Abduction, Induction, and the Robot Scientist

1. Abduction, Induction, and the Robot Scientist Ross D. King Department of Computer Science University of Wales, Aberystwyth

2. The Concept of a Robot Scientist 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*. Background Knowledge Analysis Hypothesis Formation Consistent Hypotheses Experiment Experiment selection Results Interpretation Final Theory Robot *King et al. (2004) Nature, 427, 247-252.

3. 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.

4. 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.

5. 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 .

6. Ontologies and the Relation between Abstract and Physical Objects

7. 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)

8. 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>.

9. 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.

10. Overall View of the Universe

11. 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.

12. 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.

13. Sketch of New Robotic Hardware

14. The New Robot “Adam” During Commissioning

15. 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.

16. 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.

17. 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.

18. Overall View of the Universe

19. The Correspondence View of Truth and the Verification Principle

20. “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

21. 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.

22. 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.

23. Truth Truth Relations

24. The Nature of Universals

25. 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

26. 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>.

27. Universals

28. 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.

29. 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).

30. 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.

31. 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.).

32. Some Example Growth Curves

33. 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.

34. 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.

35. Phenyalanine, Tyrosine, and Tryptophan Pathways for S. cerivisae Glycerate -2-Phosphate C00631 YGR254W YHR174W YMR323W C04302 Phosphoenol pyruvate D-Erythrose -4-Phosphate C00108 C00074 N-5’-Phospho --d-ribosyl anthranilate YDR354W 5-o-1-carboxyvinyl -3-phosphoshikimate Anthranilate YBR249C YDR035W C00279 YDR127W C01269 YER090W (YKL211C) YGL148W 3-deoxy-D-arabino- heptulosonate-7-phosphate YDR007W C00251 Chorismate C04961 1-(2-Carboxyl phenylamino)-1’- deoxy-D-ribulose- 5’-phosphate C01302 Shikimate –3- phosphate YPR060C YDR127W C03175 C00254 Prephenate 3-Dehydroquinate C00944 YDR127W YBR166C YNL316C YKL211C YDR127W C03506 3-Dehydroshikimate C00463 p-Hydroxyphenyl pyruvate (3-Indolyl)- glycerol phosphate Phenylpyruvate C02637 YGL026C Indole C00166 YDR127W C01179 C00493 YHR137W YGL202W YHR137W YGL202W Shikimate 5-Dehydroshikimate YGL026C YGL026C C02652 YDR127W TYROSINE PHENYLALANINE TRYPTOPHAN C00079 Metabolite import C00078 C00082 Growth Medium

36. Observed / Theoretical

37. Abduction and Induction

38. Hypothesis Formation and Abduction 1 • The formation of hypotheses has traditionally been the hardest part of science to envisageautomating. 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),

39. 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.

40. 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.

41. Phenyalanine, Tyrosine, and Tryptophan Pathways for S. cerivisae Glycerate -2-Phosphate C00631 YGR254W YHR174W YMR323W C04302 Phosphoenol pyruvate D-Erythrose -4-Phosphate C00108 C00074 N-5’-Phospho --d-ribosyl anthranilate YDR354W 5-o-1-carboxyvinyl -3-phosphoshikimate Anthranilate YBR249C YDR035W C00279 YDR127W C01269 YER090W (YKL211C) YGL148W 3-deoxy-D-arabino- heptulosonate-7-phosphate YDR007W C00251 Chorismate C04961 1-(2-Carboxyl phenylamino)-1’- deoxy-D-ribulose- 5’-phosphate C01302 Shikimate –3- phosphate YPR060C YDR127W C03175 C00254 Prephenate 3-Dehydroquinate C00944 YDR127W YBR166C YNL316C YKL211C YDR127W C03506 3-Dehydroshikimate C00463 p-Hydroxyphenyl pyruvate (3-Indolyl)- glycerol phosphate Phenylpyruvate C02637 YGL026C Indole C00166 YDR127W C01179 C00493 YHR137W YGL202W YHR137W YGL202W Shikimate 5-Dehydroshikimate YGL026C YGL026C C02652 YDR127W TYROSINE PHENYLALANINE TRYPTOPHAN C00079 Metabolite import C00078 C00082 Growth Medium

42. Abduction Code 1 % computes if the model predicts growth or not theoretical_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

43. Extension: Missing Arcs/Nodes M4 M1 E2 E1 E7 E3 M6 M2 E4 E6 E5 M3 M5

44. 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.

45. 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.

46. Bioinformatics Database Model of Metabolism Automated Model Completion Experiment Formation Hypothesis Formation Reaction ? Experiment Gene Identification

47. 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”.

48. 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).

49. 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.

50. Modelling Growth