OCML manual
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1. and a control body and returns the result of evaluating this in an environment in which each vari is bound to termi Chapter 7 Reference 21 7 2 2 if The first action which is carried out when evaluating an if control term is to check whether log expression is satisfied If this is the case then then control term is evaluated in the environment which satisfies log expression If log expression cannot be satisfied in the cur rent model then there are two possibilities If else control term is specified then this is evaluated and the value obtained is returned as the value of the if control term If else control term is not present and log expression cannot be proved then the constant nothing is returned 7 2 3 cond The interpreter iterates through each clause of a cond control term until it finds one whose log expression is satisfied If none is found then nothing is returned Otherwise let s assume cond clausei is the first clause whose log expression is satisfied In this case the value of the cond control term is obtained by evaluating the control term associated with cond clausei 7 2 4 loop The control construct loop provides a simple mechanism for iterating over lists It first evaluates a term which should return a list say L Then it iterates over each element of L say I and evaluates control term in an environment in which variable is bound to I 7 2 5 do The control construct do is a simple sequencing2. rel filter rest 1 rel The above definition shows an example of the use of def function The OCML function filter takes as arguments a list 1 and a unary relation rel and returns the elements of 1 which satisfy rel As illustrated by the definition the def option provides a declarative way of specifying a function the option body an effective way of computing its value for a given set of input arguments 3 7 Procedures Procedures define actions or sequences of actions which cannot be characterized as func tions between input and output arguments For example the procedure below defines the sequence of actions needed to set the value of a slot These include a unassert statement which removes any existing value from the slot and a tell statement which adds the new value Both tell and unassert are procedures The former takes a ground logical expression and adds it to the current model The latter takes a relation expression and removes from the current model all assertions which match it Note that in accordance with the uniform view of a knowledge model slot changes are carried out by means of generic assertion and deletion operations i e in terms of tell and unassert def procedure SET SLOT VALUE i s v constraint and instance of i c slot of s c body do unassert list of s i any tell list of s i v 3 8 Namespaces OCML uses Lisp symbols to name things This is convenient bu
3. Domain Modelling in OCML 4 By default all ontologies are built on top of the OCML base ontology This comprises twelve sub ontologies which include the basic definitions required to reason about basic data types e g lists numbers sets and strings the OCML system itself and the OCML frame representation Specifically the following sub ontologies are provided Meta Functions Relations Sets Numbers Lists Strings Mapping Frames Inferences This ontology defines the concepts required to describe the OCML language It includes constructs such as OCML expression functional term rule re lation function assertion etc This ontology is particularly important to construct reasoning components which can verify OCML models Defines the concepts associated with functions e g it includes relations such as domain range unary function binary function etc Defines the various notions associated with relations These include the uni verse and the extension of a relation the definition of reflexive and transitive relations partial and total orders etc This ontology defines the notions associated with sets e g empty set union intersection set partition set cardinality etc Defines the various concepts and operations required for reasoning about num bers and for performing calculations Defines the concepts and operations associated
4. taken from the Sisyphus I domain model is shown in the box below def instance harry c researcher has project babylon smoker no hacker yes works with jurgen 1 thomas d In particular the above definition shows that a slot can have multiple values In this case harry c works both with jurgen 1 and thomas d 3 5 Relations Relations allow the OCML user to define labelled n ary relationships between OCML en tities Relations are defined by means of a Lisp macro def relation which takes as arguments the name of a relation its argument schema optional documentation and a Chapter 3 Domain Modelling in OCML 7 number of relation options An argument schema is a list possibly empty of variables Relation options play two roles one related to the formal semantics of a relation the other to the operational nature of OCML These roles are discussed in the next two sections 3 5 1 Relation specification options From a formal semantics point of view the purpose of a relation option is to help characterize the extension of a relation The table below shows the relation options which can be used to provide formal relation specifications and for each option informally describes its semantics A formal semantics to these options can be given in terms of the homonymous Ontolingua constructs Relation option Role in specification iff def Specifies both sufficient and necessary conditions for the relation to hold for a gi
5. Prolog depth first search with chronological backtracking is used to control the proof process Both semantically and operationally a backward chaining rule is the same as a sufficient relation option they both provide an expression which is sufficient to verify that a tuple holds for a relation Thus one might wonder whether rules are needed at all In practice the advantage of including backward rules in the language is that these provide a modu lar mechanism for refining existing possibly generic relation specifications for instance in cases where application specific knowledge is needed to complete the specification of a relation To clarify this point let s consider an example taken from the KMI office allocation problem see chapter 9 for an extensive analysis of this application The relation has value range is defined in the parametric design task ontology to char acterize the set of possible values which can be assigned to a design parameter see chapter 6 When building an application model the generic has value range specification is usually refined so that the space of possible values that can be assigned to a particular parameter is precisely defined A modular way to achieve this is to refine the definition of the relation by means of the appropriate backward chaining rules The rules shown below fulfil this purpose for two of the classes of parameters present in the KMI office allocation domain professors and secretaries In
