Logic-Based Machine Learning

Chapter

LOGICBASED MACHINE LEARNING

Stephen Muggleton and Flaviu Marginean

Department of Computer Science

University of York

Heslington York YO DD

United Kingdom

Abstract The last three decades has seen the development of Computational

Logic techniques within Articial Intelligence This has led to the

development of the sub ject of Logic Programming LP which can

b e viewed as a key part of LogicBased Articial Intelligence The

subtopic of LP concerned with Machine Learning is known as Inductive

Logic Programming ILP which again can b e broadened to Logic

Based Machine Learning by dropping Horn clause restrictions ILP

has its ro ots in the groundbreaking research of Gordon Plotkin and

Ehud Shapiro This pap er provides a brief survey of the state of ILP

application s theory and techniques

Keywords Inductive logic programming machine learning scientic discovery

protein prediction learning of natural language

INTRODUCTION

As envisaged by John McCarthy in McCarthy Logic has turned

out to b e one of the key knowledge representations for Articial Intelligence

research Logic in the form of the FirstOrder Predicate Calculus provides

a representation for knowledge which has a clear semantics together with

wellstudied sound rules of inference Interestingly Turing Turing and

McCarthy McCarthy viewed a combination of Logic and Learning as

b eing central to the development of Articial Intelligence research This article

is concerned with the topic of LogicBased Machine Learning LBML The

mo dern study of LBML has largely b een involved with the study of the learning

of logic programs or Inductive Logic Programming ILP Muggleton

Many of the foundational results of b oth Gordon Plotkin Plotkin and

Ehud Shapiro Shapiro are still central to the study and conceptual

framework of ILP This is true despite the fact that Plotkin did not employ

Horn clause restrictions

ILP is a general form of Machine Learning which involves the construction

of logic programs from examples and background knowledge The sub ject

LOGICBASED ARTIFICIAL INTELLIGENCE

has inherited its logical tradition from Logic Programming and its empirical

orientation from Machine Learning Rob ert Kowalski Kowalski

famously describ ed Logic Programming LP with the following equation

LP Logic Control

The equation emphasizes the role of the programmer in providing sequencing

control when writing Prolog programs In a similar spirit we might describ e

ILP as follows

ILP Logic Statistics Computational Control

The logical part of ILP is related to the formation of hypotheses while the

statistical part is related to evaluating their degree of b elief As in LP the

Computational Control part is related to the sequencing of search carried out

when exploring the space of hypotheses

The structure of the pap er is as follows Section introduces the key

elements of ILP provides a formal framework Section for the later

discussion and discusses how Bayesian inference Section is used as a

preference mechanism Section describ es applications of ILP to problems

related to discovery of biological function ILP has a strong p otential for b eing

applied to Natural Language Pro cessing NLP The resultant research area of

Learning Language in Logic LLL is describ ed in Section together with some

encouraging preliminary results Conclusions concerning ongoing ILP research

are given in Section

ILP

ILP algorithms take examples E of a concept such as a protein family

together with background knowledge B such as a denition of molecular

dynamics and construct a hypothesis h which explains E in terms of B

For example in the protein fold domains Section E might consist of

descriptions of molecules separated into p ositive and negative examples of a

particular fold overall protein shap e This is exemplied in Figure for

the fold helicalupanddownbundle A p ossible hypothesis h describing

this class of proteins is shown in Figure The hypothesis is a denite

clause consisting of a head fold and a body the conjunction length

helix In this case fold is the predicate involved in the examples and

hypothesis while length p osition etc are dened by the background

knowledge A logic program is simply a set of such denite clauses Each of E

B and h are logic programs

In the context of knowledge discovery a distinct advantage of ILP over black

b ox techniques such as neural networks is that a hypotheses such as that

shown in Figure can in a straightforward manner b e made readable by

translating it into the following piece of English text

The protein P has fold class Fourhelical upanddown bundle if it

contains a long helix H at a secondary structure p osition b etween and

and H is followed by a second helix H

Such explicit hypotheses are required for exp erts to b e able to use them within the familiar human scientic discovery cycle of debate criticism and refutation

LogicBased Machine Learning

Positive Negative

H:6[79-88] H:5[111-113] H:3[71-84] H:1[19-37]

H:4[61-64] H:5[66-70]

H:1[8-17] H:2[26-33]

E:2[96-98] E:1[57-59]

H:7[99-106] H:4[93-108] H:2[41-64] H:3[40-50]

