legal meta rule sentences.
The validity of a object sentence is prescribed by a legal meta rule sentences.
The validity of legal meta sentences that describes the validity of legal object sentences is prescribed by other legal meta rule sentences.
A legal meta sentence that prescribes the validity of a legal meta sentence is called a higher or upper level legal meta sentence. The validity of each legal meta sentence is prescribed by a higher level of legal meta sentence.
The highest, final level of legal meta sentence could be called a “basic” or “fundamental” legal sentence. The validity of the final, highest legal meta sentence is to be set as a fact[1]
[1] Cf. Kelsen 1960, p.109. He proposed the concept of “basic norm (Grudnnorm)”. It is to be noted that my basic legal rule sentence does not always coincide with Kelsen’s conception. They differ in the following points: Kelsen starts on legal norms as a meaning, while I start on legal rule sentences; Kelsen’s basic norm is conceived of as a norm which gives the ground of the validity of constitution or convention as a given positive law, while my theory presents not only such a basic legal rule sentence but also fundamental rules which are always applied at any case where the validity of a legal sentence is to be decided. This has become the case of our logical analysis of legal system and legal reasoning.

14. 5.3 “Basic norm (BN)” or Basic and Fundamental Legal Meta-Sentences
LJ agrees with Kelsen partially as far as BN is necessary and it should be presupposed.
In PL: BN is expected to has a function to found the objective validity of positive order.
BN is, however, not sufficient as a cognitive scheme to systematize law in terms of the validity.
LJ insists that, besides BN, fundamental legal meta-sentences are to be presupposed to systematize law logically.

15. The most fundamental Legal meta rule sentence
(mrl):
A legal sentence S is valid for a goal G at the time T ←→
S becomes valid for G at time T1 before T &　
not(S is terminated for G after T1 and before T).
This is a fundamental legal meta rule sentence implicitly taken for granted all　regulations.
The validity of this rule sentence is presupposed in a form of a fact sentence:
(mf1):
mr1 is valid.
All other (positive) legal rule sentences regulate the fulfillment of the first requirement (S becomes valid) or the second requirement (S is terminated) of the above rule sentence.
The following fundamental legal meta rule sentence is valid to confirm that legal sentences are valid[1]:
(mrl) "A legal sentence S is valid for a goal G at the time T if and only if S becomes valid for G at time T1 before T and S is not terminated for G after T1 and before T."
This legal rule sentence cannot be found as a statutory text in any legal regulation. This is a fundamental legal meta rule sentence implicitly taken for granted by all regulations. Without this rule, no statutory legal sentence works when it comes to application. This rule is the most fundamental among legal meta rules enabling us to put a mere collection of legal sentences into a legal system. This rule is applies to every case where the validity of legal sentences is considered.
All other (positive) legal meta rule sentences regulate the fulfillment of the first requirement (S becomes valid) or the second requirement (S is terminated) of this rule.
The validity of this fundamental legal meta rule is presupposed. In the CISG knowledge base a sentence which describes this validity is set as a legal fact sentence.

16. Meta rule sentences prescribing “a legal sentence becomes valid”
The rule which decide the first requirement of the fundamental meta rule.
The accrual of validity of a complex legal sentence follows the accrual of validity of elementary legal sentences which belong to it.
(r01)
become_valid(ES,G,T) <-
element_complex_sentence(ES,CS)&
become_valid(CS,G,T)
At first I explain the rule which decide the first requirement of the fundamental meta rule

17. The accrual of the validity of a legal object sentence by exercising the right
(3AA2)
"A legal sentence 'X has an obligation to do Z' becomes valid at time T” <-
“Y requires X to do Z at time T “ &
“a legal sentence 'Y has a right to require X to do Z' is valid.”
Sentences describing rights is not a legal object sentence but a legal meta rule sentence.
This is a new understanding the relationship between right and duty.
Logical Jurisprudence does not consider sentences describing rights as a legal object sentence as in the prevailing opinion in legal theories, but as legal meta rule sentence.
This is a new understanding the relationship between right and duty.
That a person has a right to require another person to do Z, for example, means, in our opinion, that the person may issue a legal object sentence for the other person concluding that he is obligated to do Z.