6. an expression which has to be satisfied by each known instance of the relevant relation The relation options iff def sufficient prove by and lisp fun provide mech anisms for verifying whether or not a relation holds for some arguments The first two iff def and sufficient also play a specification role The others prove by and lisp fun only play an operational role Chapter 3 Domain Modelling in OCML 8 Both iff def and sufficient indicate logical expressions which can be used to prove whether some tuple is an instance of a relation From a theorem proving point of view there is an important difference between them Let s suppose we are trying to prove that a tuple say T satisfies a relation say R If a sufficient condition is tried and failed the OCML proof system will then search for alternative ways of proving that T satisfies R If an iff def condition is tried and failed then no alternative proof mechanism will be attempted The relation options prove by and lisp fun are meant to support rapid prototyping and early validation by providing efficient mechanisms for checking whether a tuple satisfies a relation The difference between prove by and lisp fun has to do with the expressions which are used as values to the two options prove by points to a logical expression lisp fun to a non logical one specifically a Lisp expression The box below provides an example of how the various types of relation opti
7. and task method levels is maintained An example of an upward relation mapping is illustrated by the definition below which is taken from an application model developed for the Sisyphus I problem The mapping is an upward one in the sense that it is used to lift van Harmelen and Balder 1992 the office allocation statements existing at the domain level to the problem solving level Specifically the goal of this mapping is to associate the relation current design model which is used by the parametric design problem solver to indicate the design model associated with the current design state to the set of in room assertions present in the current snapshot of the domain knowledge base The relation maps to is used to retrieve the parameter associated with each particular YQT member def relation mapping current design model up current design model dm if dm setofall p v and in room x v maps to p x An upward relation mapping ensures that when a task method level relation is needed the relevant information is obtained from the domain level Of course problem solving is also about inferring knowledge and retracting previously held assertions Hence OCML also supports downward relation mappings These divide into two categories add and remove The former specifies a procedure which is activated when a new relation instance is asserted The latter specifies a procedure which is activated when a relation instance is
8. different namespaces and ontologies used together in one ontology When Lisp reads a namespaced symbol it converts it to a symbol by concatenating the value of the referenced ontology s namespace uri slot with the symbol Thus _ fruit orange becomes OCML http www kmi open ac uk fruits orange It is im portant to remember that the _ syntax is merely a shorthand for the long quoted Lisp symbol If you so wish you can enter the long form directly as a normal Lisp symbol Given this namespaced variables interoperate fully with non namespaced ones The pre fixes themselves are discarded after they have been read in by the Lisp reader Namespaced symbols are case sensitive _foo is distinct from _Foo Further examples from a Lisp listener session OCML gt in ontology fruits lt OCML ONTOLOGY FRUITS gt OCML gt _colours orange OCML http www kmi open ac uk fruits orange OCML gt 8 orange OCML http www kmi open ac uk fruitsitorange OCML gt register namespace colors colours lt OCML ONTOLOGY COLOURS OCML gt in ontology colours lt OCML ONTOLOGY COLOURS OCML gt 8 orange OCML http www kmi open ac uk coloursttorange OCML gt eq _colours orange _colours orange T Chapter 3 Domain Modelling in OCML 12 OCML gt eq _colors orange _colours orange E OCML gt eq _colors orange ocml http www kmi open ac uk colours orange T OCML gt eq _c
9. is a solution to A Thus the proof mechanism supported by OCML is not complete with respect to first order logic statements In particular disjunctions can only be proved by proving each clause separately and negated expressions are only proved by default Chapter 9 Bibliography 27 9 Bibliography Motta99 Enrico Motta Reusable Components for Knowledge Modelling IOS Press 1 58603 003 5 Function Index Function Index D declarar e 5 def f unCtion 21 2 b se RR REG ECL RET 9 def instan6e ximk cas durer ERREUR HER UTE 6 def ontolOogy iced sere edo breed d 3 def e o e rut sek 10 def relation ccs dau a enin REENERT ERE 6 def r leii i tas Seet 14 disable fc watcher mode 15 E enable fc watcher mode 15 28 TU a ET 15 PUNE A air 15 T TACO EC ad dd 15 eh e EE 15 Concept Index Concept Index B forward Chaining 2 jos cea es ne ete pees Rm nhe Eet I EEN 29 N namespace sia pene da pani ia 10 O A at s de hvkese e ua pk pet ws 3 P A PP 10 R o HIR RAPERE 6 relation options cece eee eee eee eee ee 7 rule ii 14
10. primitive The control terms in its body are evaluated sequentially once only 7 2 6 repeat The control term constructor repeat repeats the control term s specified in its body until the end test is satisfied if the test has the form until test Otherwise if the test has the form while test then repeat actions stops as soon as the test fails If the end test is specified after the control terms then the control terms are carried out at least once i e the end test is verified at the end of each cycle If the end test is specified before the control terms then the test is verified at the beginning of each cycle If no test is provided then all control expression in the body of a repeat actions are repeated ad infinitum 7 2 7 return This is a simple way of exiting from the body of a loop or repeat construct When a control term such as return term is encountered the most specific loop or repeat construct in the current execution stack is exited and the value obtained from evaluating term is returned 7 3 Grammar loop control term loop for variable in term do control term do control term do actions control term repeat control term repeat actions end test control term repeat actions control term end test cond control term cond cond control clause setofall term setofall template basic log expression template nil term term Chapter 7 Reference 22 ter
11. this example the former can only go into a double room the latter into a large room next to the entrance def rule has value range 1 has value range gen m 1 if professor domain reference m 1 setofall r double a type room r usable yes def rule has value range 2 has value range gen m 1 if secretary domain reference m 1 setofall r and room r size n usable yes gt n 1 close to r kmi entrance 4 2 Forward chaining rules OCML also allows the user to define forward rules A forward rule comprises zero or more antecedents and one or more consequents Antecedents are restricted to relation expressions Chapter 4 Rule based reasoning 15 while any logical expression can be a consequent When a forward rule is executed OCML treats each consequent as a goal to be proven and attempts to prove them until one fails This mechanism makes it possible to integrate data driven and goal driven reasoning and to specify arbitrarily complex right hand sides A special operator exec is provided to allow OCML users to introduce control and therefore functional terms in the right hand side of a rule In particular two useful pro cedures are tell to assert new facts and output to produce output A simple example showing how to use these in a forward chaining rule is given below def rule has project cond has project x y then exec tell project covered by y x exec outpu
