proceedings of the workshop on causality and causal …discovery, in conjunction with the...

Kamran Karimi (Ed.)

Proceedings of the Workshop on Causality and Causal Discovery

In Conjunction with the Seventeenth Canadian Conference on Artificial Intelligence (AI'2004) London, Ontario, Canada, 16 May 2004

Technical Report CS-2004-02 April 2004 Department of Computer Science University of Regina Regina, Saskatchewan Canada S4S 0A2 ISSN 0828-3494 ISBN 0-7731-047-1

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Preface

This volume contains papers selected for presentation at the Workshop on Causality and Causal Discovery, in conjunction with the Seventeenth Canadian Conference on Artificial Intelligence (AI'2004), held in London, Ontario, Canada on 16 May 2004. Causality and discovering causal relations are of interest because they allow us to explain and control systems and phenomena. There have been many debates on causality and whether it is possible to discover causal relations automatically. Different approaches to solving the problem of mining causality have been tried, such as utilising conditional probability or temporal approaches. Discussing, evaluating, and comparing these methods can add perspective to the efforts of all the people involved in this research area. The aim of this workshop is to bring researchers from different backgrounds together to discuss the latest work being done in this domain.

The occurrence of this workshop is the result of the joint efforts of the authors, the programme committee members, and the Canadian AI organisers. This volume would not have been possible without the help of the members of the programme committee who reviewed the papers attentively. The Canadian AI'2004 organisers, General Chair, Kay Wiese (Simon Fraser University), Program Co-Chairs Scott Goodwin and Ahmed Tawfik (both from the University of Windsor), and Local Organiser Bob Mercer (University of Western Ontario), supported the workshop from the beginning to the end. Thanks to Weiming Shen for hosting the workshops at National Research Council Canada (NRC) facilities and helping with the co-ordination. The Department of Computer Science at the University of Regina, and especially Howard Hamilton contributed their time and resources towards the preparation of this volume. The efforts of all the people not mentioned by name, who in any way helped in making this workshop possible, are greatly appreciated.

April 2004 Kamran Karimi

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Editor Kamran Karimi, University of Regina

Programme committee Cory Butz, University of Regina Eric Neufeld, University of Saskatchewan Richard Scheines, Carnegie Melon University Steven Sloman, Brown University

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Table of contents Jos Lehmann and Aldo Gangemi CAUSATIONT and DOLCE …………………………………………………………………...…… 1 Bassem Sayrafi and Dirk Van Gucht Inference Systems Derived from Additive Measures …………………………………….……. 16 Kamran Karimi and Howard J. Hamilton From Temporal Rules to One Dimensional Rules ……………………………………………... 30 Denver Dash Empirical Investigation of Equilibration-Manipulation Commutability in Causal Models…….. 45

CAUSATIONT and DOLCE

Jos Lehmann and Aldo Gangemi

Laboratory for Applied OntologyInstitute of Cognitive Science and Technology

Italian National Research Councilhttp://www.loa-cnr.it/

Abstract. This paper offers an overview of CausatiOnt, a semi-formalontology conceived as a basis for (automatic) legal reasoning about cau-sation in fact. Moreover, a preliminary axiomatization in DOLCE upperontology is provided of part of CausatiOnt. This axiomatization is a steptoward making CausatiOnt, or at least part of it, more rigorous and to-ward enabling the automatic discovery of causal relations in the modelof a legal case.

1 Introduction

In the context of a research in Artificial Intelligence and Law (AI&Law), ex-tensively reported in [1] and, more concisely, in [2], the problems posed by theautomation of legal responsibility attribution are thoroughly analyzed and (par-tially) reduced to the problems posed by automatic reasoning about causation.Based on such reduction, the main contribution delivered by this research is ananalytical subsumption hierarchy - an ontology, in Artificial Intelligence (AI)terms - which semi-formally represents the knowledge (i.e. the concepts and theconceptual relations) used in the legal domain as the basis for reasoning aboutcausation. We call such ontology CausatiOnt1.This paper offers a description of a work in progress, which aims at axiomatiz-ing CausatiOnt within DOLCE upper ontology [3]. This merging is being triedbecause, despite a preliminary specification in Protégé-2000, CausatiOnt is stilltoo complex for use in automatic reasoning, as it comprises knowledge whichis, logically speaking, rather ambiguous. DOLCE, on the contrary, has a wellfounded first order characterization [4], which may help in making CausatiOntmore rigorous and, therefore, potentially useful for the automatic discovery ofcausal relations in the model of a legal case. We proceed as follows: section 2 dis-cusses the causal relation typically employed in legal reasoning, causation in fact;section 3 presents the theoretical basis and the class hierarchy of CausatiOnt;section 4 introduces the preliminary results of the axiomatization of CausatiOntin DOLCE; section 5 draws a conclusion.

1 From CAUSATIon ONTology.

2 From legal responsibility to causation in fact

Legal Theory provides various arguments (see [2], section 1.1) in favor of thefollowing legal theoretical position: reasoning about the attribution of legal re-sponsibility to a person involved in a case largely rests on causal reasoning. Froman AI&Law perspective, this strongly suggests that the automation of legal re-sponsibility attribution in one way or another requires the automation of legalcausal reasoning. This may be achieved by adopting, among other things, a suit-able ontology of causal concepts, such as the one presented in sections 3 and 4of this paper.Before presenting the ontology, we first spend some words on the relation be-tween the notion of legal responsibility and the underlying causal knowledge.This is meant to clarify the nature of such knowledge and of the causal relationthat CausatiOnt is meant to capture: causation in fact.Consider the following example, from [5].

Example 1 (The Desert Traveler). A desert traveler T has two enemies. Enemy1 poisons T’s canteen and Enemy 2, unaware of Enemy 1’s action, shoots andempties the canteen. A week later, T is found dead and the two enemies confessto action and intention.