1omd - EF-Hand

2mhr - Four-helical up-and-down bundle

Figure A p ositive and a negative example of the protein fold helicalupand

downbundle D arrangement of secondary structure units is shown for helices

cylinders and sheets arrows Each secondary structure unit is lab elled according

to the index of its rst and last amino acid residue

foldFourhelical upanddown bundleP

helixPH

lengthHhi

p ositionPHPos

interval Pos

adjacentPHH

helixPH

Figure An hypothesised denite clause for helicalup anddownbund les

LOGICBASED ARTIFICIAL INTELLIGENCE

FORMAL FRAMEWORK FOR ILP

The normal framework for ILP Muggleton and De Raedt Nienhuys

Cheng and de Wolf is as follows As exemplied by the protein folds

problem describ ed in the last subsection the learning system is provided with

background knowledge B p ositive examples E and negative examples E

and constructs an hypothesis h B E E and h are each logic programs A

logic program Lloyd is a set of denite clauses each having the form

h b b

1 n

where h is an atom and b b are atoms Usually E and E consist of

1 n

ground clauses those for E b eing denite clauses with empty b o dies and

those for E b eing clauses with head false and a single ground atom in the

b o dy

In the text b elow the logical symbols used are logical and logical

or j logical entailment 2 Falsity The conditions for construction of h

are as follows

Necessity B j E

Suciency B h j E

Weak consistency B h j 2

Strong consistency B h E j 2

Note that neither suciency nor strong consistency are required for systems

that deal with noise The four conditions ab ove capture al l the logical

requirements of an ILP system However for any B and E there will generally

b e many hs which satisfy these conditions Statistical preference is often used

to distinguish b etween these hypotheses see Section Both Necessity and

Consistency can b e checked using a theorem prover Given that all formulae

involved are denite the theorem prover used need b e nothing more than a

Prolog interpreter with some minor alterations such as iterative deep ening to

ensure logical completeness

DERIVING ALGORITHMS FROM THE

SPECIFICATION OF ILP

The suciency condition captures the notion of generalizing examples

relative to background knowledge A theorem prover cannot b e directly applied

to derive h from B and E However by simple application of the Deduction

Theorem the suciency condition can b e rewritten as follows

E j h Suciency B

This simple alteration has a profound eect The negation of the hypothesis can

now b e deductively derived from the negation of the examples together with the

background knowledge This is true no matter what form the examples take

and what form the hypothesis takes This approach of turning an inductive

problem into one of deduction is called inverse entailment Muggleton

Metho ds for ensuring completeness of inverse entailment have b een a sub ject of debate recently Yamamoto Muggleton

LogicBased Machine Learning

p(H)

Figure Prior over hypotheses Hyp otheses are enumerated in order of

descending prior probability along the Xaxis The Yaxis is the probabili ty of

individua l hypotheses Vertical bars represent hypotheses consistent with E

BAYESIAN FRAMEWORK

It is not sucient to sp ecify the ILP framework in terms of the logical

relationships which must hold b etween E B and h For any given E and B

there will b e many p ossibly innitely many choices for h Thus a technique is

needed for dening a preference over the various choices for h One approach

to doing so involves dening a Bayesian prior probability distribution over the

learners hypothesis space Muggleton a This is illustrated in Figure

According to Bayes theorem the hypothesis h with maximum

M AP

p osterior probability in hypothesis space H is as follows

h argmax P hjE

M AP

h2H

P E jhP h

argmax

h2H

argmax P E jhP h

h2H

Within ILP Bayesian approaches Muggleton b have b een used to

investigate the problem of learning from p ositive examples only Muggleton

and issues related to predicate invention Khan et al a relational

form of feature construction Learning from p ositive examples and predicate

invention are imp ortant in b oth natural language domains see Section and

in problems involving scientic discovery see Section

DISCOVERY OF BIOLOGICAL

FUNCTION

Understanding of a variety of metab olic pro cesses is at the center of

drug development within the pharmaceutical industry Each new drug costs

hundreds of millions of p ounds to develop The ma jority of this cost comes

Note that in the case of the p otentially innite hypothesis space employed in ILP it is

not p ossible to have a uniform distribution which assigns nonzero prior probabilities to all hypotheses

