Abduction, Induction, and the Robot Scientist

Ross D. King

Department of Computer Science

University of Wales, Aberystwyth

The Concept of a Robot Scientist

Background Knowledge

Analysis

Consistent

Hypotheses

Final Theory Experiment selection Robot

ExperimentResults

Interpretation

We have developed the first computer system that is capable of originating its own experiments, physically doing them, interpreting the results, and then repeating the cycle*.

Hypothesis Formation

*King et al. (2004) Nature, 427, 247-252.

Motivation: Technological

In many areas of science our ability to generate data is outstripping our ability to analyse the data.

One scientific area where this is true is in Systems Biology, where data is now being generated on an industrial scale.

The analysis of scientific data needs to become as industrialised as its generation.

Motivation: Philosophical

What is Science?

The question whether it is possible to automate the scientific discovery process seems to me central to understanding science.

There is a strong philosophical position which holds that we do not fully understand a phenomenon unless we can make a machine which reproduces it.

The Philosophical Problems

A number of classical philosophical issues arose in the Robot Scientist project: – the relation between abstract and physical objects, – correspondence semantics and the verification

principle, – the nature of Universals, – the problem of induction and its relation to abduction.– Etc.

Many of the philosophy positions we have physically implemented in the Robot Scientist originate with Carnap and the Logical Empiricism school .

Ontologies and the Relation between Abstract and Physical

Objects

Ontologies

An ontology is “a concise and unambiguous description of what principal entities are relevant to an application domain and the relationship between them”*.

*Schulze-Kremer, S., 2001, Computer and Information Sci. 6(21)

Dualism The most fundamental ontological division in our design

of the Robot Scientist is between <abstract> and <physical> objects

We argue for this ontological division because it makes explicit the separation between models and reality.

All the objects which the Robot Scientist deals with computationally are <abstract>, and all the objects it deals with physically are <physical>.

SUMO

Use of this dualism allows us also to be consistent with the SUMO upper ontology, and its associated ontologies. In SUMO the most fundamental ontological division is between <abstract> and <physical> objects.

Although SUMO has many faults, it is currently the most widely used top ontology, and no clearly better alternative exists.

Overall View of the Universe

Physical Objects By definition, <physical> objects follow the laws of

physics, e.g. yeast cells can interact with chemical compounds in their growth media and thereby grow, robot arms can move 96 well plates, etc.

The key <physical> object is the Computer. It controls the movement of all the <physical> objects.

Our new fully automated Robot Scientist has a very large amount of laboratory automation hardware designed to execute yeast growth experiments.

Hardware

We have a new fully automated robotic system, cost £450,000 from Caliper Life Sciences. It is in the final stages of commissioning.

It is designed to fully automate yeast growth experiments.

It has a -20C freezer, 3 incubators, 2 readers, 2 liquid handlers, 3 robotic arms, a washer, etc.

It is capable of initiating ~1,000 new experiments and >200,000 observations per day in a continuous cycle.

Sketch of New Robotic Hardware

The New Robot “Adam” During Commissioning

Abstract Objects Just as the key <physical> component is the

computer’s hardware, the key <abstract> component is the computer’s software.

We argue that the software/hardware identity is the key to bridging the <physical>/<abstract> dichotomy both in the Robot Scientist and elsewhere.

Turing Machines as Hardware

To me, the key to understanding the power of a computer is that it implements, in a <physical> device, an <abstract> logical program.

What distinguished Turing from the other great logicians of his time was that he proposed a model of computation that was explicitly both physical and abstract.

Denoting Rules

We need to explicitly link object in the <abstract> world to those in the <physical> world.

This is done using <denoting rules>.

Such rules are sometimes termed calls “rules of designation”, or reference rules.

Overall View of the Universe

The Correspondence View of Truth and the

Verification Principle

“What is True?”

The Robot Scientist implement a correspondence view of truth. Truth is correspondence with reality.

Within the Robot Scientists <abstract> propositions are consistently labelled as “true” or “false”.

