Formal Ontology Applied to Law
1. The limits of artificial intelligence
The aim of artificial intelligence, the reproduction of mental schemata and processes of reasoning, find a great limitation in the vastness and vagueness of common knowledge and of the language by means of which it is expressed and communicated (let us not consider the further problem of vision and of oral language comprehension). The study of processes, as it is based on logical tools, can not deal with elements of content (semantics in the linguistic sense), and thus, nor can it deal with mental activities such as interpretation, value judgements and, in general, the comprehension of meaning. «Where is the weak point of this approach? In two words, logic is fragile and rigid, diametrically opposed to the human mind which, instead, can be characterised as `flexible' or even `fluid,' as far its extraordinary capacities to face completely new situations without precedents is concerned..... Logic and its multiple descendants depend on human beings to translate every situation into an unambiguous formal notation..... Logic therefore does not know activities such as classification or recognition of forms and structures. However surprising it may seem, though, these activities play an absolutely central role in intelligence.»Foot note 35
To break free of this deadlock, recent trends of study in artificial intelligence follow two directions: 1) obtain a homogeneous «nucleus» of universal knowledge which can be used as foundation to build specialised knowledge bases; here, the multiplicity of meanings is reduced by means of generalisation, uniformization and classification processes, which utilise the comparison of situations and the search for analogies; 2) transform a large part of reasoning processes (value judgements, in particular) so that they can be brought back to deductive processes;Foot note 36 some conceptual aspects are inserted under the form of syntactic elements and the programmes utilise proof-theoretic semantics instead of model-theoretic semantics.Foot note 37
For reasons of space, in this paper, we shall deal only with the first aspect, referring the second to specialised literature.Foot note 38 After delineating the novelties in knowledge modelling developed in Artificial Intelligence, we shall note several aspects peculiar of law, attempting possible computational interpretations of legal theories.
The examination shall be purely exemplary in nature, to consider only as a first step towards developing a methodology to deal with legal knowledge: the exploration of legal theory and philosophy requires a much more in-depth investigation than the one assumed in this preliminary phase. The aspect on which we shall focus our attention is the attitude of many legal theories to offer the background for formal models of legal knowledge, or at least of several components. For example, the theory of fundamental concepts by Hofheld, or the theory of Speech Acts by Searle, from the beginning have been developed in formal structures, even though with merely descriptive objectives, and therefore make a considerable contribution to the development of computable models of knowledge. In the same manner, legal theory provides sources for formal models of reasoning; we need only consider the argumentative models developed on the theory of argumentation or on the theory of discourse (Perelman, Alexy, Wroblewski, Toulmin).
On the other hand, we must remember that the aims of AI are essentially practical, which is to say, to find a remedy for the high costs, both in terms of time and money, inevitable in building knowledge bases; common to the entire sector of developing systems based on knowledge is the necessity to use shared knowledge bases which constitute the fundamental nucleus for every specialistic application and can be reused in different contexts.
2. Knowledge Organisation
As Artificial Intelligence, until a few years ago, considered reasoning as absolutely pre-eminent to perception, another discipline, pattern recognition, attempted to find ways to reproduce the classificatory capacities of the human mind: to reduce the infinite multiplicity of reality to pre-known categories. The traditional Pattern Recognition approach consisted in breaking up the picture of reality into a series of atomic components which one attempted to label on the basis of conceptual categories. Another approachFoot note 39 is based on identifying abstract characteristics: comparison criteria are expressed along with organising groups of sets, analysing their characteristics until general attributes are identified which make classification possible, for example, several groups of figures can be compared on the basis of shape, colour, represented sign, number of elements, etc. We then continue, alternating abstraction phases and comparison phases until we discover analogies: «which is to say, the activity of choosing the important characteristics of a complex situation... and the activity of discovering similarities and differences between situations described at a high level of abstraction [Hofstadter, 1994].Foot note 40
What can be drawn from these experiences?