LOGICBASED ARTIFICIAL INTELLIGENCE

from clinical tests on ecacy and sideeects The increasing supply of data

b oth from the human genome pro ject and existing drug databases is pro ducing

increasing interest in computational techniques which could reduce drug

development costs by supp orting automated discovery of biological functions

Biological functions are regulated by the do cking of small molecules ligands

with sites on large molecules proteins Drugs such as b etablo ckers mimic

natural small molecules such as adrenaline Eectiveness of drugs dep ends

on the correct shap e and charge distribution of ligands Thus b etablo ckers

inhibit the binding of adrenaline and so stop overstimulation of heart muscle

in patients prone to heart attacks

Results on scientic discovery applications of ILP are separated b elow

b etween those related to small molecules such as ligands and those related to

proteins

SMALL MOLECULES

Structureactivi ty prediction The ma jority of pharma

ceutical RD is based on nding slightly improved variants of patented active

drugs This involves lab oratories of chemists synthesising and testing hundreds

of comp ounds almost at random The average cost of developing a single new

drug is around million In King et al it was shown that the

ILP system Golem Muggleton and Feng was capable of constructing

rules which accurately predict the activity of untried drugs Rules were con

structed from examples of drugs with known medicinal activity The accuracy

of the rules was found to b e slightly higher than traditional statistical metho ds

More imp ortantly the easily understandable rules provided insights which were

directly comparable to the relevant literature concerning the binding site of

dihydrofolate reductase

Mutagenesis In King et al Srinivasan et al the

ILP system Progol Muggleton was used to predict the mutagenicity of

chemical comp ounds taken from a previous study in which linear regression

had b een applied Progols predictive accuracy was equivalent to regression on

the main set of comp ounds and signicantly higher as opp osed to

on comp ounds which had b een discarded by the previous authors

as unpredictable using regression Progols single clause solution for the

comp ounds was judged by the domain exp erts to b e a new structural alert for

mutagenesis

Pharmacophores In a series of blind tests in collab oration

with the pharmaceutical company Pzer UK Progol was shown Finn et al

capable of rediscovering a D description of the binding sites or

pharmacophores of ACE inhibitors a hypertension drug and an HIVprotease

inhibitor an antiAIDS drug

Carcinogenicity Progol was entered into a worldwide car

cinogenicity prediction comp etition run by the National Toxicology Program

NTP in the USA Progol was trained on around available comp ounds and

made use of its earlier rules relating to mutagenicity In the rst round of the

LogicBased Machine Learning

Metho d Type Accuracy P

Ashbyy Chemist

Progol ILP

RASHy Biological p otency analysis

TIPTy Prop ositional ML

Bakale Chemical reactivity analysis

Benigni Exp ertguided regression

DEREK Exp ert system

TOPKAT Statistical discrimination

CASE Statistical correlation analysis

COMPACT Molecular mo deling

Default Ma jority class

Figure Comparative accuracies on the rst round of the Predictive Toxicology

Evaluation PTE Here P represents the binomial probabili ty that Progol and the

corresp onding toxicity prediction metho d classify the same prop ortion of examples

correctly The Default metho d predicts all comp ounds to b e carcinogenic Metho ds

marked with a y have access to shortterm in vivo ro dent tests that were unavailable

to other metho ds Ashby and RASH also involve some sub jective evaluation to decide

on structural alerts

comp etition Progol pro duced the highest predictive accuracy of any automatic

system entered Srinivasan et al see Figure

PROTEINS

Protein secondary structure prediction In Muggleton

et al Golem was applied to one of the hardest op en problems in molecular

biology The problem is as follows given a sequence of amino acid residues

predict the placement of the main three dimensional substructures of the

protein The problem is of great interest to pharmaceutical companies involved

with drug design For this reason over the last years many attempts have

b een made to apply metho ds ranging from statistical regression to decision

tree and neural net learning to this problem Published accuracy results for

the general prediction problem have ranged b etween and very close

to ma jorityclass prediction rates In our investigation it was found that the

ability to make use of background knowledge from molecular biology together

with the ability to describ e structural relations b o osted the predictivity for a