As the Robot Scientist has <physical> effectors it can verify the truth or falsehood of these propositions by specific <physical> tests

Denotation Example To illustrate the role of denotation rules we describe the

<denoting rules> for the yeast strains kept in the Robot Scientist's deep-freeze.

– <abstract> stored_yeast_strain(Yeast_strain_id)

“Yeast_strain_id” is the name of the class of all names of yeast strains.

The example proposition stored_yeast_strain(ypr060c) states that the yeast strain named “ypr060c” is stored in the Robot Scientist.

The <denoting rule> relates this <abstract> proposition to a <physical> state.

Denotation Example 2 The <physical> denotation of

stored_yeast_strain(ypr060c) is that: in the <physical> deep-freeze of the Robot Scientist there is a sample of the <physical> yeast strain named “ypr060c” (identified by a <physical> bar-code reader.

The Robot Scientist can verify the truth or falsehood of this proposition by physically comparing the yeast strains it has in its deep-freeze labelled as “ypr060c” with a sample of defined reference strains from the UK National Collection of Yeast Cultures or other similar centres.

TruthTruth Relations

The Nature of Universals

Induction and Universals

I argue that for a number of the <abstract> ontological objects used by the Robot Scientist, their truth values cannot be physically verified in finite time.

I argue that these <abstract> objects are “<Universals>”.

To reason about these <abstract> objects from their corresponding denoted <physical> objects requires an explicit induction

An Example of Universals An example proposition such as yeast_strain(ypr060c) refers

to the set of all examples of this strain named “ypr060c”.

This is a <Universal> and denotes all examples of this yeast strain in the past/present/future <physical> Universe.

To reason about yeast_strain(ypr060c), from examples, such as deep_freeze_well_content( 000000000001_0_0, ypr060c), requires an explicit induction.

The denotation of deep_freeze_well_ content(000000000001_0_0, ypr060c) is a specific <physical> sample of the strain named “ypr060c”, not the <Universal>.

Universals

Stationarity For the inductive inferences of the Robot Scientist to be valid

we need to assume stationarity between and within experiment. A central role of <meta-data> is to monitor this stationarity. The Robot Scientist, in the absence of <metadata> evidence to

the contrary, assumes that:

– All the samples of a given strain are identical.

– Yeast strains samples only differ in known ways.

– All the samples of a given chemical compounds are identical.

– Experimental conditions only vary in the measured ways.

– Etc.

Observational and Theoretical Terms

The relationship between the various types of term in the Robot Scientist experiments illuminates another area of interest in the philosophy of science: the relationship between observed and theoretical terms.

The main type of observation that the Robot Scientist is designed to perform is optical density (OD) measurement.

These observations are represented using predicates of the form:– <abstract> od_observation(Od_reader_id, Growth_plate_id, Well_id,

Time_stamp, Od_observation_id)– <abstract> od_observation_result(Od_observation_id, Od_value).

Data and Metadata There is a useful distinction between experimental

<data> and <metadata>. Metadata is data used to describe data, especially to allow a scientific experiment to be repeated.

In addition to OD readings, the Robot Scientist also measures many other experimental variables: the inoculation time of wells, the temperature of the incubators (that holds the 96-well plates), the humidity of the incubators, the O2 levels in the incubators, etc.

Calculated Terms

From the OD observations of a 96 well plate, the Robot Scientist makes calculations concerning the growth of the particular knockout strains on the plate.

These may be qualitative (growth v non-growth),

such as those in the original Robot Scientist work, or quantitative as in more recent Robot Scientist work (growth rate, maximum growth yield, etc.).

Some Example Growth Curves

Theoretical Terms It is possible, at least in principle, to work with theories that

deal exclusively with <observed terms> and <calculable terms>.

However, the history of science demonstrates that it is often more illuminating, and effective, to include <theoretical terms> - objects that are not directly observable in the experiment or calculable from the observables.

Example <theoretical terms> in the Robot Scientist's model are, genes, enzymes, he mapping of genes to enzymes, metabolic networks, paths in a metabolic networks, etc.

Correspondence Rules To map <theoretical terms> with <observable terms> and

<calculable terms> we require <correspondence rules> (Carnap 1974).