If a jury were asked to attribute the legal responsibility for T’s death, it wouldprobably have to consider the following additional information, which is leftimplicit in Example 1: T never drank from the canteen, T was found dead bydehydration.Based on such information, the jury would very probably come to an unanimousdecision and indicate Enemy 2 as the responsible person for T’s death. If askedwhy, the jury may answer: because Enemy 2 caused T’s death. If asked in whatsense Enemy 2 caused what he caused, the jury would probably say that Enemy2’s action is a counterfactual condition of T’s death, which makes it a cause.In other words, had Enemy 2 not shot the canteen, T would still be among us.But this is not true - it should be replied. Had Enemy 2 not shot the poisonedcanteen, T would have drunk from it and he would not be among us anyway.Therefore, Enemy 2’s action is not a counterfactual condition of T’s death. Is itstill its cause? - the jury should be asked. Again its answer would probably beunanimous and indicate Enemy 2’s action as the cause of T’s death in the sensethat he is the most proximate cause of T’s death. If asked to give a definitionof such proximity, the jurors would probably give a temporal definition: Enemy2’s action is the latest cause of T’s death. But, then again, it could be repliedthat from a strictly physical point of view the heat of the Sun was definitely atemporally more proximate cause than Enemy 2’s action.This “cat and mouse game” with the jury could go on for a long time becauseExample 1 is no real-life case. It is just a tricky and underspecified combinationof circumstances devised by some smart philosopher on some lazy day, with theexplicit purpose of fooling imaginary juries. The example, though, does show thefollowing: a “short circuit” in our causal understanding of a series of events hasmajor consequences on our capacity to attribute (legal) responsibility.

[2] provides a legal theoretical bridge between the legal concept of responsibilityand the causal notions that support its attribution. Such bridge consists of fiveelements: first, the distinction between causation in fact and legal causation; sec-ond, the distinction between the ontological problems posed by causation in factand the procedural problems posed by legal evidence and the burden of proof;third, the definition of legal responsibility in terms of liability and accountability;fourth, the definition of the grounds for legal responsibility attribution, amongwhich causation in fact; fifth, the definition of causation in fact. In the followingwe briefly illustrate the first and the last of these elements.The legal language makes a distinction between causation in fact and legal cau-sation. On the one hand, the problem of causation in fact is the problem ofunderstanding what actually happened (i.e. what caused what) in a case. Suchfactual interpretation is something legal experts usually take for granted andmostly see as unproblematically achieved by common sense. In Example 1 theconnection between the shooting of the canteen and T’s death by dehydrationis an instance of causation in fact, because Enemy 2 had the intention to killT, he believed that by shooting the canteen T would die (rather than be savedfrom poisoning), he shot the canteen, T died. On the contrary, the connectionbetween the poisoning of the canteen and T’s death is not an instance of causa-tion in fact, because T never drank from the canteen2. On the other hand, legalcausation is the set of criteria that should be applied either when a clear factualinterpretation of the case is missing or when legal policy considerations shouldbe applied, therefore adopting a causal interpretation that is different from thefactual causal one. In Example 1, supposing that, after the poisoning but beforethe shooting of the canteen, T had drunk from it and supposing impossible toestablish the temporal priority between the effects of poisoning and the effects ofdehydrating on T’s body, the attribution of legal responsibility should be basedon legal causation (for instance, by accepting that both Enemy 1’s and Enemy2’s conducts legally caused T’s death).Now, how to give a sufficiently general definition of causation in fact? There arevarious traditional legal theoretical approaches to the problem of giving this def-inition, most notably approaches based on the notion of causal proximity or oncounterfactuals3. Traditional approaches, though, suffer of a lack of an explicitaccount of the elements of a case that a judicial authority should consider whenassessing causation in fact. This jeopardizes consistency of application of suchtests over large corpora of cases. In order to overcome the common shortcomingof traditional approaches, Hart and Honoré propose in [6] to base legal causalassessment on an explicit definition of causation in fact, like the following one.

Definition 1 (Causation in fact). Agent A causes an event e, that mightinvolve agent B, if either of the following holds:

1. A starts some physical process that leads to e;2 Legally speaking Enemy 1’s action may be considered just as an attempt at murder-

ing T.3 Typical examples of counterfactual tests used in the legal domain are the sine qua

non and the but for tests. For detailed overviews of these approaches see [2] or [6].

2. A provides reasons or draws attention to reasons which influence the conductof B, who causes e;

3. A provides B with opportunities to cause e.4. All the important negative variants of clauses 1, 2, 3

For what concerns Example 1 the causal connection between Enemy 2 shootingand T dying is non linear and may be considered either as a case of the negativevariant of clause 1 above (Enemy 2’s conduct prevents the physical process ofhydration which leads to T’s death by dehydration) or as a case of clause 3 above(Enemy 2’s conduct provides T with the opportunity of causing his own deathby dehydration).In conclusion, Definition 1 carves a portion of causal knowledge that is veryrelevant to AI&Law research.

3 An overview of CausatiOnt

In order to make Definition 1 more rigorous and possibly useful to automaticclassification and/or interpretation, it should be reconfigured along clear onto-logical lines and restructured by means of a subsumption hierarchy, i.e. a socalled is-a hierarchy. This is exactly the original purpose of CausatiOnt, the on-tology presented in this section. It should be noticed that the presentation ofCausatiOnt given here is rather theoretical. We only occasionally exemplify theintuition behind each newly introduce notion by referring to a subset of Example1 (namely: E1 = the bullet is shot; E2 = the canteen is broken). But neitherin this section nor in the following ones do we provide a complete model of E1,E2 and of their causal connection, as this would require many more pages thanavailable or a drastic cut in the theoretical treatment of the introduced notions.

3.1 Philosophical preliminaries

The first and most obvious restructuring distinguishes in Definition 1 four mainontological levels, corresponding to four main types of causation, as usually de-scribed in the philosophical literature: physical causation, agent causation, inter-personal causation, negative causation4. Physical causation is described by thefinal part of clause 1 of Definition 1, where the definition mentions a physicalprocess that leads to an event. Agent causation is described by the initial partof clause 1, where Definition 1 mentions an agent starting a physical process.The agreement around cases of agent causation is not reached as easily as incases of physical causation. This is due to the problem of detecting the beliefs,

4 Distinguishing between varieties of causation is the pragmatic answer of the phi-losophy of causation to the (temporary?) lack of stable scientific theories of somefundamental phenomena. For instance, without a stable neuropsychological solutionof the mind-body problem, it is impossible to choose in a principled way betweena reduction of agent causation to physical causation and a reduction of physicalcausation to agent causation.