-- 1) the necessity to deal with cognitive processes as sequences, which is to say as the concatenation of phases, both perceptive and of reasoning, which succeed and alternate one another, often recursively. Generally speaking, we may hypothesise as follows: perception, representation by abstraction, search for analogies, classification, reasoning (subsumption, deduction);
-- 2) the method of validation based on the formulation of hypotheses, which are equivalent to plausible expectations, susceptible to being modified at every step, or verified (by means of pragmatic analyses, or annulling counter hypotheses, or by means of probabilistic evaluations);Foot note 41
-- 3) the construction of models by means of integrating bottom to top strategies («by bottom-top process, we mean the construction of high abstraction levels on a rather solid underlying basis of hypotheses...») and top to bottom strategies («by top-bottom process, we mean the opposite image, i.e. the attempt to build hypotheses close to the brute data specifically to provide a solid base or hypotheses that have sense on higher levels.»)Foot note 42
Considering that what has been said till now concerns the whole cognitive process of learning (and understanding), remaining on the same cognitive level, we would place the moment of legislative production as the conclusive and explicative moment of the legislator's decision-making process and jurisdictional activity as the moment of problem solving. It presupposes that the new problem, before it is solved, must be described, classified and understood; and then compared with knowledge (the norms).
Adapting the methodological hypothesis prospected above to legal domain, we would say that the following are necessary: 1) parameters of comparison, knowledge categories or primitives to which to relate the new and by which to classify and understand it (the conceptualisation of law operated by legal theory and doctrine); 2) generalisation processes which, from analogies and diversities, should lead to enriching the initial «a priori,» which could be newly reapplied and compared, recursively (a good example is case law).
2.1. Knowledge Primitives
In 1979, Ron Brachman proposed a classification of knowledge in four levelsFoot note 43
Implementative Memory cells
Logical Propositions, predicates, functions, logical operators
Conceptual Conceptual relations, primitive objects and actions
Linguistic Linguistic terms
The schema can be read from top to bottom, as a process of «reificazione» or instancing of a formal theory to reality, or from bottom to top, as a construction process, from a state of affairs described in natural language, to a computable model of the same. Under this second aspect, the passage of abstraction involves the passage from linguistic entities (names, verbs) with a definite meaning, to concepts with meanings independent of the context (roles, actions); from these to logical symbols, the semantics of which concerns the relation between these and the world; on the level of implementation, no a priori semantics is necessary.
Brachman himself noted a gap between the conceptual level, in which concepts have a specific understood meaning (i.e. the red apple) and the logical primitives with a neutral general meaning (both red and apple can be unary predicates); he proposed an epistemological intermediate level whose primitives would define the internal structure of the concepts: i.e. that a link is admissible between the concept apple and the attribute red.
Defining the structure of concepts is fundamental to controlling conceptual inferences, the most classic of which is the classification of concepts on the basis of their belonging to a taxonomic conceptual network: to be able to deduce that an object (or a concept) is an entity or sub-entity linked to a general concept by the ISA relation,Foot note 44 it is necessary to know the internal structure of this concept, in particular, what attributes or properties are necessary to define the object as subsumable (i.e. that the concept of apple must have a colour as attribute).
The epistemological level then makes it possible to bind the structure of concepts, but not the meaning, which remains formed by the sum of the understood meanings of its components: the structural content of the concepts and the interconnections of meanings are better defined, but not the meaning itself. Choices among the structures make it possible to utilise to the fullest the formalisms descriptive of knowledge representation, such as semantic networks or frames, for example, explaining the attributes (slots) necessary to define a concept; in order to reach an expressive power higher than that of first order logic; however, we have not identified what, in the entities of reality, is a slot and what is a class, an object of knowledge to which that slot refers. Continuing the example, justify the fact that apple is a concept (a class: sort), while red is not. It is a question of making ontological choices.