12. with lists It includes classes such as list and atom functions such as first rest and append and relations such as member Specifies the concepts and operations associated with strings e g string string append etc This ontology defines the concepts associated with the mapping mechanism de scribed earlier It includes only three definitions relation maps to and functions meta reference and domain reference The former takes a domain level instance and returns the associated task method level instance The latter performs the inverse function Defines the concepts associated with the frame based representation used in OCML It comprise meta classes such as class and instance functions such as direct instances and all slot values relations such as has one and has at most and procedures such as append slot value The purpose of this ontology is to provide a repository for defining functions and relations supporting the specification of KADS like inferences So far only a few such inferences have been added to this ontology to support different types of selection and sorting Environment This ontology provides a kind of environmental support for the construction of OCML models It includes special operators like exec which makes it possible to invoke procedures from rules and procedures such as output which prints out a message Chapter 3 Domain Modelling in OCML 5 Task Method This ontology provides the concept
13. OCML 6 value A value which is inherited by all instances of a class default value A value which is inherited by all instances of a class unless overridden by other values type The value of this option should be a class say C This option specifies that all values of the associated slot should be instances of C It is also possible to specify that a slot value must belong to one or more classes say Cl Cn by using the notation or C1 co Cn max cardinality The maximum numbers of slot values al lowed for a slot min cardinality The minimum numbers of slot values re quired for a slot cardinality The numbers of slot values required for a slot This option subsumes both min cardinality and max cardinality documentation The value of this option is a string provid ing documentation for a slot inheritance The inheritance mechanism used for deal ing with default values If merge is used then all default values inherited from differ ent ancestors are collected If supersede is used then default values inherited from more specific ancestors override those in herited from more generic ones 3 4 Instances Instances are simply members of a class An instance is defined by means of def instance which takes as arguments the name of the instance the parent of the instance i e the most specific class the instance belongs to optional documentation and a number of slot value pairs An example of instance definition
14. Operational Concept Modelling Language Dave Lambert and Enrico Motta Table of Contents 1 JID POODUIGEIOEL scsi aaa 1 LI Ee 1 2 Installation cortesia rana 2 2A Obtaining OCM Dessi adire e 2 2 2 Betupasseecseovesevenisbeecp8rte P eervaalce E b RB eDE CC T CERES 2 2 9 Library locations ire RE Ed PER rias 2 3 Domain Modelling in OCML 3 SE Overview aisha e EPOR REC eR S idle Pres N 3 3 11 Functional terms cocida deere 3 2 1 2 Control terms cai odos PUR 3 3 1 3 Logical expressions Li 3 9 2 Ontologles EELER n iri ceded i 3 D0 ClOSSCS raices da Shoes Loads Wed Eee ewe Heid EIS 5 Od ANSON CES Varia ti aus aban a 6 3 9 Relations siecle Ee ice 6 3 5 1 Relation specification option 7 3 5 2 Operationally relevant relation options T 3 0 3 SUMMING D cidcid ile 9 obo EUTCHIONS si rara a 9 OW erte EE Lea Lal barre 10 2 9 Namespace cu bt d e onda bea Lai ds 10 3 9 Translation between representation languages 12 3 10 The ask tell interface LL cece cee eee eee ee 12 4 Rule based reasoning 14 4 1 Backward chaining res 14 4 2 Forward chaining rmles 0 0 00 c cece eee eee eens 14 5 Modelling esues 0c 16 5 1 Object oriented and relation oriented approaches to modelling Er 16 6 Functional View of OCML 17 Gol Mappiib corale p amete eege 17 6 2 Instance mappin
15. T PARAMETER EVA_I EVA_I Solution MAPS TO YQT PARAMETER MONIKA_X MONIKA_X Solution MAPS TO YQT PARAMETER ULRIKE_U ULRIKE_U Solution MAPS TO YQT PARAMETER UWE_T UWE_T Solution MAPS TO YQT PARAMETER JOACHIM_I JOACHIM_I Solution MAPS TO YQT PARAMETER HANS_W HANS_W Solution MAPS TO YQT PARAMETER MICHAEL_T MICHAEL_T Solution MAPS TO YQT PARAMETER ANGY_W ANGY_W Solution MAPS TO YQT PARAMETER JURGEN_L JURGEN_L Solution MAPS TO YQT PARAMETER KATHARINA N KATHARINA_N Solution MAPS TO YQT PARAMETER THOMAS D THOMAS D Solution MAPS TO YQT PARAMETER HARRY C HARRY C Solution MAPS TO YQT PARAMETER ANDY L ANDY L Solution MAPS TO YQT PARAMETER MARC M MARC M Solution MAPS TO YQT PARAMETER WERNER L WERNER_L The advantage of this solution is that parameters and YQT members maintain their separate identities as shown in the next box describe instance YQT PARAMETER WERNER_L Instance YQT PARAMETER WERNER_L of class YQT PARAMETER HAS VALUE RANGE C5 123 C5 122 C5 121 C5 120 C5 119 C5 117 C5 116 C5 113 C5 114 C5 115 describe instance WERNER_L Instance WERNER_L of class RESEARCHER HAS PROJECT RESPECT SMOKER NO HACKER YES WORKS WITH ANGY_W MARC_M GROUP YQT Formally a mapping can be characterized as an association between an object say o and its meta object m o so that the entity denoted by the entity denoted by m o is the same as the entity denot
16. ble inputs of a function It specifies a logical expression which must be satisfied by the input arguments of the function The def option indicates a logical expression which defines the function This expression should be predicated over both some input arguments and the output variable Operationally the expression denoted by the constraint option provides a mechanism for testing the feasibility of applying a function to a set of arguments The expression denoted by def provides a mechanism for verifying that the output produced by a function application is consistent with the formal definition of the function Finally the options body and lisp fun provide effective mechanisms for computing the value of a function The former specify a functional term which is evaluated in an envi ronment in which the variables in the function schema are bound to the actual arguments The latter makes it possible to evaluate an OCML function by means of a procedural at tachment expressed as a Lisp function The arity of this Lisp function should be the same as that of the associated OCML function def function filter 1 rel gt sub 1 Returns all the elements in 1 which satisfy rel Chapter 3 Domain Modelling in OCML 10 def and unary relation rel list 1 list sub 1 gt and member x sub 1 holds rel x member x 1 body if null 1 71 if holds rel first 1 cons first 71 filter rest 1
17. ctional term interpreter 2 If term has the format proc term0 termn with n lt 0 where proc is a primitive 5 control operator then term is evaluated in env according to criteria which depend on proc If term has the format proc term0 termn with n lt 0 where proc is the name of a procedure and a Lisp body associated with proc exists then ocml control eval returns the value obtained by applying the Lisp body to the values obtained by evaluating each termi in env If term has the format proc term0 termn with n lt 0 where proc is the name of a procedure and no Lisp body associated with proc exists then ocml control eval returns the value obtained by applying the body of proc to the values obtained by evaluating each termi in env In all other cases ocml control eval signals an error 8 3 Proof system Procedure for proving basic goal expressions in OCML Chapter 8 Interpreters and Proof System 25 Let s suppose we want to find all solutions to a basic goal expression say G with format rel fun term where rel is the name of a relation and fun term a functional term In general we might be interested in one some or all solutions Therefore the order in which solutions are generated might be important The algorithm used by the OCML proof system is as follows 1 If rel is not a defined relation then signal an error Otherwise initialize SOL1 SOL2 SOL3 SOLA SOL5 and SOL6 to the e
