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Abduction and Induction in

Scientific Knowledge Development

Peter Flach, Antonis Kakas & Oliver Ray

AIAI Workshop 2006ECAI 2006

29 August, 2006

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Central Challenge(left from the workshops in

1990s)• How can we usefully integrate

abduction and induction• What are appropriate basic forms of these

two forms of reasoning and how far we can get with them?

• What are the limits on learning of such an integration?

• What are appropriate applications (from which we can drive this integration)?

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Central “Application Theme”

• Scientific Modelling• Not necessarily classical scientific

domains!• Domains that follow scientific

methodology.

• Declarative Modelling

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This Talk

• Chart out:• a proposal that came out from previous

workshops, and• how this was taken up till now.• some recent applications.

• Set the scene for the afternoon’s discussion

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Scientific Modelling• Development of scientific theories is

incremental where we need to exploit fully the knowledge acquired so far

• Declarative Logical Modelling can facilitate this:• Ease of Representation – a logical model

expressed directly from the expert knowledge.

• Initial knowledge on a domain is typically descriptive – well suited for logical representation.

• E.g. molecular biology/functional genomics knowledge

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Scientific Modelling and Logic

(Logic for Declarative Modelling)

• Start with models that represent the prior knowledge of our domain in a logical form, i.e in a theory T.

• Understand past and current observations, Obs, in terms of the current model T through synthetic logical reasoning that generates further information, H, such that:

• T H |= Obs• T H is consistent• H is a hypothesis on the incomplete part of the model T

• The hypothesis H explains the observations Obs according to T.

• This a process of rationalization/normalization of (the disperse set of) observations through our current model T.

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Ontological distinction of Information and Logical

Predicates• Observable Information/Predicates: describes

observations of scientific experiments. Testable directly.

• Abducible Information/Predicates: describe underlying (theoretical) relations. Missing/incomplete information that needs to be inferred – not testable directly.

• Background Information/Predicates: auxiliary information that helps us link observable and abducible information.

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EXAMPLE: A “socio-economic” model of

Universities• Language/Ontology of relations {sad/1, overworked/1, academic/1,

student/1, lecturer/1, poor/1}

• Model & background knowledgesad(X) if overworked(X), poor(X)

overworked(oliver) overworked(alex) overworked(krycia) lecturer(alex)

lecturer(krycia) student(oliver)academic(alex), …

poor(alex).

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Example of Declarative Modelling

Gene Interaction Model/Rules for Gene Interaction:

increases_expression(Expt, X) ←knocks_out(Expt, G),inhibits(G,X),not affected_by_other_gene(Expt, G, X),not affected_by_EnvFactor(Expt, X).

increases_expression(Expt, X) ←knocks_out(Expt, G),intermediary_gene(Expt,G1,G),reduces_expression(Expt,G1),inhibits(G1,X),not affected_by_EnvFactor(Expt, X).

Parameter of the model: intermediary_gene/3

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Scientific Modelling through Logic

• Any scientific model can be (is) incomplete!

• Information is separated into three types:

• Observable (phenotype) – obtained from experiments via observations

• Theoretical (functional genotype) – underlying relations that cause the observable behaviour

• Background – known relevant properties, e.g. structural or chemical information.

• Example: {sad/1, overworked/1, academic/1, student/1, lecturer/1, poor/1}

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Scientific Modelling (cnt.)

• The incompleteness of the model resides in the theoretical part (e.g poor/1)

• The task is to complete the model by finding theoretical information and developing a theory for this.• HOW do we synthesize definitions for the

unobserved theoretical relations?

• ANSWER: Scientific theories are “explanatory” and “unifying”

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Synthetic Reasoning for Declarative Problem

Solving Deduction: concerned with PREDICTION of

phenotype from a given model T |= Obs

Abduction: concerned with EXPLANATION according to a given model: produces genotype information T U H |= Obs H specific (genotype) information

Induction: concerned with GENERALIZATION of information outside the observed situations T U H |= Obs H general (genotype) information

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EXAMPLE: A “socio-economic” model of Universities (Cnt.)

• Model & background knowledge

sad(X) if overworked(X), poor(X)

overworked(oliver) overworked(alex) overworked(krycia) lecturer(alex)

lecturer(krycia) student(oliver)academic(alex), …

• Observations = {sad(alex), sad(krycia), not sad(oli)}

• Abductive Explanation ={poor(ale), poor(krycia), not poor(oli)}

Abducible

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Logical Reasoning for Scientific Analysis

Experiment

Observe

Generate hypotheses

Verify hypotheses

Revise Model

Abduction

Rationalises the

Observations

Induction

Generalizes the

rationalization

and hence the Obs

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The cycle of abductive and inductive knowledge

development

Induction Abduction

T’ = T U H

T O’= H

O

T U H |= Obs

H

H

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Integration of Abduction & Induction

Abduction: problem solving given an adequate but incomplete model of the problem domain Generates explanations: specific hypotheses on the

incomplete part of the model Rationalizes/normalizes the observations.

Integration with Induction Feed explanations to Induction. Induction: development of the model by a (partial)

theory for its incomplete part.

Tight Integration• Explanations and their Generalization are evaluated as

a whole.

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EXAMPLE: A “socio-economic” model of Universities (Cnt.)

sad(X) if overworked(X), poor(X)

overworked(oliver) overworked(alex) overworked(krycia) lecturer(alex)

lecturer(krycia) student(oliver)academic(alex), …

• Observations = {sad(alex), sad(krycia), not sad(oli)}

• Abductive Explanation ={poor(ale), poor(krycia), not poor(oli)}

• Inductive Hypotheses: poor(X) if lecturer(X)

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EXAMPLE: Verifying Hypotheses

• poor(X) if lecturer(X)

• The socio-economy specialist is sceptical as it knows that students are poor.• The hypotheses is rejected and new partial

information is now given: poor(X) if student(X)

• Model now is refined to:

sad(X) if not student(X),overworked(X),poor(X)sad(X) if student(X), alone(X)poor(X) if student(X)

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EXAMPLE: Verifying Hypotheses

• Model now is refined to:sad(X) if not student(X),overworked(X),poor(X)sad(X) if student(X), alone(X)poor(X) if student(X)

• Observations = {sad(alex), sad(krycia), not sad(oli)}

• Abductive Explanation ={poor(ale), poor(krycia), not alone(oli)}

• Inductive Hypotheses: poor(X) if young(X), lecturer(X)

(Note: “poor(X) if young(X)” is rejected because we know young(bill), rich(bill).)

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Current Situation Frameworks of Integration

Inverse Entailment HAIL

SOLDR CF-Induction

Systems of Integration Progol 5

ProLogICA HAIL (?)

INTHELEX (?) CF-Induction (?)

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Current Situation (Cnt)Applications

• Gene Regulatory Pathways• Inhibition in Metabolic Networks• Signal Networks

• Robot Navigation (Learning Action Theories e.g. Event Calculus)

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Future Outlook Challenges remain

Appropriate basic forms of reasoning: Normal & Disjunctive LP Trade off between generality & efficiency Chart out the limits of learning Understand their relevancy for scientific modelling

applications

Let applications drive the Theoretical & Practical Development Computational Bioscience Natural Language Cognitive Robotics

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CONCLUSIONS

• Use of logical inference can be powerful method for “rationalization” of scientific phenomena.• But it needs a good problem domain model with:

• Clear hypotheses of the basic model• Parameters of variation of analysis of the phenomena• Well-informed strategy of use and feedback analysis

• Offers a systematic methodology for modelling and analysis under known/engineered hypotheses.

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Microarray Gene Mutation Experiments at CMMI