The ontology of which we are speaking here is formal ontology, which combines the intuitive, informal methods of philosophical ontology with the formal methods of modern symbolic logic: as the object of classical ontology, in an intuitive manner, studies the properties, modes and aspects of being, while the method of classical logic is the rigorous reconstruction of axiomatic formal systems, formal ontology is «the systematic, formal, axiomatic development of the logic of all forms and modes of being.»Foot note 45
The ontological level is therefore placed between the conceptual level and the logical level, providing «knowledge primitives [that] satisfy formal meaning postulates, which restrict the interpretation of a logical theory on the basis of formal ontology, intended as a theory of a priori distinctions: -- among the entities of the world (physical objects, events, processes...); -- among the meta-levels categories used to model the world (concepts, properties, states, roles, attributes, various kinds of part-of-relations...).Foot note 46
Categories play a fundamental role in the philosophical/ontological dimension, as they do, as we have said, in the development of a methodology to describe and classify reality: from the viewpoint of the former, they are «fundamental classes to which entities or concepts belong,»Foot note 47 from that of the latter, they are «subdivisions of a system of classification» utilised to catalogue knowledge, for example, a database. A third level (of meaning) refers to a cognitive dimension in which they are «notions which serve as rule of investigation,» which is to say, to make predictions about objects and relations between objects in unknown situations. In the beginning, we evidenced the links between conceptual models of knowledge and processes of learning, the latter presupposing an a priori conceptual structure which is recurrently enriched by new experiences; we therefore see how the first meaning of the term «categories,» which we shall also call, in Artificial Intelligence terminology, knowledge primitives, must take into account the third definition, considering a meta-organisation (cognitive categories) of the conceptual categories.
There are therefore ontological categories which collect the entities of the world (apple, red) and meta-categories which guide the organisation of these entities. For example, meta-categories are those which differentiate apple, in as much as it is a concept because it serves to classify and enumerate entities inside a class, from red, in as much as it is a property attributable to an entity of itself already identifiable and enumerable. The distinction, fundamental for Artificial Intelligence and knowledge representation (KR), between concepts and properties traces the philosophical/ontological distinction between enumerable universals (sortal) and non-enumerables (non-sortal or characterising), a renewed version of the Aristotelian distinction between essence and accident, and the linguistic distinction between nouns and adjectives..
If first we have defined formal ontology on the level of theory, now on the level of practice, we can call it «theory of a priori distinctions (and therefore general, not depending on the particular problem considered): between things, or entities of the real world (physical objects, situations...); between relations, or entities utilised to model the structure of the real world (qualities, properties, states, roles, various types of relation part-whole).»Foot note 48
Let us reformulate the initial schema integrating it with the epistemological and ontological level: ontological primitives serve to limit the generation of models (interpretations) of logical theory to those understood, on the basis of ontological commitment; a function which, as we have said, the epistemological level, operating on the structure from inside, is not able to perform. It is therefore clear how ontological commitment is in any case tied to the subjectivity of linguistic/conceptual interpretation.
Levels Primitives Interpretation
Logical Predicates Arbitrary
Epistemological Structure primitives Arbitrary
Ontological Postulates of meaning Bound
Conceptual Cognitive primitives Subjective
Linguistic Linguistic primitives Subjective
Having thus introduced Concepts as atomic entities with which to build the model of knowledge, and categories and meta-categories as tools with which to classify and organise them, we can apply the method to legal knowledge.
3. The Primitives of Legal Knowledge
The aim is to create knowledge bases for systems which reproduce part of the jurist's activity. We must therefore model the knowledge which they commonly utilise; we can neglect part of the knowledge about norms, but we must envelop all of the knowledge object of the norms; and, as the norms deal with reality, all the knowledge of the world. We can neglect to resolve crucial matters, on the nature of the norms; on the difference between norms, directives, moral principles, value judgements; on the axiological aspect of law, in brief a large part of meta-juridical questions. This does not mean that domain must coincide exclusively with what is called positive law, because it is necessary to include:
1 -- the meta-norms (on the interpretation, the solution of conflicts, analogy, application, etc.) which serve the jurist to deal with norms,
2 -- the hierarchical relations between legal sources,
3 -- the distinction between norm and statement: the fact itself that we speak of norms instead of normative statements, involves the obvious consideration that the linguistic level (legislative text in natural language) is surpassed, in as much as the norm, intended as «meaning of the enunciation» (or of parts of an enunciation, or of several enunciations) finds a place on a conceptual level; before we move on to the logical level (first order logicFoot note 49), it is necessary to establish:
4 -- rules which bind the process of conceptualization, which we have called «meaning postulates», to enable the meta-organisation of the conceptual categories.