18. dence 1 http git or cz Chapter 3 Domain Modelling in OCML 3 3 Domain Modelling in OCML 3 1 Overview OCML provides mechanisms for defining relations functions classes instances rules and procedures OCML supports the specification of three types of constructs functional and control terms and logical expressions 3 1 1 Functional terms A functional term in short a term specifies an object in the current domain of investiga tion A functional term can be a constant a variable a string a function application or can be constructed by means of a special term constructor This can be one of the following if cond the setofall findall quote and in environment7 see appendix 1 for a description of the semantics of these terms Variables are represented as Lisp symbols beginning with a question mark e g x is a variable Strings are sequences of characters enclosed in double quotes e g string A function application is a term such as fun fun term where fun is the name of a function and fun term a functional term Functions are defined by means of the Lisp macro def function which is described in Section 3 6 Functions page 9 Functional terms are evaluated by means of the OCML function interpreter which is described in detail in appendix 1 3 1 2 Control terms Modelling problem solving behaviour involves more than making statements and describing entities in the world Control terms are needed to
19. ds of services provided by OCML i operations for extending modifying a model ii interpreters for functional and control terms and iii a proof system for answering queries about a model Extensive details on the model extension modification facilities provided by OCML were given in earlier sections The interpreters and the proof system are described in detail in appendix 1 6 1 Mapping The constructs presented so far provide extensive support for domain modelling In order to fully support the TMDA framework additional constructs are needed for specifying tasks and methods and for mapping entities at the task method level to entities at the domain level As already said the conceptual vocabulary required to model tasks and methods is not hardwired in the language but is defined as a specialized ontology This will be presented in the next chapter in the next sections I will discuss the two kinds of mapping constructs supported by OCML relation mapping and instance mapping 6 2 Instance mapping Figure 3 8 XXX illustrated a simple example in which a class of concepts at the task method level parameter is mapped to a class of concepts at the domain level employee This is a very common situation when developing systems through reuse a problem solving domain independent model imposes a particular view over a set of domain concepts Fensel and Straatman 1996 A simple case is one in which a domain view is constructed by direct associa
20. e structure for inheritance and automatic classification relation orientation is normally associated with constraint based and rule based reasoning While the integration of multiple paradigms provides the aforementioned benefits when describing or interacting with a knowledge model it is useful to abstract from the various modelling paradigms and inference mechanisms integrated in the model and characterize it at a uniform level of description Specifically in accordance with a view of knowledge as a competence like notion Newell 1982 it is useful to decouple the level at which we describe what an agent knows from the level at which we describe how the agent organizes and infers knowledge Such an approach is used for instance in the Cyc system Lenat and Guha 1990 which integrates multiple knowledge representation techniques the heuristic level but provides a uniform interface to the Cyc knowledge base the epistemological level A similar approach is also followed by Levesque 1984 which describes a logic based query language which can be used to communicate with a knowledge base at a functional level independently from the data and inference structures present in the knowledge base Chapter 6 Functional View of OCML 17 6 Functional View of OCML A functional view of a knowledge representation system focuses on the services the system provides to the user Levesque 1984 Brachman et al 1985 Basically there are three kin
21. ed as first argument The relation holds has a special status because it is the only relation with variable arity supported by OCML 3 5 3 Summing up The set of relation options discussed here aims to provide a flexible and versatile range of modelling constructs supporting various styles of modelling While the emphasis is on operational modelling OCML also supports formal specification Moreover it provides facilities for integrating a specification with efficient proof mechanisms 3 6 Functions A function defines a mapping between a list of input arguments and its output argument Formally functions can be characterized as a special class of relations as in KIF Genesereth and Fikes 1992 However in operational terms there is a significant difference between a function and a relation functions are applied to ground terms to generate function values relation expressions can be asserted or queried Thus in accordance with the operational nature of OCML functions are distinguished from relations Functions are defined by means of a Lisp macro def function This takes as argument the name of a function its argument list an optional variable indicating the output argument as in Ontolingua this is preceded by an arrow gt optional documentation and zero or more function specification options These are def constraint body and lisp fun The option constraint provides a way to constrain the domain i e the set of possi
22. ed by o Genesereth and Nilsson 1988 This notion can be formalized in OCML by means of the following definition def relation maps to x y This relation allows the user to specify an association between an object at the task layer and one at the domain layer Formally y denotes the object denoted by the object denoted by x no op iff def y denotation x 6 3 Relation mapping Instance mapping works only in those cases in which imposing a view over a domain can be reduced to creating task level mirror images for a finite number of domain level objects A more general scenario is one in which there is some relation defined at the task method level which needs to be reflected to the domain level in a dynamic fashion A well known example is that in which domain concepts or statements are viewed as hypotheses at the problem Chapter 6 Functional View of OCML 19 solving level This association is typically dynamic given that hypotheses are considered as such only for a particular time slice of the problem solving process These situations can be modelled in OCML by means of relation mappings A relation mapping provides a mechanism to associate rules and procedures to a relation say R so that when a query of type R is posed or assertions of type R are made at the task method level these events can be reflected to the domain level The purpose of these reflection actions is to ensure that the consistency between domain
23. g NEIERENS e I7 6 3 Relation mapping isso iii 18 7 Retference n oak p i oriei 20 7 1 Functional Term Constructors eee 20 Tell getoa eerde e aetna 20 rn A all ts cite gees faa nox ee ie ee Eelsten 20 1 59 EEN 20 7 1 4 im environment ccc cece hen 20 Io A ots antl iano 20 CLO ernia 20 dele COn a ei 20 7 2 Control Term Constructore La 20 7 2 1 iIM CNVITONMENE 0 ccc cence eect ee hn 20 12 95 A III 21 AS PA AI 21 1 2 4 lOO0Du tistethcisse el ia ae 21 2 D du utu LE LI MILD IPM LU ee 21 PA lidest 21 4 220 SObDUEPixireeweddesmreeneseerciesbest uu dd cose PPP Ae wees 2 Co TAM lle dae 21 7 4 Inheritance and Default Values LL 23 8 Interpreters and Proof System 24 8 1 Functional term nterpreter 0000 cece ccs 24 8 2 Control term mterpreter 0 0 c cece eee eee nee eee 24 8 3 Proof SYStOM iure ala rn 24 8 4 Proof rules for non basic goal expressions L 0 25 9 Bibliography es SC Ke s ENEE E 27 Function Index Gorica aU LR P EAS 28 Concept IndeX erh EE See ege e Rh rh hb bd an 29 ii Chapter 1 Introduction 1 1 Introduction 1 1 Provenance This manual is substantially based on chapter 4 and appendix 1 of Reusable Components for Knowledge Modelling page 27 by Enrico Motta Dave Lambert reformatted it as Texinfo reorganized the material to something more appropriate to a user manual and added the installation and namespace sections Chapte