18. Meta rule sentences prescribing “a legal sentence is terminated”
These decide the fulfillment of the second requirement of the fundamental meta rule.
(02)
The validity of elementary legal sentence is
terminated if the complex legal sentence is
terminated.
(mr4b)
The validity of elementary legal object sentences is
terminated when the obligation, which it describes,
is fulfilled.
Secondly I explain about the meta rule which decide the fulfillment of the second requirement of the fundamental meta rule.
I introduce you two meta rules:
(02)
The validity of elementary legal sentence is terminated if the complex legal sentence is terminated.
Complex legal sentences lose their validity on the day when a fixed term is expires, when the termination condition is met or when contract avoidance becomes effective.
(mr4b)
"The validity of elementary legal object sentences is terminated when the obligation which it describes ,is fulfilled."
For example, an object sentence which prescribe “it is obligatory for A to deliver the goods” is terminated when the goods is delivered.

19. ６ Demonstration of the availability of LJ on Systematization of CISG
I would like to demonstrate the availability of LJ to systematize law in terms of validity of legal sentences on an example of CISG.
The systematization of contract law is realized in LES-5. It has the legal knowledge of contract law and the CISG (United Nations Convention on Contracts for the International Sale of Goods.)
It can infer the result of the application of the CISG to a certain concrete case. It can explain the process of inference and the reason. It can show the logical structuer of legal knowledge.
LJ has provided the theoretical basis of the analysis of legal knowledge and the construction of the knowledge base.
The LES-5 might prove the availability of LJ.
Go to demo on off-line;

20. Systematization of CISG in terms of the validity of legal sentences
1 Problem: case 8f
2 Resolution:
3 Inference to deduce the changes of the validity of legal (object) sentences
4 Meta-inference to deduce the validity of legal meta rule sentences, which apply to solve the problem.
5 Functions of fundamental rules sentence and basic rule sentences

21. 1 Problem: case8f
1. On April 1, a New York manufacturer of agricultural machines, A (Anzai), dispatched to the Hamburg branch of a Japanese trading company, B (Bernard), a letter containing the following proposal: A will sell B a set of agricultural machines comprised of a tractor and a rake; the price of the tractor is $50,000; A will deliver the machinery to B by May 10; B must pay A the price of the machinery by May 20; the machinery will be transported by an American frieght vessel. 2. The proposal reached B's letter box on April On April 9, B telephoned A and said, "I accept your offer. However, I want the machinery transported by Japanese container ship." 4. A delivered the agricultural machinery to a Japanese container ship at the port of New York on May The machinery was delivered to B's Hamburg branch on May B examined the machinery on June B paid A $58,000 on May 20. (The market price of the rake was $8,000). 8. On August 10, the machinery malfunctioned because of a defective connecting gear. 9. B notified A of the malfunction immediately. 10. On September 1, B demanded that A repair the lack of conformity within one month. 11. A did not repair the defect by October On October 10, B declared the contract avoided. 13. On December 10, B made restitution of the machine to A. 14. On december 20, A made restitution of the $58,000 price to B, plus interest, and gave compensation for damages B had suffered.

22. 2 Resolutins

24. 3 Inference to deduce the changes of the validity of legal (object) sentences

27. Basic legal rule sentences presupposed
(blr1)
States may conclude any convention according to their agreements.
(blr2)
States may set articles on conditions of its validity or effective date and terminative date into the convention.
(3AA2_1)
IF X may set the legal sentence S and X set S in fact, then the sentence S becomes valid
Fact1
State A, B, … and N have agreed with to concluded the CISG on 10/4/1980 in Vienna.
They set the article 99 concerning the effective condition of CISG into the convention.
The article 99 of the CISG became valid on 10/4/1980

28. 7 Conclusion LJ has a similar target as Kelsen’s PL.
LJ may have more stable standing points and more precise methods than PL.
LJ starts from three primitives and analyze a legal system in terms of thee types of alternative basic concept of legal sentence.
LJ provides a model according to which legal system is actually explained as a deductive system.
LJ clarified thereby not only ‘basic rule sentences’ but also fundamental legal meta-rules sentences.
LJ make it enable to realize inference of validity relationship between legal sentences in terms of meta rule sentences.
LJ contributes to develop a deductive knowledge base.
LJ may contribute to develop a true science of law.
It is to be noted that the most of theses in LJ introduced here are found through the analysis of real legal texts to construct a legal knowledgebase.

29. The most important words:
Finally,
The most important words:

30. Thank you!