Jusletter IT

Consider the question «What is the smallest entity of a legal system?» This is similar to the question «What is the smallest particle of the world?» In ancient Greece, this question was asked by philosophers, and Democritus’ answer was «the atom» («indivisible»). Since then, physicists have discovered subatomic particles (chiefly electrons, protons and neutrons) and currently an answer to this question is «the meson». In legal theory, the smallest entity question above can have different answers. Hans Kelsen¹ answered «the norm», whereas Hajime Yoshino² offered «the legal sentence». In legal documentation, different approaches exist, too. Some legal document systems take the entire document of a regulation (legal act, legal source) as the smallest entity, whereas others take the articles or paragraphs of a legal act, see e.g. RIS³. However, others even distinguish between grammatical sentences.

This granularity and the different ideas could be viewed in connection with the modally indifferent substrate (MIS). Kelsen considers the legal norm to be the decisive entity. According to Kelsen⁴, Ought is a mode that comprises MISs. In contrast, we think that, in addition to legal norms, legal terms can be viewed as a separate layer of self-dependent entities of law. A paradigm shift in the granularity is that, in addition to norms, the core legal elements comprise legal terms.

Suppose an act A is prescribed to the addressee of a norm. This can be expressed as Obligatory(A) or in other words O(A), which connects the Ought O with the intended action A. According to Kelsen, A is an MIS that is imbedded in the mode O.

In our view, it is interesting that O as well as A appears in a logical context. Therefore, we can treat O, the mode of obligation (prescription), abstractly. The reason for this is that the background of obligation involves the entire deontic field. The modes comprise concepts such as permission P, prohibition (forbidden, vetum) F, liberty L and probably other modalities, and could therefore be defined alternatively; see arrow (1) in Fig. 1. For other constructs, see, for example, Ilmar Tammelo⁵ and Ota Weinberger⁶.

On the other hand, a legal term A could also be viewed in relationship to other legal terms; see arrow (2) in Fig. 1. Legal ontologies attempt to develop such relationships and make use of them, for example, in searches. In European Union law, such stereotypical relationships of legal terms occur as an MIS. In addition to this, there is the translation problem. The reason is that separate legal terms, e.g., A, B and C, in different national legal orders, could have different systemic significance. This produces different mappings of legal terms to the structural backgrounds of the terms in respective legal orders.

The formula O(A) represents a simple form. In legal texts, multiple legal terms A, B and C, might occur in a single norm and, thus we have O(A-B-C), see Fig. 2. To summarise, both the modes of obligation and the elements of MISs could constitute the subject matter of logical analysis.

Fig. 2: A legal system is composed of norms. A norm comprises instances of modally indifferent substrates (MISs), e.g., A, B and C. 

Relations between a norm N(A) and the normative status of the duty can be discussed in more detail, see Lachmayer⁷. Four cases can be created:

1. N(A) – commandment (obligatory rule, Gebot);
2. ¬N(A) – absence of commandment;
3. ¬N(¬A) – absence of prohibition;
4. N(¬A) – prohibition (prohibitive rule, Verbot).

Here the meaning of negation is based on intuition and is not formalised more strictly. Negation of an action, ¬A, means an omission of this action A. Negation of a norm, ¬N(...), means an absence of this norm in the regulation. From each of the four cases above, a respective normative status is derived:

1. N(A) → O(A) – From a commandment, an obligatory duty arises (Aus dem Gebot ergibt sich eine gebietende Pflicht).
2. ¬N(A) → ¬O(A) – From the absence of a commandment, no obligatory duty arises (Aus dem Mangel des Gebotes kann keine gebietende Pflicht abgeleitet werden).
3. ¬N(¬A) → ¬O(¬A) – From the absence of a prohibition, no prohibitive duty arises (Liegt kein Verbot vor, so folgt daraus keine verbietende Pflicht).
4. N(¬A) → O(¬A) – From a prohibition, a prohibitive duty arises (Liegt ein Verbot vor, so ergibt sich eine verbietende Pflicht).

The spirit of commandment and the spirit of prohibition are expressed by 5 and 8 respectively.

Sixteen subsets can be made from the set of four statuses {O(A), ¬O(A), ¬O(¬A), O(¬A)}. In other words, its powerset consists of 2⁴ = 16 elements. Each element forms a row in the table which is depicted in Fig. 3.