5 -- assumptions as to the structure of the norm: the norm, too, is a primitive concept which must necessarily be defined, in as much as it can itself become content, object (we need only consider the meta-norms).
Of the five points we have delineated, and which do not claim to constitute an exhaustive list, the first two points are computationally treated as processes, instead of as components of knowledge: we shall speak of them only briefly, referring, as we have already said, to literature on the topic.
In a model of normative system considered as a theory, the properties of completeness and consistence required by logical laws contrast with a legal reality of inconsistency (conflicts between norms) and non-completeness (gaps). What is more, the passage from statements to propositions is filtered through interpretative processes.
The rediscovered interest for the theory of argumentationFoot note 50 is due to the contemporaneous development of non-monotonic logic systems. In these, the difficulty of finding intuitively valid semantics lies, to a great degree, in the fact that, from a single theory, inconsistent conclusions can be (non-monotonically) inferred; the problem can be solved considering the default theories (or Brewka's sub-theories, or Reiter's default logic extensionsFoot note 51) as arguments capable of justifying these conclusions. It is evident how this perspective matches perfectly with the dynamics of the legal debate in which both parties, departing from the same normative and factual premises, build arguments in defence of opposite claims.
In the argumentative model, the problems of inconsistency (conflicting norms) are solved by admitting conflicting conclusions from consistent subsets, while the problem of incompleteness finds a remedy in: a) inferring solutions by default, which can be invalidated by new knowledge of the facts (i.e. presumptions); b) inferring conclusions based on analogical argumentations which surpass the normative gaps and can be equally defeated.Foot note 52
The «choice» between consistent but mutually exclusive subsets, in other words between «arguments,» is guided by criteria (hierarchy, types of interpretation, search for most significant precedent) which, from semantic, are transformedFoot note 53 into syntactic criteria to evaluate the force of the arguments.
We therefore feel it appropriate to not consider these aspects as elements of knowledge in themselves, but as formal definitions of terms such as validity, applicability, which as ways of being, status of norms are elements of knowledge. In computable models,Foot note 54 they are generally expressed with meta-predicates which, like the normative predicates, are part of argumentations (and especially counter-argumentations) and therefore provide argumentative strategies.Foot note 55
Point 3, too, can be considered as included in the extensive meaning of the predicate of applicability, comprehensive of the interpretative passage from the enunciation to the norm; we therefore move on to examine point 4.
The traditional approaches to the conceptualization of knowledge, the so-called terminological logics,Foot note 56 are based on the assignment of a name to each element considered primitive (whether it be an individual or a property), and which will become a predicate on the logical level. Semantic rules are lacking, however, so that the models of the theory built in this language (the model of normative system), are only those intended, which is to say compatible with the underlying meaning assumptions. Semantics which can not be extensional (i.e. the meaning of a class of legal subjects can not be identified with the set of individuals), but have intrinsic characteristics. Picking up the previous discourse, it is not sufficient to define the content and relations of the concepts utilised in a legal context, which is to say to build models «from the bottom,» but to identify the (meta-)categories to organise these concepts, which have universal legal value (even though subjective), which is to say, to build the models «from the top,» search for the ontological foundations of these categories.
3. 1. Legal Ontology
As we have already said, one of the merits (at least for artificial intelligence) of formal ontology is that of providing meaning postulates which make it possible to formally identify the ontological categories, surpassing the indefiniteness of intuitive distinctions: i.e., the already recalled classification of the objects of realityFoot note 57 into sortal entities (which «supply principles for distinguishing and counting individual particulars which they collect») and non sortal entities, (which «supply such principles only for particulars already distinguished, or distinguishable, in accordance with some antecedent principle or method»).
Sortality presupposes countability, which is to say the capacity to distinguish one sortal entity from another and reidentifiability («this is the same P as before»). Another fundamental notion is that of rigidity: the class of sortal predicates is divided into:
-- the class of sortals ontologically rigid or substantial, in as much as lacking this predicate, the individual loses his identity (like apple), but not divisible, in as much as the same predicate can not be attributed to components of the entity,
-- non-substantial sortal predicates which, though countable, are not rigid (like. student).