desires and intentions of the agent that starts the physical process. Things be-come even more complex when considering interpersonal causation, described byclauses 2 and 3. One might be tempted to consider interpersonal causation justas a subcase of agent causation, where the psychological state of an agent exertsa causal influence on another agent. Things are not that simple, though. Thecausal influence that an agent may exercise on someone else may be physical innature or psychological or a combination of the two. Finally, the most elusivecase of causation is negative causation. Definition 1 refers to negative causationin clause 4 as to all the important negative variants of the preceding clauses. It isontologically very difficult, almost paradoxical, to accept the general idea thatsomething that does not exist can cause anything. For reasons of space we cannot analyze the subtleties of this fascinating problem here.In [2] definitions are given for physical and agent causation within the widerstructure of CausatiOnt and some analytical material is provided on interper-sonal and negative causation, which are both left as research objectives. In thispaper we limit the scope of the presentation of CausatiOnt to the knowledgeneeded for defining physical causation (shown in figure 1). In other words, wepresent only the knowledge needed for assessing causal relations between events,without considering actions.Before starting with the detailed presentation of the class hierarchy shown infigure 1, the following general philosophical biases of CausatiOnt with respectto physical causation should be highlighted:

Cognitivism CausatiOnt is based on the assumption that causal relations areneither purely ontological nor purely epistemological. Therefore, the repre-sentation of causal knowledge cannot be limited to the ontological elementsof causal relations (i.e. the entities). It must be extended to the epistemo-logical elements (i.e. the categories) and to the phenomenological relationsbetween them (i.e. the dimensions). This extension might seem as a nonparsimonious scientific practice. But it gives us some room to explain whatin causal reasoning pertains to us as observing entities and what pertainsto the world as observed entity. Furthermore, by not limiting ourselves toontology we provide a clear way of distinguishing semantically similar terms(e.g., matter, a category; mass, a dimension; object, an entity). In a similarfashion, we are able to adopt the distinction defined in [7] between causality(a category, representing general causal principles) and causation (a reifiedrelation, i.e. an entity, representing particular causal relations). All this willfurther be explained in section 3.2.

Singularism According to singularism, physical causation relates events, i.e.particular changes of the world located in space and time5 [8].

Functionalism Functionalism [9], [10], [11] may be seen as the continuation ofsingularism by other means. The main difference from singularism is thatfunctionalism seeks sharper tools than the notion of change for detecting

5 Ducasse would for instance say that the cause of the particular change E2 is E1 ifE1 alone occurred in the immediate environment of E2 immediately before. This, ofcourse, begs the question - what is the definition of ‘immediate environment’?

physical causation. The various functionalist views proposed so far try toreduce the notion of causation to physical notions, such as energy or mo-mentum transfer between physical processes, in accordance to contemporaryPhysics6.

Formalism According to CausatiOnt, like according to most treatments ofcausal relations, physical causation has the formal properties of transitiv-ity, asymmetry and non reflexivity.

Energy

Category of Existence

isa

Matter

isa

Change

isa

Space

isa

Process

Physical Entity

isa

Object

isa

Dimension

Noesis

isa

Category

isa

Entity

isa

Quality

Category of Experience

isa

Time

isa

Quantity

isa

isa isa

Causation

Physical Causation

isa

Occurrence

isa

Event

isa

isa isa

Causality

isa

Fig. 1. General hierarchy of CausatiOnt

3.2 CausatiOnt

We present here the class hierarchy shown, at different levels of detail, in figures1 and 2. This hierarchy is an image of a preliminary specification of Causa-tiOnt in Protégé-2000, a fairly liberal knowledge representation tool, based onthe classical is-a relation. Protégé-2000’s liberalism includes the possibility ofdistinguishing among the following data types in an ontology. Class, i.e. a set of(prototypical) individuals (so called instances). A class has a name, that uniquelyidentifies it and, possibly, a number of slots that intensionally describe it; it isrelated by is-a relations to its subclasses and by i-o (instance of) relations to itsinstances. Slot, i.e. a (user defined) binary relation between the instances of aclass and the instances of another class, or a literal (symbolic or numeric). System

6 For instance, a functionalist would consider a relation between E1 and E2 as causal,if the actual physical intersection between E1 and E2 involves exchange of a con-served quantity (e.g. energy). Such exchange may be seen as a criterion for furtherspecification of the ‘immediate environment’ used by singularists

class, i.e. a class that has classes as its instances (i.e. a metaclass). The creationof system classes is usually used in order to expand Protégé-2000’s knowledgemodel because classes and slots are all instances of system class. Constraint, i.e.an assertion that restricts the domain and the range of slots.Protégé-2000 variegated data types allow to represent knowledge that pertainsto, at least, three logical orders (instances, classes, system classes). Such spec-ifications may then be subject to further specification in order to fully expressthem at the first order. In the rest of this section we provide exactly the firstliberal specification of CausatiOnt. For each introduced notion we provide asynthetic natural language definition, some comments and the indication of howthe notion is implemented in Protégé-2000. Next section provides indications ofhow CausatiOnt has been imported into DOLCE, in order to axiomatize it in asemantically well founded model.

Definition 2 (Noesis). Noesis is the psychological counterpart of experience(i.e. perception, learning and reasoning).

The notion of noesis has a rather long philosophical tradition, which dates backto Greek Philosophy. As far as we are concerned, we adopt here the notion ofnoesis in its broadest cognitive sense. We consider all the experiences of an in-dividual human being to be physical phenomena. On the one hand, perceptualexperiences (e.g. perceiving the form of the canteen) are the result of the inter-action between the physical world (i.e. light) and an individual’s sensory system(e.g. his optic nerve and other parts of his brain). On the other hand, intellec-tual experiences (e.g. thinking about the notion of form) occur in the brain, i.e.they too are physical phenomena. Besides their physical nature, though, bothperceptual and intellectual experiences generally seem to have a psychologicalcounterpart, i.e. a part of which the individual is aware (i.e. the form of the can-teen, in the example of perceptual experiences, and the notion of form, in theexample of intellectual experiences). Any such psychological counterpart of anexperience is noesis. Noesis is represented in Protégé-2000 as a standard class,with no slots.

Definition 3 (Category). Category is knowledge-related (i.e. epistemological)noesis.

