1 Abduction and Induction in Scientific Knowledge Development Peter Flach, Antonis Kakas & Oliver Ray AIAI Workshop 2006 ECAI August, 2006

2 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)?

3 Central “Application Theme” Scientific Modelling Not necessarily classical scientific domains! Domains that follow scientific methodology. Declarative Modelling

4 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

5 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

6 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.

7 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.

8 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 knowledge sad(X) if overworked(X), poor(X) overworked(oliver) overworked(alex) overworked(krycia) lecturer(alex) lecturer(krycia) student(oliver) academic(alex), … poor(alex).

9 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

10 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}

11 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”

12 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

13 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

14 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

15 The cycle of abductive and inductive knowledge development InductionAbduction T’ = T U H T O’= H O T U H |= Obs H H

16 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.

17 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)

18 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)

19 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).)

20 Current Situation  Frameworks of Integration  Inverse Entailment  HAIL  SOLDR  CF-Induction  Systems of Integration  Progol 5  ProLogICA  HAIL (?)  INTHELEX (?)  CF-Induction (?)

21 Current Situation (Cnt)  Applications Gene Regulatory Pathways Inhibition in Metabolic Networks Signal Networks Robot Navigation (Learning Action Theories e.g. Event Calculus)

22 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

23 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.

24 Microarray Gene Mutation Experiments at CMMI