restricted subproblem to around on an indep endently chosen test set

Discovery of fold descriptions Protein shap e is usually

describ ed at various levels of abstraction At the lower levels each family

of proteins contains members with high sequence similarity At the most

LOGICBASED ARTIFICIAL INTELLIGENCE

abstract level folds describ e proteins which have similar overall shap e but

are very dierent at the sequence level The lack of understanding of shap e

determination has made protein fold prediction particularly hard However

although there are around known folds around half of all known proteins

are members of the most p opulated folds In Turcotte et al Progol

was applied to discover rules governing the most p opulated protein folds

The assignment to folds was taken from the SCOP Structural Classication

of Proteins database Brenner et al Progol was used to learn rules

for the ve most p opulated folds of the four classes alphaalpha b etab eta

alphab eta and alphab eta The rules had an average crossvalidated

accuracy of The rules identied known features of folds For instance

according to one rule the NAD binding fold where a short lo op b etween the rst

b etastrand and alphahelix is required to bind to biological cofactor molecule

NAD A questionnaire designed by Mike Sternberg requested named folds to

b e paired with fold descriptions generated by Progol The questionnaire was

sent to a selection of the worlds top protein scientists Progol successfully

identied structural signatures of protein folds that were only know by the

worlds top exp ert Dr Murzin Cambridge

LEARNING LANGUAGE IN LOGIC

The telecommunications and other industries are investing substantial eort

in the development of natural language grammars and parsing systems

Applications include information extraction database query esp ecially over

the telephone to ols for the pro duction of do cumentation and translation of

b oth sp eech and text Many of these applications involve not just parsing but

the pro duction of a semantic representation for a sentence

WHY IS ILP GOOD FOR NLP

Hand development of such grammars is very dicult requiring exp ensive

human exp ertise It is natural to turn to machine learning for help in

automatic supp ort for grammar development The currently dominant

paradigm in grammar learning is statisticallybased Magerman Collins

Brisco e and Carroll Krotov et al Krotov et al This

work is all with a few recent smallscale exceptions fo cussed on syntactic or

lexical prop erties No treatment of semantics or contextual interpretation is

p ossible b ecause there are no annotated corp ora available of sucient size The

aim of statistical language mo deling is by and large to achieve wide coverage

and robustness The necessary tradeo is that depth of analysis cannot also b e

achieved Statistical parsing metho ds do not deliver semantic representations

capable of supp orting full interpretation Traditional rulebased systems on

the other hand achieve the necessary depth of analysis but at the sacrice of

robustness handcrafted systems do not easily extend to new types of text or

application

In this paradigm disambiguation is addressed by asso ciating statistical

preferences derived from an annotated training corpus with particular

syntactic or semantic congurations and using those numbers to rank parses

While this can b e eective it demands large annotated corp ora for each new

application which are costly to pro duce There is presumably an upp er limit

LogicBased Machine Learning

What is the highest p oint of the state with the largest area

answerP highpointSP largestA stateS areaSA

What are the ma jor cities in Kansas

answerC majorC cityC locCS

equalSstateidkansas

Figure Form of examples

on the accuracy of these techniques since the variety of language means that

it is always p ossible to express sentences in a way that will not have b een

encountered in training material

The alternative metho d for disambiguation and contextual resolution is to

use an explicit domain theory which enco des in a set of logical axioms the

relevant prop erties of the domain While this has b een done for small scale

domains eg Hobbs et al the currently fashionable view is that it is

impractical for complex domains b ecause of the unmanageably large amount

of handco ded knowledge that would b e required However if a large part of

this domain knowledge could b e acquired semiautomatically this kind of

practical ob jection could b e met From the NLP p oint of view the promise of

ILP is that it will b e able to steer a midcourse b etween these two alternatives of

large scale but shallow levels of analysis and small scale but deep and precise

analyses ILP should pro duce a b etter ratio b etween breadth of coverage and

depth of analysis

HOW CAN ILP BE USED FOR NLP

In grammar learning the logical theory to b e synthesised consists of grammar

rules together with semantic representations Examples are sentences from the

language b eing learned and the background knowledge represents an existing

partial grammar p erhaps supplemented with constraints on the p ossible forms

of rules In grammatical disambiguation and contextual interpretation the

theory to b e synthesised consists of a set of axioms or logical statements

prescribing prop erties of the domain relevant to these tasks These prop erties

may include an ontology or type hierarchy and p erhaps default statements

ab out typical prop erties of and relations holding b etween the entities in

the domain The examples consist of b oth correct and incorrect analyses

or contextual interpretations for sentences or sentencecontext pairs where

contexts can b e represented as disambiguated sentences The background

knowledge may consist of a partial domain theory or an enco ding of whatever

existing constraints on disambiguation or interpretation are known The

resulting theory is used as a lter on hypothesised alternative interpretations

GEOGRAPHIC DATABASE QUERIES

ILP has b een used for learning grammar and semantics using the CHILL

system Zelle and Mo oney b In this case background knowledge and

examples were taken from an existing database of US geographical facts Each

example consisted of a sentence paired with its semantics as shown in Figure gure taken from Mo oney