A category is a kind of noesis, which cannot be (philosophically) reduced to anyother kinds. It must therefore be postulated. Categories form the intellectualbackground of our noetic experience of the world (i.e. of our perception, learningand reasoning about the world). Even though categories play a crucial role innoesis, we are hardly aware of them in our experience. When perceiving, learn-ing or reasoning we are not fully aware of the categories that are supportingour effort. For instance, when reasoning about (i.e. having an intellectual expe-rience of) or perceiving (i.e. having a physical experience of) an entity (e.g. anobject, say, the bullet or the canteen), a number of categories (e.g. matter andquantity) make our experience possible, even though they are not immediatelypresent to our mind and/or to our sensory system. Categories are, therefore,here understood as in (Kantian) Epistemology: as the basic notions on which

our (intellectual and perceptual) experience builds up7. Our intent is to use cat-egories as purely descriptive notions that clarify the intuitive meaning of theterms that are used in reasoning about entities (which we call the dimensions,see below). As shown in figure 1 we distinguish between two main groups ofcategories: the categories of existence and the categories of experience. The op-position between these two types of categories is the epistemological equivalentof the opposition, within noesis, between entity (or Ontology) and category (orEpistemology). In other words, just like in noesis, where we distinguish existence(the entity) from knowledge (the category), in category we distinguish betweenthe knowledge of what exists (category of existence) from the knowledge of themodes of knowledge (category of experience). These second categories describehow we know what exists (or, rather, how we know the categories of existence).Categories of existence encompass notions such as space, matter, energy, change,causality; whereas category of experience encompass notions such as quantity,quality and time8. Categories are all represented in Protégé-2000 as subclassesof noesis, with no slots.Two categories of existence that deserve some attention here are change andcausality. On the one hand, we postulate change as a separate category fromtime following the philosophical position [13] according to which change must beassumed as distinct from time in order for objects to keep their identity throughthe occurrence of events (i.e. temporal individuals) that change them. Further-more, following [7] we propose to distinguish causality from causation and to seethe former as a kind of change. In other words we propose to see causality as anur -element of our knowledge of what exists: causality is a piece of our knowledgeof how what exists can change. For instance, in Example 1 there is a causalityrelation between, on the one hand, the shooting of the bullet or the poisoning ofthe canteen (possible causes) and, on the other hand, the death of the traveler(possible effect). But there is a relation of causation only between the shootingof the bullet (actual cause) and the death of the traveler (actual effect). Wetherefore propose to see causality as the epistemological counterpart of an on-tological dependence. In other words, the build up of experience by means ofcausality requires the concurrent presence of certain categories of existence. Forinstance, we propose here to adopt the following ontological dependence betweencategories of existence as the standard notion of causality: energy cannot existwithout matter, matter cannot exist without space.

Definition 4 (Dimension). Dimension is experience-related (i.e. phenomeno-logical) noesis. A dimension relates two categories.

7 We want to avoid to use here the expression a priori for describing the status ofcategories. As a matter of fact, under a noetical perspective nothing is a priori andone may see categories as the result of evolution, both of individuals and of species.

8 The main philosophical rationale behind having time as a category of experience isthe idea that when we talk about time we do not connote an entity or a naturaldimension that exists with independence of what we are as (human) observers. Thefoundation of the notion of time rests on the biology of the observer [12].

The cognitive build up provided by the categories allows dimensions to emerge.The standard example of a dimension is mass. By experience, all physical ob-jects have a mass, which is the quantity of matter they comprise. We never have,though, a concrete experience of either matter or quantity as such. Therefore,we must assume their existence as categories, rather than as entities, and em-ploy them in the definition of the notion of mass. In other words, the concretenotion of mass relates the epistemological to the ontological part of our noeticexperience. We experience objects (ontology) as having mass (phenomenology),which relates two categories: matter and quantity (epistemology). In the defini-tions of dimensions, we associate categories to one another with the expression‘experienced by means of’. This is to underline the fact that the definition ofdimensions in terms of categories is not an ontological but a phenomenologicaldefinition. We therefore say, for instance, that mass is matter experienced bymeans of quantity (rather than mass is a quantity of matter), where the experi-ence of matter by means of quantity is a purely intellectual one, as both matterand quantity are categories, not entities. Furthermore, it should be noticed thatwe use the expression ‘experienced by means of’ also in the definition of entitiesin terms of dimensions. In this case, the expression ‘experienced by means of’refers to the perceptual (rather than the intellectual) experience of an entity (e.g.an object) through a dimension (e.g. mass).The following dimensions have been defined: volume (i.e., space experienced bymeans of quantity), form (i.e. space experienced by means of quality), location(i.e., space experienced by means of time); mass (i.e., matter experienced bymeans of quantity), material (i.e., matter experienced by means of quality), state(i.e., matter experienced by means of time); work (i.e., energy experienced bymeans of quantity), energy-form (i.e., energy experienced by means of quality),power (i.e., energy experienced by means of time); direction (change experiencedby means of quantity), transition (change experienced by means of quality), pe-riod (change experienced by means of time).All dimensions are represented in Protégé-2000 as instances of the class dimen-sion. This, in turn, is a subclass both of noesis and of standard slot, which isa type of system class. In other words, the instances of the class dimension areparticular kinds of slots, which by definition associate a category of existencewith a category of experience.

Definition 5 (Entity). Entity is existence-related (i.e. ontological) noesis.

The notion of entity indicates something that exists separately from other thingsand has a clear identity. In Example 1 everything is an entity. Entity is repre-sented in Protégé-2000 as a subclass of noesis with no slots.

Definition 6 (Physical entity). Physical entity is an entity experienced bymeans of one or more of the following dimensions: volume, form, location, mass,material, state, work, energy-form, power, direction, transition, period.

Physical entity is represented in Protégé-2000 as a subclass of entity with noslots.

Physical Causation

CausationCause Instance EventEffect Instance Event

isa

Entity

Physical Entity

isa

Occurrence

isa

ProcessTransition Instance Dimension

Direction StringEnergy-Form String

Power IntegerWork IntegerPeriod Integer

isa

ObjectLocation StringForm String

Material StringState Integer

Volume IntegerMass Integer

isa

EventSubject Instance Object

Occurence-of Instance Process

isa isa

Fig. 2. Entities in CausatiOnt

Definition 7 (Object). Object is a physical entity which is experienced bymeans of all of the following dimensions: volume, form, location, mass, ma-terial, state.