The most important correspondence rule is the one that relates the predicate observed_growth(Experiment) to the <theoretical term> path in the model of metabolism.

This correspondence is the key concept in the model: the idea that paths in metabolic pathways from growth metabolites to a set of essential metabolites can be related to growth of a cell.

Glycerate-2-Phosphate

Phosphoenolpyruvate

D-Erythrose-4-Phosphate

3-deoxy-D-arabino-heptulosonate-7-

phosphate

3-Dehydroquinate

3-Dehydroshikimate

5-Dehydroshikimate Shikimate

Shikimate –3-phosphate

5-o-1-carboxyvinyl-3-phosphoshikimate

Chorismate

Prephenate

p-Hydroxyphenylpyruvate

TYROSINE

Phenylpyruvate

PHENYLALANINE

Anthranilate

TRYPTOPHAN

N-5’-Phospho--d-ribosylanthranilate

1-(2-Carboxylphenylamino)-1’-deoxy-D-ribulose-

5’-phosphate

(3-Indolyl)-glycerol

phosphateIndole

YBR249CYDR035WYBR249CYDR035W

YGR254WYHR174WYMR323W

YGR254WYHR174WYMR323W

YDR127WYDR127W

YDR127WYDR127W

YDR127WYDR127W

YDR127WYDR127W

YDR127WYDR127W

YDR127W

YDR127W

YPR060CYPR060C

YBR166CYBR166C

YHR137WYGL202WYHR137WYGL202W

YNL316CYNL316C

YGL148WYGL148W

YDR354WYDR354W

YDR007WYDR007W

YKL211CYKL211C

YGL026CYGL026C

YGL026CYGL026CYGL026CYGL026C

YER090W(YKL211C)YER090W(YKL211C)

C00631

C00074

C00279

C04961

C00944

C02637

C02652

C00493

C03175

C01269

C00251

C00254

C01179 C00166

C03506

C01302

C00108

C04302

C00463

C00078C00079C00082

YHR137WYGL202WYHR137WYGL202W

Phenyalanine, Tyrosine, and Tryptophan Pathways for S. cerivisae

Growth Medium

Metabolite import

Observed / Theoretical

Abduction and Induction

Hypothesis Formation and Abduction 1

The formation of hypotheses has traditionally been the hardest part of science to envisage automating. Indeed, many philosophers of science have openly expressed views that hypothesis formation could only be truly accomplished by humans.

Hypothesis formation has traditionally been closely associated with the “problem of induction”.

We argue that most hypothesis formation in modern biology is abductive rather than inductive (Reiser et al, 2002),

Hypothesis Formation and Abduction 2

What are hypothesised in the Robot Scientist, and in most of molecular biology, are factual relationships between objects, e.g. the gene ypr060c codes for enzyme chorismate mutase, gene ypr060c exists at location 675628- 674858 (C) on chromosome 16, etc.

N.B. these relationship are ground. Induction is still required by the robot, but only to reason about Universals.

This emphasis on abduction is very different from the general account of the role of induction in science, which appears heavily physics centred and based on universal laws e.g. conservation of energy.

Model of Metabolism The model of metabolism used by the Robot Scientist is that of

“metabolic graphs” (Reiser et al, 2002) and (Bryant et al, 2002).

Each vertex corresponds to a set of compounds that are available to the cell.

The cell has a unique start vertex corresponding to the nutrients available to the cell in the growth medium.

An edge corresponds to a reaction and the destination of an edge is the set of available compounds plus the reaction's products.

A pathway corresponds to a monotonically increasing set of compounds available to the cell.