24. he two base ontologies Both the Ontolingua and OCML base ontologies provide a rich set of definitions for domain modelling In order to comply with the requirements imposed by the TMDA framework the OCML base ontology provides support also for specifying tasks and problem solving methods 3 3 Classes OCML also supports the specification of classes and instances and the inheritance of slots and values through isa hierarchies Classes are defined by means of a Lisp macro def class which takes as arguments the name of the class a list possibly empty of superclasses optional documentation and a list of slot specifications as illustrated by the definitions in the next box These show a number of classes taken from the domain model for the Sisyphus I office allocation problem Linster 1994 Chapter 9 This problem consists of allocating members of the YQT laboratory to the appropriate offices according to a number of constraints def class YQT member has project type project smoker type boolean cardinality 1 hacker type boolean cardinality 1 works with type YQT member belongs to group type research group value yqt def class researcher YQT member def class secretary YQT member def class manager YQT member OCML provides support for the usual slot specification machinery which is found in frame based languages Specifically it provides the following slot options Chapter 3 Domain Modelling in
25. ighlighted Assertions inherited through an isa hierarchy are always cached at definition time This means that they are retrieved at step 2 when the goal is matched against the current set of known facts The results returned by non logical mechanisms such as Lisp attachments and prove by are only merged with the results obtained by simple assertion matching step 2 In other words they are meant to provide efficient proof mechanisms which override those provided by definition forming options such as iff def and sufficient 8 4 Proof rules for non basic goal expressions Non basic goal expressions are proven in OCML using the following rules and A B This expression is satisfied if both A and B can be proven in the current model or A B This expression is satisfied if either A or B can be proven in the current model Chapter 8 Interpreters and Proof System gt AB lt gt A B not A exists schema or var A forall schema or var gt A B 26 This expression is satisfied if either A can not be proven or if B can be proven in each environment which is a solution to A This expression is satisfied if both gt A B and gt B A can be proven This expression is satisfied if A cannot be proven in the current model This expression is satisfied if A can be proven in the current model This expression is satisfied if either A can not be proven or if B can be proven in each environment which
26. m constant variable string fun term findall term the term in env term quote term if term cond term fun the name of a function or a term constructor A symbol whose first character is not constant variable A symbol whose first character is string A lisp string e g string log expression quant log expression basic log expression quant log expression forall schema or var log expression exists schema or var log expression basic log expression and log expression or log expression gt log expression log expression lt gt log expression log expression not log expression rel expression schema or var schema variable schema variable schema nil rel expression rel term rel a symbol naming a relation findall term findall template basic log expression in env term in environment pairs body pairs nil pair pairs pair variable term body term quote term term quote term the term the template basic log expression if term if log expression then term else term then term term else term term cond term cond cond clause cond clause log expression term in env control term in environment pairs control body pairs nil pair pairs pair variable term control body control term control term term in env contr
27. mpty set and go to step 2 2 Retrieve all the assertions present in the current model whose type i e first element is rel Match each assertion with G All successful matches we call this set SOLI provide solutions to G Go to step 3 3 If a Lisp attachment exists for rel then evaluate it in the Lisp environment to find eventual additional solutions to G say SOL2 Go to step 8 4 If a prove by proof condition say prove rel expression has been specified for relation rel then compute all solutions to prove rel expression say SOL3 Each of these is also a solution to G Go to step 8 5 Ifa iff def proof condition say iff rel expression has been specified for relation rel then compute all solutions to iff rel expression say SOL4 Each of these is also a solution to G Go to step 8 6 If a sufficient proof condition say suff rel expression has been specified for relation rel then compute all solutions to suff rel expression say SOL5 Each of these is also a solution to G Go to step 7 7 Ifa backward chaining rule has been specified associated with relation rel then invoke it to find all other solutions to G say SOL6 Go to step 8 8 The set of all solutions to query G is obtained by appending the lists SOL1 SOL2 SOL3 SOL4 SOL5 and SOL6 The algorithm shown above provides an operational semantics for the various relation forming constructs provided by OCML In particular the following two points should be h
28. ned by instantiating template in the returned environment If no solutions are found then the constant nothing is returned 7 1 4 in environment The primitive in environment takes a list possibly empty of pairs varl term1 and a body and returns the result of evaluating this in an environment in which each vari is bound to termi 7 1 5 quote The value of an expression such as quote term is term 7 1 6 if The first action which is carried out when evaluating an if term is to check whether log expression is satisfied If this is the case then then term is evaluated in the environment which satisfies log expression If log expression cannot be satisfied in the current model then there are two possibilities If else term is specified then this is evaluated and the value obtained is returned as the value of the if term If else term is not present and log expression cannot be proved then the constant nothing is returned 7 1 7 cond The interpreter iterates through each clause of a cond term until it finds one whose log expression is satisfied If none is found then nothing is returned Otherwise let s assume cond clausei is the first clause whose log expression is satisfied In this case the value of the cond term is obtained by evaluating the term associated with cond clausei 7 2 Control Term Constructors 7 2 1 in environment The primitive in environment takes a list possibly empty of pairs varl term1