In Example 1 objects are the bullet and the canteen. Object is represented inProtégé-2000 as a subclass of entity with slots (its dimensions).

Definition 8 (Process). Process is a physical entity experienced by means ofall of the following dimensions: work, energy-form, power, direction, transition,period.

In Example 1 being shot and being broken are processes. Process is representedin Protégé-2000 as a subclass of entity with slots (its dimensions).

Definition 9 (Occurrence). Occurrence is a reified relation between objects,processes and/or occurrences.

Occurrence is represented in Protégé-2000 as a subclass of entity with no slots.

Definition 10 (Event). Event is an occurrence of a process (the occurrenceof) which changes the value of a dimension of an object (the subject).

In Example 1 an example of event is the trigger being pulled.Finally, the notion of causation may be defined.

Definition 11 (Causation). Causation is an occurrence of two events, thecause and the effect.

Definition 11 is the counterpart within CausatiOnt of definition 1. It is very broadand it is needed as a definitional node in the ontology. In other words, all the

clauses that provide the sufficient conditions for more restrictive (and thereforemore interesting) causal relations are provided in the definitions subsumed byDefinition 11. This does not mean that the relation introduced in Definition 11is indistinguishable from simple sequencing of events. Definition 11 introduces atype of occurrence. This has, of course, a rather strong implication: by definitionall reified relations between events are causal relations.

Definition 12 (Physical causation). Physical causation is causation betweenan event E1, which is an occurrence of a physical process P1 (the occurrence of)involving an object O1 (the subject), and event E2, which is an occurrence of aphysical process P2 (the occurrence of) involving an object O2 (the subject). Arelation of physical causation holds between E1, the cause, and E2, the effect, ifthe following conditions are met:

1. O1 and O2 are not the same object, according to the adopted identity criterionfor objects.Comment: the subjects must be truly distinguished objects.

2. P1 and P2 are not the same process, according to the adopted identity crite-rion for processes.Comment: an event cannot cause itself. By this clause we adopt the viewthat causation is a non reflexive relation.

3. P1’s period precedes P2’s period.Comment: the cause temporally precedes the effect. Even for processes thatare temporally distributed (i.e. continuous) the causing process starts be-fore the caused one. By this clause we adopt the view that causation is atemporally asymmetric relation.

4. P1’s energy-form is the same as P2’s energy-form or E2 is reducible to eventsE2,1. . . E2,n such that:(a) E2,1. . . E2,n are occurrences of processes P2,1. . . P2,n, which all have the

same energy form of P1.(b) E2,1. . . E2,n have as their subjects objects O2,1. . .O2,n, which are the

grains of O2, according to the adopted structural constraints.Comment: in the interaction between two objects energy is transferred ortransformed. In this latter case, the transformation of energy should be re-ducible to a transfer of energy between the cause and the events occurringto the structural components of the object of the effect (its grains accordingto a chosen granularity).

5. P1’s direction is the same as P2’s direction or P1’s power is greater or equalto P2’s power or P1’s work is greater or equal to P2’s work.Comment: this clause accounts for the fact that usually changes of one signcause changes of the same sign (i.e. an increase can usually only be caused byan increase and a decrease by a decrease). If this condition cannot be tested(which might be the case when lack of information makes it impossible toestablish the directions of either P1 or P2) or if it is not satisfied, one maywant to use the principle of the dispersion of energy in order to distinguishthe cause from the effect.

6. The category of existence of P2’s transition can not exist without the categoryof existence of P1’s transition, according to the adopted causality constraint.Comment: changes in O1’s dimensions can only affect those dimensions of O2that are ontologically dependent on the dimensions changed in O1, accordingto the adopted causality constraint between categories of existence.

It should be added that we take physical causation to be a transitive relation.Definition 12 is represented in Protégé-2000 as a subclass of causation with slots.The conditions listed in the definition should be implemented as a series of con-straints.The information given on E1 and E2 so far may be used by the reader for anintuitive testing of clauses 1, 2, 3, 6 of definition 12. Clauses 4 and 5 are moredifficult to test, not only for what concerns the information given here on E1 andE2, but in general for any two couples of non repeatable events. In conclusion,the most important characteristic of definition 12 is its use of a controlled vo-cabulary, which defines terms that pertain to three distinct philosophical levels:epistemology, phenomenology and ontology. Such modularity makes it possibleto define causation by means of several types of traditionally distinct criteriaemployed within the same one definition: formalism (clauses 1, 2), singularismand functionalism (clauses 3, 4, 5), cognitivism (clause 6).

4 Preliminary axiomatization of CausatiOnt in DOLCE

DOLCE (Descriptive Ontology for Linguistic and Cognitive Engineering) is anontology of particulars, as shown in the top class of Figure 3. DOLCE is basedon a fundamental distinction between four types of entities: Endurants, Perdu-rants, Qualities and Abstract entities. Endurants are wholly present (i.e., alltheir proper parts are present) at any time they are present. Endurants roughlycorrespond to objects in CausatiOnt. Perdurants, on the other hand, just extendin time by accumulating different temporal parts, so that, at any time they arepresent, they are only partially present, in the sense that some of their propertemporal parts (e.g., their previous or future phases) may be not present. Perdu-rants roughly correspond to processes in CausatiOnt. DOLCE’s third branch isQuality. Qualities can be seen as the basic entities we can perceive or measure:shapes, colors, sizes, sounds, smells, as well as weights, lengths, electrical charges,etc. Qualities may be clustered in quality types. The term ‘quality’ is often usedas a synonymous of ‘property’, but this is not the case in DOLCE: qualities areparticulars, properties are universals. Qualities inhere to entities: every entity(including qualities themselves) comes with certain qualities, which exist as longas the entity exists. DOLCE’s qualities are not comparable to CausatiOnt’s di-mensions, because the latter are not entities. DOLCE distinguishes between aquality (e.g., the capacity of the canteen in Example 1), and its value (e.g., 1liter). Values are Abstracts, called qualia in DOLCE, and describe the positionof an individual quality within a certain conceptual space, called here qualityspace. Such quality spaces are subsumed by the fourth branch of DOLCE, i.e.abstract entities, and they are called Regions. So when we say that two canteens