Figure 3: Sixteen subsets of the set of four elements which head the columns 

One cannot agree to treat the negation of an action, ¬A, as an omission of A. Indeed, there is a difference between an omissive action and a negative action. The following example is provided by Giovanni Sartor⁸:

• For the omissive action NON (Brings_j [k is injured]) to take place, it is sufficient that j did not cause k’s injury.
• For the negative action Brings_j (NON [k is injured]) to take place, it is instead required that j prevents k from being injured (which presupposes that without j’s intervention k would have been injured).

Sartor considers «this distinction to be sufficiently intuitive, though its analysis would require various philosophical considerations and distinctions».

To explain Fig. 3, the system called Standard Deontic Logic or KD can also be used. KD is formulated with the following axioms, see, e.g., André Valente⁹:

• KD0 All (or enough) tautologies of propositional calculus
• KD1 O(p → q) → (O(p) → O(q)) – the so called K-axiom
• KD2 O(p) → P(p) – «obligatory implies permitted»
• KD3 P(p) → ¬O(¬p) – «obligation is the duality of permission»
• KD4 F(p) → ¬P(p) – «forbidden is not permitted»
• KD5 p, p → q |– q – modus ponens
• KD6 p |– O(p) – O-necessitation

A subsequent theme to explore is the classification of norms according to their structure. Kelsen distinguishes categorical norms and hypothetical norms. Categorical norms «command a certain behaviour unconditionally – under all circumstances». Kelsen also says this about hypothetical norms:

«[E]very general norm establishes a relationship between two sets of facts, which may be described in the statement: Under certain conditions, certain consequences ought to take place. This is…the formulation of the principle of imputation, as distinguished from the principle of causality».¹⁰

To begin exploring the structures of norms, we list some of them:

• Hypothetical norm, if condition then reaction (consequences), and categorical norm; see Kelsen (1960, § 25) (Fig. 4)

Fig. 4: Distinguishing between hypothetical and categorical norms. 

• Condition-reaction-finality, see Luhmann¹¹ (Fig. 5). Luhmann distinguishes conditional programming (e.g., «if it is dark then switch the lights on») from finality programming (e.g., «switch the lights on in order to read»).

Fig. 5: Luhmann’s (2004) concept of norm.

• Double norm (Doppel-Norm): state of affairs → commanded behaviour, otherwise sanction. Kelsen (1991, ch. 15 and 35) distinguishes primary norms that command a certain behaviour from secondary norms that decree sanctions for the non-observance of norms (sanction-decreeing norms), see Fig. 6.

Fig. 6: Double general norm refers to a primary norm, which does not need to be expressly formulated, or a secondary norm. 

• To-Do norms and To-Be norms, see Sartor¹²
• State of affairs (SF) → legal consequence (LC). Read «when a state of affairs (SF) is given, then the legal consequence (LC) applies». A more general format is SF₁,… SF_n → LC₁,… LC_m. This is generally used in computer science and specifically in ontology related issues in the context of semi-automated legal reasoning and in engineering software compliant with the law, see Oberle et al.¹³

Consider the norm structure of three elements: 1) a condition, 2) an ought and 3) a finality (or, in other words, a purpose, goal or telos). An ought is composed of four elements: a subject, a modus, an action, and an object. Thus the structure of a norm is as follows (Fig. 7):

1. condition
2. ought
   1. subject
   2. modus
   3. action
   4. object
3. finality (or, in other words, a purpose, goal, telos),

Fig. 7: The structure of a norm.

Further, we aim to classify norms according to the presence of a subset of these elements as the structural parts of a norm. The types of norm are distinguished by taking into account the three generalised elements: 1) a condition, 2) an ought, and 3) a telos. Three elements allow us to build eight subsets. The elements can be denoted by 3 variables (c, o, t) where each may or may not be present or, in other words, takes the value true (1) or false (0).

1. (1, 1, 1): complete norm. Example: «If it is dark switch the lights on to make it light».
2. (1, 1, 0): no telos. Conditional norm, a classical one. Example: «If it is dark switch the lights on».
3. (0, 1, 1): teleological norm, task norm (Aufgabennorm, Auftragsnorm) of Weinberger¹⁴. For example, in EU law purposes are usually set out in preambles.
4. (1, 0, 1): To-Be norm. Example: «If it is dark it should be light». The subject and other variables may be implicit. This makes an object-oriented (object-regulated) structure.
5. (1, 0, 0): incomplete.
6. (0, 1, 0): categorical norm. A classical norm with «ought». Action is implicit.
7. (0, 0, 1): too little, although this depends on interpretation, e.g., listing purposes in the preamble of a law. Legal principles can be modelled in this way. However, a principle is distinct from a norm.
8. (0, 0, 0): no norm.

The eight combinations above are shown in Fig. 8.