29. ng to classes This object centred approach is in a sense orthogonal to the relation centred one which I used when discussing relations and logical expressions The former focuses on the entities populating a model and then associates properties to them the latter centres on the type of relations which characterize a domain and then uses these to make statements about the world These two approaches to modelling representation have complementary strengths and weaknesses and for this reason they are often combined in knowledge representation and modelling languages to provide hybrid formalisms Fikes and Kehler 1985 Yen et al 1988 In the context of a knowledge modelling language rather than a knowledge representa tion one the main advantage gained from combining multiple paradigms is one of flexibil ity Both object oriented and relation oriented approaches provide conceptual frameworks which make it possible to impose a view over some domain The choice between one or the other can be made for ideological or pragmatic reasons e g whether the target de livery environment is a rule based shell or an object oriented programming environment In the specific context of an operational modelling language such as OCML another ben efit which is gained by providing support for both object oriented and relation oriented modelling is that these approaches are naturally associated with particular types of infer ences Object orientation provides th
30. nterpreters and Proof System 8 1 Functional term interpreter The OCML interpreter is implemented by means of a Lisp macro ocml eval This evaluates a functional term term in an environment env according to the following rules 1 2 3 If term is a variable then the binding of term in env is returned If term is a string or a constant then term is returned If term has the format pfun term0 termn with n lt 0 where pfun is a primitive term constructor then term is evaluated in env according to criteria which depend on pfun If term has the format fun termo termn with n lt 0 where fun is the name of a function and a Lisp body associated with fun exists then ocml eval returns the value obtained by applying the Lisp body to the values obtained by evaluating each termi in env If term has the format fun term0 termn with n lt 0 where fun is the name of a function and no Lisp body associated with fun exists then ocml eval returns the value obtained by applying the body of fun to the values obtained by evaluating each termi in env In all other cases ocml eval signals an error 8 2 Control term interpreter Control terms are interpreted in a manner analogous to functional terms The control term interpreter is implemented by a Lisp macro ocml control eval which has the following behaviour 1 If term is a functional term then it is evaluated according to the rules given in ref Fun
31. ny value locally specified for slot s of I 2 I has inherited some default values as well as non default ones In this case the default values are ignored and rule i is applied We say that the default values are overridden by the non default ones 3 I has inherited only default values and local values have been specified As in the previous case the default values are ignored and only the local values are considered 4 I has inherited only default values and no local values have been specified In this case there are two possibilities If the inheritance facet has not been specified or it has been specified and it is merge all default values apply If the inheritance facet has been specified and it is supersede then the value of s in I is obtained by i ranking the ancestors of I according to the class precedence order of the parent of I and ii retrieving the default value of the first class in the class precedence order which specifies a default value for s The details of the algorithm used to compute the class precedence order are given at pp 782 786 of the Common Lisp specification Steele 1992 This algorithm produces a total order if this exists based on two ordering principles i a class say C precedes all its direct superclasses and ii a direct superclass of C precedes the direct superclasses of C specified to its right in the list of direct superclasses of C Chapter 8 Interpreters and Proof System 24 8 I
32. ol term if control term cond control term do control term loop control term repeat control term return control term if control term if log expression then control term else control term then control term control term else control term control term cond control term cond cond control clause cond control clause log expression control term loop control term loop for variable in term do control term do control term do actions control term repeat control term repeat actions end test control term repeat actions control term end test end test while test until test test log expression return control term return term if control term if log expression then control term else control term return control term return term Chapter 7 Reference 23 7 4 Inheritance and Default Values Generally speaking default values are values which apply unless other alternatives can be used In the OCML language the notion of default value is operationalized as follows Instances inherit values and default values from their superclasses down the inheritance hierarchy specified by instance of and subclass of links For a given slot say s of a sample instance say I the following scenarios can arise 1 I has not inherited any default value In this case the value of s in I is given by all the values I has inherited from its superclasses plus a
33. olours orange _colours 0range NIL The notation _ is modelled after the WSML syntax for IRIs _ http www deri org foo J 3 9 Translation between representation languages While OCML is an excellent language for knowledge modelling poor taste is widespread and we must often translate to and from other representations For this we use the translate generic function translate takes 4 required arguments keywords indicating source and destination lanuages an object in the source language and a stream to write the output to translate ocml rdf colours standard output XXX At present not all translations are available through this interface and the methods of returning the result are idiosyncratic 3 10 The ask tell interface In particular in the case of OCML this generic idea of providing a uniform level of de scription to a hybrid formalism has been instantiated by providing a Tell Ask interface Levesque 1984 which use logical expressions i e a relation oriented view when modify ing or querying an OCML model independently of whether the query in question concerns a class a slot or a ordinary relation The key to this integrated view is the fact that classes and slots are themselves relations classes are unary relations and slots are binary ones In addition to supporting a generic Tell Ask interface this property makes it pos sible to provide rich specifications of classes and slots In particula
34. ons can be used concurrently to specify a relation and to support constraint checking and efficient proofs The relation has value shown below associates a design parameter to its value in a design model The definition specifies that v is the value of a parameter p in a design model dm if and only if the pair p v is an element of dm In addition it also specifies the constraint that the value of a parameter has to be a member of its value range if this has been specified Finally the definition includes a prove by option whose value is an expression which can be used for verifying whether the relation is satisfied for a triple p v dm This expression provides an efficient proof method by weakening the iff def statement which formally defines relation has value but does not contribute to the specification def relation HAS VALUE p v dm Parameters have values w r t a particular design model iff def and parameter p design model dm element of p v dm constraint or and exists er has value range p vr element of v vr not exists vr has value range p vr prove by element of p v dm A meta option for non operational specifications As shown above OCML provides a number of relation options which play both a spec ification and an operational role However in some cases we might want to use a keyword only for specification and not operationally for instance when we kn