Particular

Perdurant

isa

Abstract

isa

Quality

isa

Endurant

isa

Event

isa

Stative

isa

Physical Object

Physical Endurant

isa

State

isa

Process

isa

Abstract Region

Region

isa

Physical Region

isa

isa

Physical Quality

isa isa

Fig. 3. General hierarchy of DOLCE

have (exactly) the same capacity, in DOLCE we mean that their capacity quali-ties, which are distinct entities, have the same position in the measure-for-fluidsspace, that is they have the same capacity quale. This distinction between qual-ities and qualia is inspired by the so-called trope theory. Its intuitive rationale ismainly due to the fact that natural language - in certain constructs - often seemsto make a similar distinction. Each quality type has an associated quality spacewith a specific structure. For example, lengths are usually associated to a metriclinear space, and colors to a topological 2D space etc. For a full specification andformal characterization of DOLCE refer to [4]9. Our first effort in axiomatizingCausatiOnt in DOLCE10 has been directed at importing CausatiOnt’s epistemo-logical and phenomenological branches into DOLCE. As shown in figure 4 andin the following set of definitions, categories are Abstract regions (definitions1-10). By (11) we have defined CausantiOnt’s relation ExperiencedByMeansOfin terms of DOLCE’s relation ExactLocation, which generically locates any typeof particular in a region. In (12-13) we have hooked up categories and DOLCE’squalities, by means of DOLCE’s relation QLocation, which relates qualities toregions. In (14) we have defined the ontological constraint for causality. Finallyin (15) we give an example of how dimensions should be defined in DOLCE asa relation between a particular and a region.

Categoryc(x) → AbstractRegion(x) (1)Categoryc(x) ≡ (2)CategoryOfExistencec(x) ∨∨CategoryOfExperiencec(x)

9 Available on http://wonderweb.semanticweb.org/deliverables/D18.shtml10 In order to avoid confusion with DOLCE’s original predicates, in the following all

the predicates introduced in DOLCE from CausatiOnt are distinguished by the su-perscript c.

Physical Endurant

Category

Category of Existence

isa

Category of Experience

isa

Abstract Region

isa

ExperiencedByMeansOf

Region

isa

Quality

InherentIn

MainCategory

QLocation

Fig. 4. Import of CausatiOnt into DOLCE

CategoryOfExistencec(spacec) (3)CategoryOfExistencec(matterc) (4)CategoryOfExistencec(energyc) (5)CategoryOfExistencec(changec) (6)CategoryOfExperiencec(quantityc) (7)CategoryOfExperiencec(qualityc) (8)CategoryOfExperiencec(timec) (9)ExactLocation(changec, causalityc) (10)ExperiencedByMeansOfc(x, y) =def (11)CategoryOfExistencec(x) ∧ CategoryOfExperiencec(y) ∧∧ExactLocation(x, y)

HasCategoryc(x, y) =def (12)Quality(x) ∧ Categoryc(y) ∧QLocation(x, y)

MainCategoryc(x, y, z) =def (13)Quality(z) ∧HasCategoryc(z, x) ∧HasCategoryc(z, y) ∧∧ExperiencedByMeansOfc(x, y)

CausalityOrderc(x, y, z, w) =def (14)Quality(z) ∧Quality(w) ∧∧∃x∗MainCategoryc(x, x∗, z) ∧

∧∃y∗MainCategoryc(y, y∗, w) ∧∧(x = spacec → (y = spacec ∨ y = matterc ∨ y = energyc)∧(x = matterc → (y = matterc ∨ y = energyc)∧(x = energyc → (y = energyc))

V olumec(x, y) =def (15)PhysicalEndurant(x) ∧ ∃zInherentIn(z, x) ∧QLocation(z, y) ∧∧MainCategoryc(spacec, quantityc, z)

5 Conclusion

Based on axioms (1-15) further research efforts will be directed at defining therelation of causation in DOLCE by means of a representation paradigm calledDescriptions and Situations, which extends DOLCE and is now under devel-opment. Once this definitional phase is complete, an implementation of the re-sulting knowledge structure will be attempted. All this is aimed at creating theconceptual basis of a tool for automatic testing, relative to Definition 1, of (legal)models of causation in fact.

References

[1] Lehmann, J.: Causation in Artificial Intelligence and Law - A modelling approach.PhD thesis, University of Amsterdam - Faculty of Law - Department of ComputerScience and Law (2003)

[2] Lehmann, J., Breuker, J., Brouwer, B.: Causation in ai&law (to appear). AI andLaw (2004)

[3] Gangemi, A., Guarino, N., C., Oltramari, A., Schneider, L.: Sweetening ontologieswith dolce. In: Proceedings of EKAW 2002: 166-181. (2002)

[4] Masolo, C., Borgo, S., Gangemi, A., Guarino, N., Oltramari, A.: Wonderweb de-liverable d18 - final report. Technical report, National Research Council - Instituteof Cognitive Science and Technology (2003)

[5] Pearl, J.: Causality. Cambridge University Press (2000)[6] Hart, H., Honore, T.: Causation in the Law. Oxford University Press (1985)[7] Hulswit, M.: A semeiotic account of causation - The cement of the Universe from

a Peircean perspective. PhD thesis, Katholieke Universiteit Nijmegen (1998)[8] Ducasse, C.: On the nature and observability of the causal relation. Journal of

Philosophy 23 57-68 (1926)[9] Russell, B.: Human Knowledge. Simon and Schuster (1948)

[10] Salmon, W.: Scientific Explanation and the Causal Structure of the World. Prince-ton: Princeton University Press (1984)

[11] Dowe, P.: Causality and conserved quantities: A reply to salmon. Philosophy ofScience 62, 321-333 (1995)

[12] Maturana, H.: The nature of time. http://www.inteco.cl/biology/nature.htm(1995)

[13] Lombard, L.: Event - A metaphysical study. Routledge and Kegan Paul (1986)

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From Temporal Rules to One Dimensional Rules