Glycerate-2-Phosphate

Phosphoenolpyruvate

D-Erythrose-4-Phosphate

3-deoxy-D-arabino-heptulosonate-7-

phosphate

3-Dehydroquinate

3-Dehydroshikimate

5-Dehydroshikimate Shikimate

Shikimate –3-phosphate

5-o-1-carboxyvinyl-3-phosphoshikimate

Chorismate

Prephenate

p-Hydroxyphenylpyruvate

TYROSINE

Phenylpyruvate

PHENYLALANINE

Anthranilate

TRYPTOPHAN

N-5’-Phospho--d-ribosylanthranilate

1-(2-Carboxylphenylamino)-1’-deoxy-D-ribulose-

5’-phosphate

(3-Indolyl)-glycerol

phosphateIndole

YBR249CYDR035WYBR249CYDR035W

YGR254WYHR174WYMR323W

YGR254WYHR174WYMR323W

YDR127WYDR127W

YDR127WYDR127W

YDR127WYDR127W

YDR127WYDR127W

YDR127WYDR127W

YDR127W

YDR127W

YPR060CYPR060C

YBR166CYBR166C

YHR137WYGL202WYHR137WYGL202W

YNL316CYNL316C

YGL148WYGL148W

YDR354WYDR354W

YDR007WYDR007W

YKL211CYKL211C

YGL026CYGL026C

YGL026CYGL026CYGL026CYGL026C

YER090W(YKL211C)YER090W(YKL211C)

C00631

C00074

C00279

C04961

C00944

C02637

C02652

C00493

C03175

C01269

C00251

C00254

C01179 C00166

C03506

C01302

C00108

C04302

C00463

C00078C00079C00082

YHR137WYGL202WYHR137WYGL202W

Phenyalanine, Tyrosine, and Tryptophan Pathways for S. cerivisae

Growth Medium

Metabolite import

Abduction Code 1% computes if the model predicts growth or nottheoretical_growth(Experiment) ←

growth_medium(Experiment, {Growth_medium}) ∧essential_metabolites({Essential_metabolites}) ∧ path({Growth_medium}, {Essential_metabolites})

% path(Starting_point, End_point)path({X}, {Y}) ← edge({X}, {Y})path({X}, {Z}) ← edge({X}, {Y}) ∧ path({X}, {Z})

edge({X}, {Y}) ← reaction({A}, {B}) ∧ subset({A}, {X}) ∧ union({X}, {B}, {Y})

reaction({Reactants}, {Products}) ← reaction(Enzyme, {Reactants}, {Products}) ∧ ¬ reaction_removed(Enzyme)

% growth_medium(Experiment, {Metabolites})growth_medium(experiment1, {a})

% essential_metabolites({Metabolites})essential_metabolites({c, d}).

reaction_removed(Gene, Enzyme) ← ¬ gene(Gene).encodes(Gene, Enzyme) % The abducible

% reaction_details(Enzyme, {Reactants}, {Products})reaction(e1, {a}, {b})reaction(e2, {a}, {c})reaction(e3, {b}, {d})reaction(e4, {c}, {d})

gene(g1)gene(g2)¬ gene(g3) % example gene knocked out

Extension: Missing Arcs/Nodes

M1

M5M3

M2M6

M4

E1

E2

E7

E4

E5

E3

E6

Extension to a Genome Scale Model of Yeast Metabolism

We have extended our model of aromatic amino acid metabolism to cover most of what is known about yeast metabolism.

Includes 1,166 ORFs (940 known, 226 inferred)

Growth if path from growth medium to defined end-points.

83% accuracy (based on 914 strain/medium predictions)

Challenging for a purely logical approach.

This Model is Incomplete

It is not possible to find a path from the inputs (growth medium) to all the end-point metabolites using only reactions encoded by known genes.

This suggests automated strategies for determining the identity of the missing genes - new biological knowledge.

One strategy, based on using EC enzyme class of missing reactions, is to identify genes that code for this EC class in other organism, then find homologous genes in yeast.

Automated Model Completion

BioinformaticsDatabase ?

Model ofMetabolismHypothesis

Formation

ExperimentFormation

Gene Identification

Reaction

Experiment

Testing Hypotheses 1

A key philosophical step in the Robot Scientist's cycle of experimentation is the process of deciding on the truth or falsehood of hypotheses.

The abductive hypothesis generation stage generates a set of models, each of which has a different abduced encodes(Gene_id, Enzyme_id) proposition.

These propositions allow for each model, the deduction of whether on not the model predicts growth for a particular experiment, e.g. whether the proposition theoretical_growth(experiment_1) is provable or not for the metabolites used in the experiment named “experiment_1”.