35. ow that the value of the keyword in question is a non operational expression To cater for these situations OCML provides a special meta keyword no op which can be used to indicate that the enclosed relation option only plays a specification role An example of its use is shown by the defi nition of relation range which is shown below In the example the keyword no op is used to indicate that the iff def specification of the relation is not operational in particular it is not normally feasible to test the range of a function on all its possible inputs def relation RANGE f r relation The range of a function or a binary relation is a relation which is true for any possible output of the function or second argument of the binary relation no op iff def or and function f r Chapter 3 Domain Modelling in OCML 9 forall args result gt apply f r args result holds relation result and binary relation f r forall x y gt holds f r x y holds relation y In the above definition it is worth highlighting the use of the special meta relation holds An expression such as holds lt r gt lt arg1 gt lt argn gt is satisfied if and only if the expres sion lt r gt lt arg1 gt lt argn gt is satisfied Thus holds has variable arity it can take one or more arguments In particular the number of additional arguments in a holds statement reflects the arity of the relation pass
36. r because these are relations it is possible to characterize them by means of the relation options discussed in section Section 3 5 Relations page 6 For instance the definition below specifies the class of empty sets in terms of an iff def relation option def class EMPTY SET set set iff def not exists x element of x set The generic Tell Ask interface Tell a generic assertion making primitive OCML provides a generic assertion making primitive tell which provides a uniform mechanism for asserting facts independently of whether these refer to slot filling assertions new class instances or simply relation instances For example I can use tell to add a new value to the list of projects carried out by harry_c as follows tell has project harry_c mlt HAS PROJECT HARRY_C MLT Analogously I can add a new instance of class researcher simply by stating tell researcher mickey_m RESEARCHER MICKEY_M The relation centred view makes it possible to examine the contents of an OCML model simply by asking whether a logical statement is satisfied The OCML proof system will then carry out the relevant inference and retrieval operations depending on whether the relation being queried is a slot a class or an ordinary relation The process is however Chapter 3 Domain Modelling in OCML 13 transparent to the user For instance I can find out about the projects in which harry_c is involved after the assertion sho
37. r 2 Installation 2 2 Installation OCML is implemented in Lisp and currently runs under Lispworks and SBCL 2 1 Obtaining OCML You can obtain the development version of OCML using Git git clone http kmi forge open ac uk git ocml git This should leave you with a directory called ocml 2 2 Setup OCML uses the ASDF system definition package You can find out more about ASDF at http www cliki net asdf If you have ASDF installed make sure the ocml asd file is accessible from asdf central registry and then load it CL USER gt asdf operate asdf load op ocml or if you re using a Lisp which integrates ASDF with require just do CL USER gt require ocml You then need to initialize OCML CL USER gt ocml initialize ocml 2 3 Library locations OCML finds its libraries the ontologies via logical pathnames The logical host ocml holds the translations Immediately after loading OCML this will be set to include the basic OCML library CL USER gt logical pathname translations ocml ocml library basic home djl dev ocml library basic Additional translations can be added for instance in the IRS the translations look like this CL USER gt logical pathname translations ocml ocml library basic home djl dev ocml documentation library basic ocml library home djl dev irs live code ocml library v5 0 Translations earlier in the list take prece
38. removed In the case of relation current design model relation mappings are needed to ensure that when the design model considered by the problem solver is modified the relevant changes are reflected onto the domain model see definition below def relation mapping current design model down add lambda x do unassert in room any m any r loop for pair in x do if maps to first pair z tell in room z rest pair Finally the definition below shows the remove downward mapping associated with re lation current design model it simply removes the domain level assertions associated with the design model which is passed as argument to the relation instance being retracted def relation mapping current design model down remove lambda x loop for pair in x do if maps to first pair z unassert in room z rest pair Chapter 7 Reference 20 7 Reference 7 1 Functional Term Constructors 7 1 1 setofall setofall finds all solutions i e environments to basic log expression and then returns the list obtained by instantiating template in all the returned environments ensuring that the list contains no duplicates If no solutions are found then the empty list is returned 7 1 2 findall findall is the same as setofall except that it does not remove duplicate solutions 7 1 3 the the finds one solution i e environment to basic log expression and then returns the list obtai
39. s required to model tasks and problem solv ing methods i e to support the construction of task and problem solving models This set of ontologies provides a rich modelling platform from which to build other on tologies and or problem solving models It is natural to compare the OCML and Ontolingua base ontologies Farquhar et al 1996 There are two aspects which distinguish these two sets of ontologies their nature and their scope The first difference is related to the operational nature of OCML The Ontolingua base ontology is not concerned with operationality and therefore includes many non operational definitions The OCML base ontology is concerned with providing support for the construc tion of operational models As a result it attempts to minimize the number of non executable specifications A typical approach is to weaken a non operational definition to make it exe cutable For instance let s consider the function universe In the Ontolingua base ontology the universe of a relation is defined as the set of all objects for which the relation is true Of course this is not an operational definition However we can provide a weaker version of universe called known universe which returns the set of all entities which are part of a tuple satisfying the relation in question This function can be either defined separately from universe or attached to it to provide an operational definition The second difference concerns the scope of t
