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Nonmonotonic Abductive – Inductive Learning Oliver Ray Department of Computer Science University of Bristol AIAI'07, September 15th, 2007 Aix-en-Provence

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Nonmonotonic Abductive – Inductive Learning Oliver Ray Department of Computer Science University of Bristol AIAI'07, September 15th, 2007 Aix-en-Provence (for temporal process modelling in bioinformatics and AI)

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Motivation: Learning Temporal Theories Machine Learning: automated methods needed to handle the volume and complexity of data generated by modern experimental and data logging techniques. Inductive Logic Programming: produces expressive human-understandable hypotheses, exploits prior domain knowledge, and facilitates incremental knowledge update. Abductive–Inductive Learning: combines explanation and generalisation, allows for non-observation predicate learning, supports non-monotonic inference. Non-monotonic Learning of Temporal Theories: Infer temporal models of systems or processes from (partial) domain knowledge and (partial) observations.

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Problem: Induction of Process Models Given: temporal logic calculus partial process model scenarios/narratives Find: (more) complete model that extends the partial model and explains the given narratives and scenarios wrt. the temporal calculus

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Given: temporal logic calculus…event calculus partial process model…events, fluents, time scenarios/narratives…happens, holds, initially Find: (more) complete model …initiates, terminates Problem: Induction of Process Models that extends the partial model and explains the given narratives and scenarios wrt. the temporal calculus

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Given: temporal logic calculus…event calculus partial process model…events, fluents, time scenarios/narratives…happens, holds, initially Find: (more) complete model …initiates, terminates B E H NM ILP Problem: Induction of Process Models that extends the partial model and explains the given narratives and scenarios wrt. the temporal calculus

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Example: E. coli Lactose Metabolism E. coli growth medium add_lactose sub_glucose add_glucose sub_lactose ACTIONS (Events) pres_lactose pres_glucose meta_lactose EFFECTS (Fluents)..…TIME..… (Integers)

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Transcriptional Regulation of LAC Operon polymeraseactivator cAMP repressor PromOplac(z)lac(y) CAP allolactose PromOplac(z)lac(y)CAP galactosidasepermease (a) Lactose metabolising genes not expressed (b) Lactose metabolising genes expressed (low glucose) (high lactose)

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Event Calculus Axioms holdsAt(F,T2) happens(E,T1), T1

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Partial LAC Process Model % ontology time(0..9). event(add_gluc). event(add_lact). event(sub_gluc). event(sub_lact). fluent(pres_lact). fluent(pres_gluc). fluent(meta_lact). % behaviour initiates(add_gluc, pres_gluc, T). initiates(add_lact, pres_lact, T). terminates(sub_gluc, pres_gluc, T). terminates(sub_lact, pres_lact, T).

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LAC Scenario / Narrative % actions initially(pres(gluc)). happens(add(lact),1). happens(sub(gluc),2). happens(sub(lact),3). happens(add(lact),4). happens(add(gluc),5). happens(sub(lact),6). happens(sub(gluc),7). % observations not holdsAt(meta(lact),1), not holdsAt(meta(lact),2), holdsAt(meta(lact),3), not holdsAt(meta(lact),4), holdsAt(meta(lact),5), not holdsAt(meta(lact),6), not holdsAt(meta(lact),7), not holdsAt(meta(lact),8). n.b. in general, could have partial knowledge of actions and/or observations, many actions per timepoint, etc.,

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Language and Search Bias % domain specific mode declarations modeh(2, initiates(#event,#fluent,+time) ). modeh(2, terminates(#event,#fluent,+time) ). modeb(3, holdsAt(#fluent,+time) ). modeb(3, not holdsAt(#fluent,+time) ). % built-in preference criterion: Occam’s Razer % (greedily )prefer the simplest (i.e., smallest ) % hypothesis that correctly explains the data n.b. in general, need ways to constrain the search space both syntactically and semantically

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Abductive–Inductive Learning Abduction 1 Deduction 2 = a1 :ana1 :an K= a 1 d 1 d 2 … d m 1 : a n d 1 d 2 … d m n Given: B,E,M Return: H n n n Induction 3 H= A 1 D 1 D 2 … D m 1 : A n D 1 D 2 … D m n n n n head atoms of K are abductive explanation of the examples E : i.e., B |= e. body atoms of K are deductive consequences of the theory B: i.e., B |= d i. H is a compressive theory subsuming the theory K : i.e., H K. IDEA: construct and generalise an initial ground hypothesis K called a Kernel Set

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Abductive Phase

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Deductive Phase

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Inductive Phase

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DEMO CLICK ME!

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Related Work Sakama Baral Otero & Lorenzo Muggleton & Moyle Inoue, Iwanuma & Nabeshima

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Conclusion XHAIL provides a (stable model) semantics and proof procedure for NM-ILP It uses mode declarations in the construction of a Kernel Set to reduce generalisation search space It is well suited to learning temporal theories in the Event Calculus (which provides a more intuitive event-based formalism than pure first order logic) But, still need to investigate stability, noise, confidence, …

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