Kamran Karimi and Howard J. Hamilton

Department of Computer Science University of Regina

Regina, Saskatchewan CANADA S4S 0A2

{karimi, hamilton}@cs.uregina.ca

Abstract. In this paper we propose a new algorithm, called 1DIMERS (One Dimensional Investigation Method for Enregistered Record Sequences), to mine rules in any data of sequential nature, temporal or spatial. We assume that each record in the sequence is at the same temporal or spatial distance from others, and we do not constrain the rules to follow any monotonic direction, meaning that the rules can involve condition attributes in previous and next records relative to the decision attribute. Removing the conceptual temporal limitations makes 1DIMERS a generalised form of TIMERS (Temporal Investigation Method for Enregistered Record Sequences). TIMERS merges consequent records together, and then finds causal or acausal relationships among the variables in the merged records. The kind of rules discovered by TIMERS has also been called sequential rules. In general the passage of time is limited to one direction, which has been used in our previous work to distinguish between causality and acausality. Since in principle it is possible to move back and forth along a sequence, with general sequential data we can no longer intuitively speak of causality and acausality based on a direction. As a result, in 1DIMERS we substitute the terms "causality" and "acausality" with "forward-predictive" and "backward-predictive," respectively. 1DIMERS and TIMERS may each be applicable to a different problem depending on the user's choice, and we give examples of each program's applicability. In previous work we have been using C4.5 as the classifier for creating temporal rules. Here we employ CART as well, which has the ability to regress as well as classify, and show that the results are independent of the underlying rule discovery program.

1. Introduction

Given a sequence of records, the problem we are considering is finding rules for predicting the value of a decision attribute that appears in each record. The traditional approach is to look for a relationship among the decision attribute and other attributes within the same record. One example rule would be [If(a = 6) then (decision = false)]. This method may not produce good results if there is an inter-record relationship among the attributes. Bounded by temporal constraints, in such a case we usually expect only the previous records to affect the current decision attribute, but here we investigate the possibility that the decision attribute's value is determined by attributes not only in previous records, but in next records, or both previous and next records. One example rule in this context would be: [If{(acurrent-1 = 2) AND (bcurrent+1 = 2)} then (decisioncurrent = false)].

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The attributes are now qualified with their position relative to the position of the decision attribute. In this example, "current-1" could be read as "previous," and "current+1" could be read as "next."

Relying on data records that appear one after the other in a sequence from a single source (so they are related), sets our approach apart from methods such as [16] than do not consider any ordering among the input records. In this paper we use the term "one-dimensional" instead of "sequential" to avoid confusion with common terminology. Though the data we deal with is sequential in nature, it need not obey any temporal order. Also, the attributes in each record in the sequence can represent any number of dimensions, temporal or spatial. "One-dimensional" here refers to the fact that there is a single temporal or spatial ordering among the records. Also, a sequence implies an unbreakable order, while in this paper we present rules that go back or forth (or both) in the sequence to predict the value of a decision attribute. This usage may not be suitable for real-time execution of temporal rules (we can't give a verdict until sometime in the future). We expect them to be of value in cases where predictive power is of more importance, or we are processing stored temporal data where at any given instant the future and past are available. Alternatively we may be processing spatial data, where future and past are simply substituted by notions of nearby locations (neighbourhood), and considered available. Lifting the restriction of following an inherent order in rules opens the door to new methods of analysing data. Other than that, there are hints that in spite of the intuitive appeal of finding patterns and rules in temporal sequences of data such as time series in a fixed temporal direction, in some cases the results may not be useful [6].

Sequential data and sequential rules have been studied before [1, 4, 20]. For example, in [4] the authors provide a genetic algorithm solution to the problem of detecting rules that manoeuvre a plane that is being chased by a missile in a two dimensional space. Discrete attributes such as speed, direction of the missile, turning rate of the plane, etc. are measured during 20 time steps. It is assumed that after 20 steps the missile will stop the chase. The rules discovered in that paper form part of a plan, and the genetic algorithm changes parts of the plan to make them better suitable to solving the problem. Since the aim of the plans is to prevent a hit, the system is developed to produce rules that come up with evasive actions. The rules are then used in a simulator to measure their effectiveness. Time is obviously the sequencing factor in this example. In this paper we provide one example of sequential data that resembles this application in the sense that it consists of 15 measurements made after a failure is detected in a robot. The observations are then used to classify failure types. However in general we are interested in predicting the value of an attribute that is included in each record. "Being hit," or "failure" does not appear in any of the records, while an attribute such as soil temperature can be measured at regular intervals along with other related variables. Other examples in this paper address the problem of predicting the value of such an attribute.

The remainder of the paper is organised as follows. Section 2 provides background for our work and also presents intuitive examples of the concepts used in the paper. Section 3 formally presents the 1DIMERS (One Dimensional Investigation Method for Enregistered Record Sequences) algorithm, which is a generalised version of TIMERS (Temporal Investigation Method for Enregistered Record Sequences). In Section 4 we present the

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results of experiments with TIMERS, showing its effectiveness in solving temporal problems. The results of running TIMERS on a Robot learning problem, involving fixed number of relevant records (w = n = 15), are presented. It is a classification problem, with discrete values for the decision attribute. Other experiments in Section 4 show that TIMERS is effective for solving regression problems, where the decision attribute is continuous, and provide the results of running CART on two datasets. C4.5's results are provided for comparison purposes. 1DIMERS overlaps with TIMERS in its method, and for comparison's sake its results are provided in each case after trying TIMERS. Section 5 looks at another application domain that closely resembles the temporal domain, and that is spatial sequential data, and shows that the same techniques are effective there. TIMERS and 1DIMERS' results are presented and compared. Section 6 concludes the paper.

2. Background

Our previous work focuses on discovering temporal rules [7, 8] that allow us to predict what happens next, given previous observations. A temporal rule is a rule that involves time, i.e. the condition attributes appear at different times than the decision attribute. We divide temporal rules into two possible categories, causal, and acausal. A causal relation is one that involves attributes in the past affecting the decision attribute in the future [19]. The past affecting the future is the normal direction of time, and provides our definition of causality with an intuitive sense. We also consider the case where the future observations affect the past. We consider future affecting the past as a sign of acausality [15], or temporal co-occurrence. In an acausal relationship, the attributes just happen to be observed together over time, while none is causing the other. In this case there may be a hidden cause that has escaped our observation. Other than causality and acausality, the third possibility is that the relationship between the condition attributes and the decision attribute is instantaneous, meaning that value of the decision attribute is best determined by the condition attributes at the same time.