40. specify actions and describe the order in which these are executed OCML supports the specification of sequential iterative and conditional control structures by means of a number of control term constructors such as repeat loop do if and cond8 A Lisp macro def procedure makes it possible to label parametrized control terms i e to define procedures Control terms are evaluated by means of a control interpreter This is described in appendix 1 3 1 3 Logical expressions OCML also provides the usual machinery for specifying logical expressions The simplest kind of logical expression is a relation expression which has the form rel fun term where rel is the name of a relation and fun term is a functional term More complex expressions can be constructed by using the logical operators and or not gt lt gt and quantifiers forall and exists Operational semantics is provided for all operators and quantifiers Relations are defined by means of the Lisp macro def relation 3 2 Ontologies OCML organises its knowledge models using ontologies When an ontology is defined say 0 it is possible to specify which ontologies are included in 0 and as a result 0 will include all the definitions from its parent ontologies When conflicts are detected e g the same concept is defined in two different parent ontologies a warning is issued Primitives for loading and selecting ontologies are also provided Chapter 3
41. t has project cond rule deduced project covered by S S y x enable fc watcher mode def instance larry e researcher has project tigris smoker no hacker yes works with harry_d This produces the output has project cond rule deduced project covered by TIGRIS LARRY E While forward rules can be useful in a number of situations when building application models e g to define watchers which are triggered whenever some situation arises in a knowledge base they are not essential to the model building process The reason for this is that knowledge level modelling is mainly about constructing definitions while forward chaining rules are about behaviour Thus they can be used in place of procedures to describe behaviour but they cannot replace constructs for relation or function specification run fc rules Function run Function Explicitly run forward chaining rules in the current ontology enable fc watcher mode amp optional packets Function disable fc watcher mode Function Enable and disable the automatic triggering of forward chaining rules trace fc Function untrace fc Function Turn on and off the tracing of forward chaining rules Chapter 5 Modelling issues 16 5 Modelling issues 5 1 Object oriented and relation oriented approaches to modelling When describing classes and instances I made use of standard object oriented terminology and talked about slots having values and instances belongi
42. t awkward when dealing with ontologies on a global scale OCML now supports a convenient interface for namespaces which is very similar to the XML namespaces scheme Three things are involved in this extension 1 OCML ontologies must indicate the URI which identifies them 2 Namespaces prefixes are registered with OCML before use 3 Namespaced symbols are prefixed with _ Ontology definitions should include a namespace uri initialization argument which is a string holding the URI identifying the ontology If you do not supply a namespace URI OCML will assign one based on the ontology s name def ontology colours author dave Chapter 3 Domain Modelling in OCML 11 namespace uri http www kmi open ac uk colours files def ontology fruits author dave namespace uri http www kmi open ac uk fruits files Next we tell OCML which prefixes we intend to use register namespace colours colours register namespace fruit fruits We can then use these prefixes in ontologies using a Lisp reader macro _ Classes instances and relations can all be named in this way Viz in ontology colours def class _colour def class _blue _colour def class _red _colour def class _orange _colour in ontology fruit def class _fruit def class _orange _fruit _colors has colour _colours orange Here _colours orange and _fruit orange are different symbols from
43. tion of task level concepts to domain level concepts For instance a parametric design view over the Sisyphus I domain can be imposed simply by creating parameter instances and associating them to YQT members Thus the set of parameters and the set of YQT members are associated but kept distinct This solution is appealing for two reasons it supports reuse of modular components and does not confuse the two different types of concepts parame ters and YQT members maintain different sets of properties and different semantics thus avoiding a situation in which a design parameter has a wife and a YQT member has a value range Instance mapping is supported in OCML by means of the Lisp macro def upward class mapping This takes the names of two classes as arguments and associates each instance of the first class to a purpose built instance of the second class By default the relation maps to is used to associate the task level instance to the domain level one In the Sisyphus I application model we should then state def upward class mapping yqt member yqt parameter The above form iterates over each instance of class yqt member say I creating a new instance of class yqt parameter say Meta I and associating this to I i e asserting maps to Meta I I Hence if we now ask for the mapping between parameters and YQT members we get the following results Chapter 6 Functional View of OCML 18 ask maps to z x t Solution MAPS TO YQ
44. ven set of arguments sufficient Specifies a sufficient condition for the relation to hold for a given set of arguments constraint Specifies an expression which follows from the definition of the relation and must be true for each instance of the relation def This is for compatibility with Ontolingua it specifies a constraint which is also meant to provide a partial definition of a relation axiom def A statement which mentions the relation to which it is associated It provides a mechanism to associate theory axioms with specific relations 3 5 2 Operationally relevant relation options Relation options also play an operational role Specifically some relation options support constraint checking over relation instances while others provide proof mechanisms which can be used to find out whether or not a relation holds for some arguments The table below lists the relation options which are meaningful from an operational point of view and informally describes their relevance to constraint checking and theorem proving Relation option Supports constraint checking Provides proof mechanism sufficient No Yes prove by No Yes lisp fun No Yes iff def Yes Yes constraint Yes No def Yes No As shown in the table constraint checking is supported by the following keywords constraint def and iff def While these have different model theoretic semantics from a constraint checking point of view they are equivalent They all specify
45. wn above these are now babylon and mlt by using the Lisp macro ask to pose the query has project harry_c c The resulting interaction with the OCML proof system is shown below ask has project harry_c c Solution HAS PROJECT HARRY_C BABYLON More solutions y or n Solution HAS PROJECT HARRY_C MLT More solutions y or n y No more solutions This uniform relation centred view over OCML models also provides a way to index inferences For instance when answering the above query the OCML proof system will first retrieve and order all inference mechanisms applicable to a query of type has project e g these might include assertions of type has project relation options associated with has project and the relevant backward rules13 and will then try these in sequence to generate one or more solutions to the query Chapter 4 Rule based reasoning 14 4 Rule based reasoning OCML can reason with backward and forward chaining rules 4 1 Backward chaining rules A backward rule consists of a number of backward clauses each of which is defined according to the following syntax backward clause relation expression if logical expression Each backward clause specifies a different goal subgoal decomposition When carrying out a proof by means of a backward rule the OCML interpreter will try to prove the relevant goal by firing the clauses in the order in which these are listed in the rule definition As in
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