In traditionally utilised terminology, substantial predicates correspond to types, while non-substantial predicates correspond to roles.Foot note 58
The property of divisibility instead applies for the non-sortal predicatesFoot note 59 which, in turn, can be
-- ontologically rigid, or pseudo-sortal (i.e. collective names and high-level predicates: event, individual, to which we shall return);
-- non ontologically rigid, or characterizing, (like the colour red).
These distinctions represent one step further than terminological logic in as much as they make it possible: to formally distinguish attributes (which correspond to the characterising non-sortal predicates) from concepts (sortal predicates and pseudo-sortals), to formally define the relations of subordination and disjunction between the concepts and to identify, within the pseudo-sortal predicates, the class of categorial predicates (individuals, events, physical objects) which identify the cognitive meta-categories of which we have already spoken. The general schemaFoot note 60 is:
Returning to law, let's begin with the categorial predicates to verify whether they are congruous for legal reality. Legal phenomena (or components of phenomena) can be distinguished Foot note 61into four large subclasses: subjects, objects, acts, facts. Objects and facts represent the more immediately real aspect, while subjects and acts represent the more properly human aspect. Subject and object are spatial phenomena: they constitute the point of connection between successive cases in point (i.e.: the transfer of property of a possession can be seen as a change of the proprietor subject, or as a change of status of the subject from proprietor of the right of property to creditor of the counter-performance); while facts and acts belong to the category of temporal phenomena: they characterise cases in point connected and temporally differentiated.Foot note 62
Facts are the content of both the consequence (effectual) and the case in point (causal), with a further specification: an effectual fact will commonly consist of an act, which is to say a behaviour, and it will always be referable to a subject: indeed, there would be no sense in foreseeing a natural phenomenon, which as such is independent of human will, as a legal effect, nor would there be sense in not identifying a usufructuary subject of the norm.
Is there correspondence between general ontological categories and legal ontological categories? Law will probably require the insertion of second level ad hoc postulates, on which we shall make several intuitive observations which, however, will require further in-depth examination:
-- Facts/physical events: law does not take all physical events into consideration, but only those relevant for the organisation and regulation of social groups; what can the discriminating feature between facts that concern law and facts for which the legal order is indifferent, be? Perhaps social effects (Reinach, 1989). For Reinach, who developed the richest contribution to legal phenomenology, the universal structure of law consists in social acts which, generating a priori normative relations -- -- obligations, duties, etc. -- -- have an existence independent from specific positive law which regulates them; and positive law, on the other hand, by imposing obligations and instituting rights, can not leave out of consideration facts and social relations which justify their creation. Among social acts, promise is the one which for Reinach has greater importance because it produces modifications of the states of affairs which have social relevance. Promise can be born of a hidden mental state, i.e. when the will to not keep it is left unexpressed; it can be not received by the subject; it is, in any even, a linguistic act that causes mutations in the normative sphere both of the maker and of the receiver, every time the legal system asserts its relevance.Foot note 63 The mental/linguistic mechanism of the promise can be applied to a large part of legal phenomena.
-- Acts: the same consideration made above applies for acts: what is the characteristic which makes it possible to identify acts relevant for law? The class of actions which are object of norms has a wider extension than human actions, including i.e. «actions depending on language,» or «speech acts,» of great importance for legal domain (Searle, 1969). Acts could therefore be identified with the propositional content of the illocutionary acts, those classes of illocutive acts which have illocutive aims consonant with the finalities of law, which is to say, binding, directive, declarative.Foot note 64
The theory of speech acts, of which Searle himself with Vanderveken (1985) elaborated the logic, offers a great wealth of indications for a characterisation of legal acts, permitting their representation as autonomous primitive entities compared with the other elements of the norm. The different mental position (perceptive states) of the subjects about the objects of reality, which alone can be true or false, generates the states of affairs which, as such, can be positive or negative, certain, possible, probable but, in any event, timeless. Thus, the promise expresses the will to obtain performances from others, the command expresses the will to obtain a new state of things, a question expresses a state of uncertainty, an assertive act can express a conviction. The conviction depends on a unitary underlying mental state, though admitting various degrees of certainty, while the assertion which expresses it is a punctual act, tied to a definite propositional structure of the language.