Testing Hypotheses 2

These deductions are monitored by a meta-logical program which determines the truth or falsehood of the theoretical_growth proposition in the various models.

This leads to the key idea of the Robot Scientist: we can use the <physical> Robot Scientist's effectors to actually execute the <physical> experiment and determine whether growth occurs or not.

In the <physical> experiment, growth is determined by observation of the plates used in the experiment and denotation rules of the form described above. This procedure results in determination of the truth or falsehood of growth of the proposition <abstract> observed_growth(experiment_1).

Testing Hypotheses 3 This results in a set of theoretical_growth(experiment_1) propositions

with different truth values, each one associated with a particular abduced hypothesis, and a single observed_growth(experiment_1) proposition with an empirically determined truth value.

In the cases where the truth values of theoretical_growth(experiment_1) and observed_growth(experiment_1) are different, we have the classical philosophy of science case of a conflict between theory and observation.

We can then either take the simple approach of eliminating from consideration all the abduced hypotheses which result in incorrect predictions about observations, or preferably, we can take a probabilistic approach and decrease appropriately the probability of these hypotheses.

Modelling Growth

Applications of Philosophy

Generic ontology of experiments

e-Science

Ontology of science(formalization of scientific

methods, technologies, infrastructure of science)

EXPOOntology of

scientific experimentsconcepts: 220language: OWL

Classification of experiments

• Controlled vocabulary for scientific experiments.

• Formalized computational representation of scientific experiments.

• Unified standard for representation, annotation, storage, and access to experimental results.

• Automated reasoning over experimental data and conclusions.

Experiment Method

Scientific Experiment

Experiment goal

Experiment design

Experiment object

Experiment action

Experiment results

Soldatova et al. (2006) Royal Society Interface

SUMO

MSIChEBI

Upper level

Generic level

Domain level

EXPO

SubjectOfExp. ObjectOfExp.

Domain Model

FuGO

PSI

Measurement ontology

Bibliographic Data Ontology

BiblioReference Mes.Unit

MOPlant

ontology

The Position of EXPO

EXPO’s top classes

EXPO development

Concepts: 220

Language: OWL

http://sourceforge.net/projects/expo

EXPO v.1Tool: Hozo Ontology Editor

The need for a Robot Scientist ontology (EXPO-RS)

The robot requires detailed and formalized description: domains, background knowledge, experiment methods, technologies, hypotheses formation and experiment designing rules, etc.

Integrity of data and metadata.

Open access of the RS experimental data and metadata to the scientific community.

Soldatova et al. (2006) Bioinformatics

EXPO-RS Formalization of the entities involved in Robot Scientist

experiments.

A controlled vocabulary for all the participants of the project.

Identification of metadata essential for the experiment's description and repeatability.

Coordination of the planning of experiments, their execution, access to the results, technical support of the robot, etc.

Modelling a database for the storage of experiment data and track experiment execution.

EXPO-RS: Metadata

EXPO-RS: equipment

EXPO-RS: equipment functionality

EXPO-RS for the DB

Conclusions

The Robot Scientist concept represents the logical next step in scientific automation.

A major motivation for the development of the Robot Scientist was to help illuminate our understanding of science.

I argue that the Robot Scientist helps to clarify such issues in the philosophy of science as: the problem of induction and its relation to abduction, the relation between abstract and physical objects ,correspondence semantics, the verification principle, the nature of Universals, the relation between observed and theoretical terms.

Acknowledgements Ken Whelan Aberystwyth Amanda Clare Aberystwyth Larisa Soldatova Aberystwyth Mike Young Aberystwyth Jem Rowland Aberystwyth Andrew Sparkes Aberystwyth Wayne Aubrey Aberystwyth Emma Byrne Aberystwyth Philip Reiser Aberystwyth Ffion Jones Aberystwyth Ugis Sarkans Aberystwyth (EBI) Douglas Kell Manchester (Aberystwyth) Steve Oliver Manchester Stephen Muggleton Imperial College (York) Chris Bryant Robert Gordons (York) David Page Wisconsin

BBSRC, EPSRCCaliper Life Sciences, PharmDM