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Notation3 Logic: A Practical Introduction

Dörthe Arndt and William Van Woensel

Notation3 Logic: A practical Introduction

Dörthe Arndt and William Van Woensel

RuleML Webinar 23.02.2022

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Outline

N3 and the Web

Reasoning with N3

Applications

Notation3 Logic: A practical Introduction

Dörthe Arndt and William Van Woensel

RuleML Webinar 23.02.2022

�Slide 2

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Outline

N3 and the Web

Reasoning with N3

Applications

Notation3 Logic: A practical Introduction

Dörthe Arndt and William Van Woensel

RuleML Webinar 23.02.2022

�Slide 3

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Semantic Web

Idea: provide a machine-understandable version of the Web

Why? A Semantic Web enables computers to use the Web for you.

How? Logical Representation of knowledge in graphs.

Notation3 Logic: A practical Introduction

Dörthe Arndt and William Van Woensel

RuleML Webinar 23.02.2022

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Resource Description Framework (RDF)

Simple triples:

:William :likes :spaghetti. -> “William likes spaghetti”

Blank nodes:

_:x :likes :spaghetti. -> “Someone likes spaghetti.”

Notation3 Logic: A practical Introduction

Dörthe Arndt and William Van Woensel

RuleML Webinar 23.02.2022

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Notation3 Logic

Extension of RDF

Rules

Quotations

Built-ins

Notation3 Logic: A practical Introduction

Dörthe Arndt and William Van Woensel

RuleML Webinar 23.02.2022

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Rules

{:William :likes :spaghetti.}=>{:William :likes :pizza.}.

“If William likes spaghetti, he also likes pizza.”

Notation3 Logic: A practical Introduction

Dörthe Arndt and William Van Woensel

RuleML Webinar 23.02.2022

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Universal Variables

{?x :likes :spaghetti.}=>{?x :likes :pizza.}.

“If someone likes spaghetti, this person also likes pizza.”

Notation3 Logic: A practical Introduction

Dörthe Arndt and William Van Woensel

RuleML Webinar 23.02.2022

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Quotations of formulae

:Doerthe :thinks {:William :likes spaghetti, :pizza}.

“Doerthe thinks that William likes spaghetti and pizza.”

Notation3 Logic: A practical Introduction

Dörthe Arndt and William Van Woensel

RuleML Webinar 23.02.2022

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N3 quotation vs RDF-star

N3 quotation is for graphs:

:Doerthe :thinks {:William :likes spaghetti, :pizza}.

RDF-star is for triples:

:Doerthe :thinks <<:William :likes spaghetti>>.

RDF-star and N3 quotation are compatible, some reasoners support both.

Notation3 Logic: A practical Introduction

Dörthe Arndt and William Van Woensel

RuleML Webinar 23.02.2022

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Built-ins

Predicates with special meanings

“Traditional” N3 built-ins:

https://www.w3.org/2000/10/swap/doc/CwmBuiltins

“New” built-ins are currently discussed.

Notation3 Logic: A practical Introduction

Dörthe Arndt and William Van Woensel

RuleML Webinar 23.02.2022

�Slide 11

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Outline

N3 and the Web

Reasoning with N3

Applications

Notation3 Logic: A practical Introduction

Dörthe Arndt and William Van Woensel

RuleML Webinar 23.02.2022

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Reasoners

Classical Reasoners: EYE and Cwm

Recent developments: jen3, N03, …

We use EYE in our examples

Notation3 Logic: A practical Introduction

Dörthe Arndt and William Van Woensel

RuleML Webinar 23.02.2022

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Queries and Closure

N3 reasoners can give either

the deductive closure of an N3 graph or the result of a query

Notation3 Logic: A practical Introduction

Dörthe Arndt and William Van Woensel

RuleML Webinar 23.02.2022

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Deductive Closure

Given:

:William :likes :spaghetti.

{?x :likes :spaghetti.} => {?x :likes :pizza}.