Fig. 8: A taxonomy of norms according to the three elements including telos. 

Further, we distinguish the types of norms taking into account the four elements: 1) a subject, 2) a modus, 3) an action, and 4) an object. Four elements allow us to build 16 subsets. The elements can be denoted by 4 variables (s, m, a, o) where each may or may not be present.

1. (1, 1, 1, 1): a complete norm. Results with transitive actions, i.e. actions, which require a direct subject. Example: «You ought to open the door.»
2. (0, 1, 1, 1): no subject. A To-Be norm. Examples from construction laws: «Room height ought to be a minimum of 2.30 metres», «Building height ought to be a maximum of 12 metres».
3. (1, 0, 1, 1): no modus. A description or an allegation. Example: «You open the door.»
4. (1, 1, 0, 1): no action. Action is not regulated or implicit. Examples: «You ought the car (keep in order)», «Police ought (keep) order».
5. (1, 1, 1, 0): no object. Results with intransitive verbs. Examples: «You ought to go», «He ought to be punished».
6. (0, 0, 1, 1): no subject, no modus. Indicative descriptive interpretation, usually a passive sentence. Example: «A car is driven».
7. (0, 1, 0, 1): incomplete.
8. (0, 1, 1, 0): subject is interpretative, e.g., «everybody», «all». Examples: «Smoking prohibited», «No stopping».
9. (1, 0, 0, 1): incomplete.
10. (1, 0, 0, 1): descriptive. Example: «Peter speaks».
11. (1, 1, 0, 0): subject with modus. Example: «Peter is free».
12. (1, 0, 0, 0): a modally indifferent substrate, MIS. Example: «Peter». Leads to a taxonomy of subjects.
13. (0, 1, 0, 0): MIS. Example: «Ought». Leads to a taxonomy of deontic modalities.
14. (0, 0, 1, 0): MIS. Example: «To drive». Leads to a taxonomy of actions.
15. (0, 0, 0, 1): MIS. Example: «A car». Leads to a taxonomy of objects.
16. (0, 0, 0, 0): no norm.

The above 16 combinations are shown in Fig. 9.

Fig. 9: A taxonomy of norms according to the combinations of 4 elements: 1) subject, 2) modus, 3) action, and 4) object. 

A subject and an action are essential in a To-Do norm, whereas an object and an action are essential in a To-Be norm. This essential feature of To-Do and To-Be norms is depicted in Fig. 10.

Fig. 10: Distinctions between To-Do norms and To-Be norms.

Essentially five types of relationships have been considered during the development of a thesaurus and ontology in the LOIS project: see Tiscornia¹⁵, Peters et al.¹⁶ and Schweighofer and Liebwald¹⁷. The overall architecture of LOIS is shown in Fig. 11. The term ontology is understood as in computer science. According to the generally accepted wording of Gruber¹⁸, an ontology is an explicit formal specification of a common conceptualisation with term hierarchies, relations and attributes that makes it possible to reuse this knowledge for automated applications. The five relations mentioned above are logical, monolingual, ones:

• Synonymy (Synonym)
• Near synonymy (Fast-Synonym)
• Antonymy (Gegenteil)
• Hyperonymy/Hyponymy (Ober-/Unterbegriff)
• Implemented_as (Umgesetzt durch)

Here language relations can also be mentioned:

• eq_synonym
• eq_near_synonym
• eq_has_hyperonym / eq_has_hyponym

Fig. 11: The overall architecture of LOIS (Tiscornia 2007). 

We propose to consider three more relations:

• Dialectical relation. This means a term of dialectical antithesis or, in other words, a dialectical antonym
• Context relation.
• Metaphorical relation. This means a metaphor of a term.

These can be called weak relations – in contrast to strong logical ones. Relations in law form a separate theme, which is outside the scope of this paper¹⁹. A legal thesaurus comes before a legal ontology. A thesaurus comprises terms and their relations. An ontology extends beyond this and comprises more advanced formalisations including rules. Hence, a thesaurus appears before an ontology.

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Vytautas Čyras, Docent, Vilnius University, Faculty of Mathematics and Informatics, Vilnius, vytautas.cyras@mif.vu.lt, http://www.mif.vu.lt/~cyras/.

 

Friedrich Lachmayer, Professor, University of Innsbruck, Faculty of Law, Innsbruck, friedrich.lachmayer@uibk.ac.at, http://www.legalvisualization.com.

 

V. Čyras has been supported by the project «Theoretical and engineering aspects of e-service technology development and application in high-performance computing platforms» (No. VP1-3.1-ŠMM-08-K-01-010) funded by the European Social Fund.