-- Subjects/individuals: the legal concept of person presupposes the existence of a subjectivity and capacity of persons to create law to regulate legal and social relations; the category of legal subjects leaves the physical existence of the individual out of consideration, and therefore embraces a sphere wider (the conceived, incorporated bodies, public agencies) than the individuals characterised by general ontology. It is a question of formally defining, in a postulate, the requisites of subjectivity, legal capacity, capacity to act.
-- Objects: certainly the objects of law are a category wider than physical objects: we need only consider obligations, wherein the object of law is a legal relationship.
-- Legal relationships: the Hofheld theory of fundamental legal conceptions has already been utilised in knowledge-based systems.Foot note 65 Hofheld identifies the primitive relations capable of expressing all of the possible legal relations existing between subjects in eight concepts (right, duty, privilege, non-right, disability, immunity, power, liability); he provides examples, taken from jurisprudence, but instead of defining the content, he formally defines the relations of opposites/contraries between them. Contrary to Bentham and Austin, who recognise freedom as the state in which there is no obligation towards the holder of a right, for Hofheld, the concept of right is always tied to that of duty, as a relation between two subjects is always presupposed. The concepts of the second groupFoot note 66 serve to create or modify those of the first.
KangerFoot note 67 systematised the theory of fundamental concepts utilising propositional logic, the logic of action and deontic logic.
LindhalFoot note 68 developed the theory of legal positions in a complete formal system. To each fundamental legal concept of Hofheld corresponds a series of possible positions, rigorously defined by the conjunction of logical expressions which, in addition to connectives and axioms of classic logic, also utilise the deontic and action operators.Foot note 69 The advantages of utilising this logic, of which computerised versions exist, in a universal representation language, makes it possible to substitute the modality operators of formal ontology with the deontic operators in order to express the characteristic of prescriptivity of law.
We make no claim that the categories we have examined (to which we would add the spatial dimension and temporal interval) are exhaustive; we do intend, however, to sketch a methodology which remains to be further investigated. Space is not sufficient to even briefly hint at the possible contents of the classes of concepts (sub-categorial), for which dogmatics more than the theory of law, will be examined; nor of the class of attributes, which certainly will present aspects (i.e. legitimated, responsible, null) peculiar of law. An example of attribute has already been provided with regards to validity and applicability.
While validity is a concept of doctrine,Foot note 70 the contents of the applicability concept must be identified on the pragmatic level; computational models normally assume as verifiedFoot note 71 the requisite of formal validity, intended as validity of the process of legislative production, and instead utilise a meaning of applicability which includes a narrow version of the concept of validity. Doctrine (Guastini, 1994) distinguishes a type of weak invalidity, belonging to norms, from a strong invalidity, or non-existence, belonging to legislative statements and normative sources in general; «invalidity is a property of rules... while non-existence is a property of legal sources» (p. 222). The conditions of applicability include the respect of the rules on contents and the consistence with higher order norms. Also included are the meta-norms which regulate the application of norms of positive law, which is to say the sphere of application and the norms considered applicable on the basis of interpretative processes of subsumption, extensive, restrictive interpretation, etc.
The lacking development of knowledge-based systems, programmes capable of performing complex reasoning, is principally due to the difficulty to build knowledge bases which are sufficiently broad (amount of knowledge) and in-depth (detail of the semantic/conceptual aspects). The modelling of knowledge is also the focus of theoretic research in artificial intelligence and object of the investigation of cognitive sciences. Attaining increasingly higher levels of abstraction, the process of universalisation has therefore touched philosophical dimensions, looking for ontological foundations of the primitives (with a cognitive term: a priori) of knowledge.
In law, a methodology of legal knowledge representation need to be consistent both with the results of formal ontology and the contributions of legal theory: the present work is just a possible starting point towards a promising field of investigation.
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Istituto per la Documentazione Giuridica
del Consiglio Nazionale delle Ricerche
Issue #02. Juy 1995. Pp. 44-45.
SORITES, ISSN 1135-1349
Issue #02. Juy 1995. Pp. 44-45.