Closure:

:William :likes :spaghetti.

{?x :likes :spaghetti.} => {?x :likes :pizza}.

:William :likes :pizza.

The deductive closure is the set of all triples which can be derived from a dataset

Notation3 Logic: A practical Introduction

Dörthe Arndt and William Van Woensel

RuleML Webinar 23.02.2022

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Query result

Given:

Facts and rules: William :likes :spaghetti.

Query: {?x :likes :spaghetti.} => {?x :likes :pizza}.

Result:

:William :likes :pizza.

A query is a special rule. Query reasoning provides all the results of the rule marked as query. The reasoning process can include other rules as well.

Notation3 Logic: A practical Introduction

Dörthe Arndt and William Van Woensel

RuleML Webinar 23.02.2022

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Example

Example execution in EYE (https://github.com/josd/eye)

From now on we will only consider deductive closures.

Notation3 Logic: A practical Introduction

Dörthe Arndt and William Van Woensel

RuleML Webinar 23.02.2022

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N3 Online editor

We provide an N3 online editor: http://ppr.cs.dal.ca:3002/n3/editor/

Spaghetti-example: http://ppr.cs.dal.ca:3002/n3/editor/s/4yxZnYnt

Notation3 Logic: A practical Introduction

Dörthe Arndt and William Van Woensel

RuleML Webinar 23.02.2022

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Existential rules

:William :likes :spaghetti.

{?x :likes :spaghetti.} => {?x :loves _:z}.

:William :loves _:z.

Link to example: http://ppr.cs.dal.ca:3002/n3/editor/s/E303UvWf

Notation3 Logic: A practical Introduction

Dörthe Arndt and William Van Woensel

RuleML Webinar 23.02.2022

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Rule-producing rules

:Researcher rdfs:subClassOf :Person.

{?x rdfs:subClassOf ?y.} => {{?z a ?x}=>{?z a ?y}}.

{?z a :Researcher}=>{?z a :Person}.

Link to example: http://ppr.cs.dal.ca:3002/n3/editor/s/XK5icom2

Notation3 Logic: A practical Introduction

Dörthe Arndt and William Van Woensel

RuleML Webinar 23.02.2022

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Forward vs. Backward Chaining (in EYE)

In N3 you can indicate how a rule should be applied:

Forward-chaining:

{?x :likes :Spaghetti}=>{?x :likes :Pizza}.

Backward-chaining:

{?x :likes :Pizza}<={?x :likes :Spaghetti}.

Link: http://ppr.cs.dal.ca:3002/n3/editor/s/rQEyElOC

Notation3 Logic: A practical Introduction

Dörthe Arndt and William Van Woensel

RuleML Webinar 23.02.2022

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Negation predicates

Different predicates which can express (scoped) negation as failure.

Example: log:collectAllIn

Built-in that collects all occurrences of a pattern in a list.

Link: http://ppr.cs.dal.ca:3002/n3/editor/s/4wCFscuz

Notation3 Logic: A practical Introduction

Dörthe Arndt and William Van Woensel

RuleML Webinar 23.02.2022

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Link traversal

The built-in log:semantics allows us, to access the content behind a uri.

:doerthe foaf:knows git:william.n3 .

{ ?x foaf:knows ?y.

?y log:semantics ?content.

}=>{

?x :friendInfo ?content

}.

Try it: http://ppr.cs.dal.ca:3002/n3/editor/s/uNpYRH12

Notation3 Logic: A practical Introduction

Dörthe Arndt and William Van Woensel

RuleML Webinar 23.02.2022

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Graph operations

The predicate log:includes allows us to search for patterns in graphs.

{:william :likes :Spaghetti, :Pizza, :Fish.}

log:includes {:william :likes :Pizza}.