We proposed the TIMERS method to detect a causal or acausal relation among temporal sequences of data [11, 13, 14]. TIMERS provides a set of tests and guidelines, for judging the nature of a relationship. It is partly performed by software, and partly by the domain expert who is analysing the data. Following this algorithm, we generate classification rules from the data, using an operation called flattening. Flattening merges consecutive records in the normal, forward, direction of time (for the causality test) or the backward direction of time (for the acausality test). The number of records merged is determined by a time window w, and represents our guess as to how many records may be involved in an inter-record relationship. The quality of the rules, determined by their training or predictive accuracy, allows us to judge the data as containing a causal or acausal relation. TIMERS performs three tests: One without flattening, to test the instantaneous hypothesis, and two others to determine the temporal characteristics of the data. The order to consider goes from instantaneous, to acausal, to causal. So if the results of an instantaneous test is about the same or better than the other two, then we declare the relationship among the decision and condition attributes to be instantaneous. Otherwise if the results of the acausality test is about the same, or better than the causality test, then we

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declare the relationship as acausal. Otherwise the relationship is causal. This order implies that when dealing with temporal relationships, the tendency is to declare it as acausal. More explanation is provided in [13], where an algorithm for flattening data in both forward and backward directions is provided.

In a sequential spatial dataset it is reasonable to assume that there may be connections between records at the neighbouring positions, before and after the current record. In this paper we introduce the sliding position flattening method which includes forward and backward flattening as special cases. The principle behind the sliding position method is that both previous and next records can be influential in determining the current value of the decision attribute. In a temporal domain this means considering both past and future observations. With any fixed window size w, the new flattening algorithm first places the current decision attribute at position one, and uses the next w-1 records to predict its value. This corresponds to a backward flattening in TIMERS, where future values are used to predict the past. Then the current attribute is set at position 2, and the previous record (position one) and the next w-2 records are used for prediction. This case has no correspondence in our previous algorithm in [13]. This movement of the current position continues and at the end it is set to w, and the previous w-1 records are used for prediction. This corresponds to forward flattening in TIMERS.

As an example consider four temporally consecutive records, each with four fields: , , , . Suppose we are interested in predicting the value of the last (Boolean) variable. Using a window of size 3, we can merge them as in Table 1. The decision attribute is indicated in bold characters. When it comes to the record involving the decision attribute, we do not consider any condition attributes in the same record as the decision [13]. The Record.value notation in Table 1 means that we are only including the decision attribute. For example, would contain , where false is the decision attribute in R3. This is to make sure that minimum amount of data is shared between the original record and the flattened record.

Instantaneous. w = 1 (original data)

Forward (Causality). w = 3

Backward (Acausality). w = 3

Sliding position. w = 3

R1 = R2 = R3 = R4 =

Table 1. Results of flattening using the forward, backward, and sliding position methods

Normal flattening (vs. sliding position flattening) with a window size of w reduces the number of records by w-1. It is possible that not all the data in a dataset follow each other temporally, but only every n records. For example, every two records were generated one after the other, but there is no relationship between the first record and the third record, or any other record. In this case we consider the window size w to be the same as n, and

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perform flattening so that every consecutive n records are merged into one, and thus the number of flattened records is divided by n. Sliding position flattening increases the number of records.

TIMERS and 1DIMERS perform a series of pre-processing operations, notably flattening, then provide the processed data to another software to generate rules or trees and evaluate them. A post-processing phase can then follow, in which the data are presented to the user in a sequentially meaningful way. We have tried C4.5 [17] before, and because of its availability of source code, have been able to integrate it into our TimeSleuth software [9, 12]. TimeSleuth performs all processing before and after running C4.5 and hence partially implements both the TIMERS and 1DIMERS algorithms. Results of comparing TimeSleuth with other causality miners appear in [14]. Being a classifier, to apply data with continuous variables to C4.5, one has to perform discretisation on the decision attribute, which is not always reasonable with continuous data. In this paper we use another package called CART [2] which can classify as well as perform regression. We evaluate our method with CART as the underlying rule-discoverer, and we show that it performs with little basic variation with different rule-discovery programs.

To use CART we had to perform many of the pre- and post-processing operations "by hand," i.e., using tools that were not integrated into CART. We performed flattening with TimeSleuth, and then deleted the current-time attributes using Mcrosoft Excel. The results for CART were not presented in a temporally valid way since CART, like most other data mining and machine learning algorithms, does not consider any order among its input records. So in the output a variable from the future could precede a variable from the past, for example.

3. The 1DIMERS Algorithm

Modern physics has established time and space as a unity, where one is inconceivable without the other. However, time remains an anomaly because unlike the spatial dimensions, it seems that one cannot move back in time, although experiments have shown that at the particle level, this is in fact possible [5]. Discovering temporal associations that predict the future, based on past observations, is possible, and one can conceptually use the same idea for one-dimensional space as well. Our previous work has used the distinction between moving back and forth in time as the basis of distinguishing causality on one side, and acausality (or temporal co-occurrence) on the other. Since we do not consider an explicit representation of time as necessary (time is implicitly present in the order of the records), a measure such as length can be substituted for time.

Consider the problem of drilling a well. The well can be regarded as a one-dimensional entity. As the drill is making its way through the ground, new points are explored and registered. When we stop, we have a series of records that follow each other along the line. While it seems that the data was produced in a certain temporal order, one could argue that if the drilling were started from the opposite side, then we would be encountering the points from the reverse direction of time. It makes perfect sense to analyse the drilling data in any direction of time, with the results being valid in both cases.

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Of course now it is not possible to talk about cause and effect because what happens to precede something in one direction, will be following it in the opposite direction.

1DIMERS is an evolution of TIMERS. It changes the terminology from a temporal domain to a spatial domain and provides a more general flattening method, as intuitively described in Section 2. In 1DIMERS an instantaneous rule becomes a punctual rule (happens on a point instead of at an instant). A causal rule becomes a forward-predictive rule. An acausal rule becomes a backward-predicitve rule. The intuitive distinction of causal vs. acausal rules does not exist here. "Forward" and "backward" in 1DIMERS simply refer to the original direction of the data. The lack of distinction between the two possible directions of movement on a line side steps some conceptual problems and debates about causality [3]. In 1DIMERS two new categories are added to one-dimensi

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