Examples:

http://ppr.cs.dal.ca:3002/n3/editor/s/HPX9ZCKY

http://ppr.cs.dal.ca:3002/n3/editor/s/BFg3hpTT

Notation3 Logic: A practical Introduction

Dörthe Arndt and William Van Woensel

RuleML Webinar 23.02.2022

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Proofs

[] a r:Proof, r:Conjunction;

r:component <#lemma1>;

r:gives {:William :likes :pizza.}.

<#lemma1> a r:Inference;

r:gives { :William :likes :pizza.};

r:evidence ( <#lemma2> );

r:rule <#lemma3>.

<#lemma2> a r:Extraction;

r:gives { :William :likes :spaghetti.};

r:because [ a r:Parsing; r:source <William.n3>].

<#lemma3> a r:Extraction;

r:gives { {?x_0_1 :likes :spaghetti} => {?x_0_1 :likes :pizza}.};

r:because [ a r:Parsing; r:source <spaghetti_rule.n3>].

N3 reasoners

produce proofs.

Notation3 Logic: A practical Introduction

Dörthe Arndt and William Van Woensel

RuleML Webinar 23.02.2022

�Slide 25

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Outline

N3 and the Web

Reasoning with N3

Applications

Notation3 Logic: A practical Introduction

Dörthe Arndt and William Van Woensel

RuleML Webinar 23.02.2022

�Slide 26

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Using N3 as Lingua Franca for Clinical Decision Support

Interoperable Electronic Health Records (EHR)

Open EHR standards: HL7 FHIR (RDF), openEHR

Use biomedical ontologies to annotate data

⇒ N3 does not suffer impedance mismatch

Natively refer to OWL classes, HL7 FHIR resources

Records vs. facts:

HL7 FHIR: keeps records (Dr. X diagnosed Y with Z)
RDF: stating of absolute facts (Y has Z)

⇒ Use quoted graphs in N3

Quote and describe graphs of statements

{ :patientY :has :viral_pneumonia }

:diagnosed_by :doctorX ;

:diagnosed_on "22-02-2022" .

Notation3 Logic: A practical Introduction

Dörthe Arndt and William Van Woensel

RuleML Webinar 23.02.2022

�Slide 27

EHR are used to store electronic patient data, and are used at points of care, specialists, hospitals

Major problem with EHRs is interoperability – each product tends to be a closed data silo – at least 5-6 vendors in NS alone (nightingale, practimax, telus, ..)

But, vendors are being pushed to be interoperable; to that end, the EHR should support a well-known EHR standard

(FHIR, openEHR have a different focus: HL7 FHIR: standardize data exchange between systems; openEHR: standardize underlying data model within system)

both standards rely on biomedical ontologies (SNOMED, ICD9/10, DMTO, ..) to annotate health data

noticed when working with N3 (but, YMMV ): no impedance mismatch when working with FHIR RDF and OWL taxonomies in N3� not trying to force a graph structure into OO model; no need for external libraries (Java, Python JS, ..)

N3 is a superset of RDF, natively work with graph-based model

There are some well-known pitfalls with RDF in HL7 FHIR

one of them being that HL7 FHIR rather records who did what (e.g., "Dr. X diagnosed patient Y with Z, e.g.,viral pneumonia")

But RDF states absolute facts (patient Y has viral pneumonia)

.. ways around this, such as reification of a diagnosis blank node

but, N3 has a built-in way of doing this! quoted graphs

= occurrences of RDF graphs (not stated as true, merely quoted)

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Model-driven UIs using N3 + HL7 FHIR

⇒ Generate UI for health data input¹

Applies validation constraints (input ranges, datatypes)
Submits validated, self-contained EHR record
Currently, supporting HTML+RDFa as UI format

diary_observations a fhir:PlanDefinition ;

fhir:PlanDefinition.action ( [

fhir:PlanDefinition.action.definitionUri :diagnose_cough_wheezing_stridor ] ... ) ]

:diagnose_cough_wheezing_stridor a fhir:ActivityDefinition ;

fhir:ActivityDefinition.title "Is your cough, wheezing or stridor less, the same ... " ;

fhir:ActivityDefinition.observationResultRequirement [

fhir:ObservationDefinition.code :code_cough ; …

fhir:ObservationDefinition.permittedDataType :dt_int, :1_10_scale ] .

1 http://ceur-ws.org/Vol-3055/paper4.pdf

Notation3 Logic: A practical Introduction

Dörthe Arndt and William Van Woensel

RuleML Webinar 23.02.2022

�Slide 28

we have put our money where our mouth is - we’ve done some small-scale projects using N3 within EHR and CDS

Both HL7 FHIR, openEHR offer high-level descriptions of health data: terminology codes, labels in different languages

And, constraints: such as the datatype (e.g., numeric, boolean), units (e.g., BPM, percentage), and data ranges.

An FHIR plan-definition can list a number of activity-definitions: in this case, the activity involves a personal observation about coughing intensity

this resource define a requirement that the observation result needs to adhere to

with the taxonomy code of the medical concept (SNOMED code for cough) and valid datatypes and ranges for input values

one can see how this info can be used as a starting point to auto-generate a UI for health data input

in our case, we generate HTML+RDFa UI, which applies the validation constraints, and annotates the health data w/ medical, unit concept

in essence, submitting a self-contained, EHR patient record

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Model-driven UIs using N3 + HL7 FHIR (2)

UiTemplates

Select certain types of health data descriptions
Select appropriate UI code snippet (HTML+RDFa)
Instantiate the UI code from health data description

:tpl-int_range_field a tpl:UiTemplate ;

tpl:select :select-int_range_field

tpl:generate [

tpl:ui :ui-int_input ;

tpl:placeholders ('_code_' '_prefix_' '_id_' '_min_' '_max_' '_step_' '_suffix_’);

tpl:values ( ?code ?label ?id ?min ?max ?step ?range )

] .

{ ?req fhir:permittedDataType :dt_int .

?range!fhir:low fhir:value ?min .

?range!fhir:high fhir:value ?max .. }

Notation3 Logic: A practical Introduction

Dörthe Arndt and William Van Woensel

RuleML Webinar 23.02.2022

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Introspection and Rule Generation

N3 rule introspects and outputs UI-generating rule

{ ?tpl a tpl:UiTemplate ;

tpl:select [ rdf:value ?selection ] ;

tpl:generate [

tpl:ui ?element ; tpl:code ?ui_code ;

tpl:placeholders ?placeholders ; tpl:values ?values ] .

( ?selection

{ ?element tpl:code ?ui_code .

( ?ui_code ?placeholders ?values ) string:replaceAll ?output }

) log:conjunction ?premise .

} => { ?premise => { ?element tpl:generated ?output } } .

replace placeholders with selector values

pattern-match with UiTemplate

Notation3 Logic: A practical Introduction

Dörthe Arndt and William Van Woensel

RuleML Webinar 23.02.2022

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Evidence-based CDS using N3

Requires computerization of clinical guidelines

PROForma, Asbru, GLIF3, GASTON, CIG Ontology, ..

Most CDS support a Task-Network Model (TNM)

Workflow with sequential, parallel, composite, decision, .. tasks
Typically have additional focus (intentions, temporal, ..)

But, no formal execution semantics

Makes it difficult to re-use, extend the work

⇒ Use N3 rules to define a Finite State Machine

Make available as resource for others to re-use and build on
https://github.com/william-vw/glean

Notation3 Logic: A practical Introduction

Dörthe Arndt and William Van Woensel

RuleML Webinar 23.02.2022

�Slide 31

Evidence-based CDS requires the computerization of clinical guidelines

Guidelines have recommendations of diagnosis, prognosis, treatment of certain illness (diabetes)

Range of representation languages available: …

Most CDS support a Task-Network Model representation of clinical guidelines

Essentially, this constitutes an executable workflow with sequential, parallel, composite, decision tasks

Similar to activity model, BPMN, .. but with an additional focus: clinical intentions, temporal aspects

However, none of the current languages have a formal execution semantics

This makes it difficult to build on the existing work (guessing as to many aspects of the CDS)

Our goal: use N3 rules to define execution semantics in terms of a Finite State Machine (FSM)

Make available as resource for others to re-use and build on

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Evidence-based CDS: Finite State Machine

Finite State Machine (FSM):

Tasks can be in a finite number of states (one at a time)

Transition between these states, depending on conditions

Decisional crite ria, other task states, temporal constraints, ..

Notation3 Logic: A practical Introduction

Dörthe Arndt and William Van Woensel

RuleML Webinar 23.02.2022

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High-level State Transition Formalism

{ { ?composite a :CompositeTask ; state:in :Active ; :subTask ?sub .

<> log:notIncludes { ?prev :next ?sub }

} a state:Guard .

?sub state:in :Inactive

} state:transit { ?sub state:in :Ready } .

{ ?e1 :next ?e2 . ?e1 state:in :Completed } rdf:type state:Guard .

?e2 state:in :Inactive

} state:transit { ?e2 state:in :Ready } ;

state:reason :readyNextOfCompletedEntity .

Notation3 Logic: A practical Introduction

Dörthe Arndt and William Van Woensel

RuleML Webinar 23.02.2022

�Slide 33

We propose a high-level formalism to specify state transitions, based on N3

1st example:

(basic semantics of a sequential relation: if prior task is done, we can start with next task)

the guard condition states that ?e2 is targeted by a sequential relation (next), where the prior task ?e1 is in the completed state

in that case, ?e2 will be moved from inactive to ready

2nd example:

(if a composite task is active, we’ll ready its subtasks as well)

the guard condition references a CompositeTask (?composite) in the active state, which has a subtask (?sub)

this subtask does not rely on a prior task, i.e., the dataset does not include (log:notIncludes) a sequential relation targeting ?sub (this is an example of SNAF)

(in that case, the sequential relation would govern the state transition; see prior code snippet)

if the guard condition is met, ?sub will be moved from the inactive to the ready state.

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Using Linear Logic for State Transitions

Reduce state-transition rules to linear logic rules in N3

After active => completed, task should no longer be in inactive
Linear logic [2] consumes premise after deriving conclusion
Possible to indicate “stable truth” that will not be consumed

Notation3 Logic: A practical Introduction

Dörthe Arndt and William Van Woensel

RuleML Webinar 23.02.2022

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Introspection and Rule Generation (2)

N3 rule introspects and outputs new Linear Logic N3 rule

{ ?premise state:transit ?conclusion ;

log:includes { ?target state:in ?oldState . ?guard a state:Guard } .

?conclusion log:includes { ?target state:in ?newState } .

?premise state:reason ?reason .

( { ?guard a log:StableTruth } { ?target state:in ?oldState } )

log:conjunction ?newPremise .

( ?conclusion

{ [ a state:Log ; state:target ?target ; state:reason ?reason ;

state:from ?oldState ; state:to ?newState ; state:time ?now ] }

) log:conjunction ?newConclusion

} => { ?newPremise log:becomes ?newConclusion } .

pattern-match with state-transition rule

construct new premise

construct new conclusion

Notation3 Logic: A practical Introduction

Dörthe Arndt and William Van Woensel

RuleML Webinar 23.02.2022

�Slide 35

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Outline

N3 and the Web

Reasoning with N3

Applications

Notation3 Logic: A practical Introduction

Dörthe Arndt and William Van Woensel

RuleML Webinar 23.02.2022

�Slide 36

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Can your use case benefit from N3?

Try it: http://ppr.cs.dal.ca:3002/n3/editor/

Join the W3C Community group: https://www.w3.org/community/n3-dev/

Notation3 Logic: A practical Introduction

Dörthe Arndt and William Van Woensel

RuleML Webinar 23.02.2022

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