LOGICBASED ARTIFICIAL INTELLIGENCE

Accuracy 30

Chill Geobase 20

0 0 50 100 150 200 250

Training Examples

Figure CHILLs accuracy on learning grammar and semantics

The data was gathered by asking sub jects to generate appropriate questions

Each question was then paired with appropriate logical queries to give

examples Figure taken from Mo oney shows CHILLs accuracy

on progressively larger training sets averaged over trials The line lab elled

Geobase shows the accuracy of an existing commerciallydeveloped hand

co ded system for the same domain CHILL outp erforms the existing system

when trained on or more examples

MORPHOLOGY

Mo oney and Cali Mo oney and Cali have applied ILP to learning

the past tense of English verbs Learning of English pasttense has b ecome

a b enchmark problem in the computational mo deling of human language

acquisition Rumelhart and McClelland Ling In Mo oney

and Cali it was shown that a particular ILP system FOIDL could

learn this transformation more eectively than previous neuralnetwork and

decisiontree metho ds FOIDLs rstorder default rule style representation was

demonstrated by the authors as pro ducing a predictive accuracy advantage in

this domain

However more recently Muggleton and Bain Muggleton and Bain

have shown that ILP prediction techniques based on Analogical Prediction

AP pro duce even higher accuracies on the same data AP is a halfway house

b etween instancebased learning and induction Thus AP logical hypotheses are

generated on the y for each instance to b e predicted The form of examples

and hypotheses is shown in Figure A comparison of learning curves for

various systems is shown in Figure The horizontal line lab elled Default

rules represents the following simple Prolog program which adds a d to verbs

ending in e and otherwise adds ed

pastAB splitABe splitBAd

LogicBased Machine Learning

Examples Hyp otheses

pastworryworried

pastwhizwhizzed pastAB splitACrry splitBCrried

pastgrindground

Figure Form of examples and hypotheses for past tense domain

English past tense 100

60 Predictive accuracy (%) 50 AP CProgol4.4 (induction) FOIDL FOIL 40 IFOIL Default rules

30 50 100 150 200 250 300 350 400 450 500

Training Set Size

Figure Learning curves for alphab etic English past tense Comparisons were

made b etween AP CProgol FOIDL FOIL IFOIL and a handco ded set of

default rules Results were averaged over random chosen training sets of sizes

with accuracies measured over test sets of size

pastAB splitBAed

The dierences b etween AP and all other systems are signicant at the

level with and examples

WHY IS NLP GOOD FOR ILP

From the ILP p oint of view NLP has recently b een recognised as a

challenging application area Some successes have b een achieved in using

ILP to learn grammar and semantics Zelle and Mo oney b Zelle and

Mo oney Zelle and Mo oney a Cussens et al The existence

within NLP problems of hierarchically dened structured data with large

amounts of relevant logically dened background knowledge provides a p erfect testb ed for stretching ILP technology in a way that would b e b enecial in other

LOGICBASED ARTIFICIAL INTELLIGENCE

application areas Bratko and Muggleton Sternberg et al King

et al Srinivasan et al Finn et al The York system Progol

Muggleton is arguably the most general purp ose and widely applied

ILP system Most ILP systems concentrate on the issue of learning a single

usually nonrecursive concept and assume a set of completely and correctly

dened background predicates By contrast NLP applications need techniques

to deal with simultaneous completion and correction of a set of related often

recursively dened predicates It is also exp ected to b e necessary to implement

new techniques for automatic augmentation of the set of background predicates

Khan et al in order to handle incompleteness of available vocabulary

CONCLUSION

In his presentation of ILP biological discovery results to the Royal So ciety

Sternberg et al Sternberg emphasised the asp ect of joint human

computer collab oration in scientic discoveries Science is an activity of human

so cieties It is the authors b elief that computerbased scientic discovery

must supp ort strong integration into the existing so cial environment of human

scientic communities The discovered knowledge must add to and build on

existing science The ability to incorp orate background knowledge and reuse

learned knowledge together with the comprehensibility of the hypotheses have

marked out ILP as a particularly eective approach for scientic knowledge

discovery

In the natural language area ILP has not only b een shown to have higher

accuracies than various other ML approaches in learning the past tense of

English see Section but also shown to b e capable of learning accurate

grammars which translate sentences into deductive database queries Zelle and

Mo oney b see Section In b oth cases follow up studies Thompson

et al Dzeroskiand Erjavec have shown that these ILP approaches

to natural language problems extend with relative ease to various languages

other than English

The area of Learning Language in Logic LLL is pro ducing a number of

challenges to existing ILP theory and implementations In particular language

applications of ILP require revision and extension of a hierarchically dened set

of predicates in which the examples are typically only provided for predicates

at the top of the hierarchy New predicates often need to b e invented and

complex recursion is usually involved Similarly the term structure of semantic

ob jects is far more complex than in other applications of ILP Advances in

ILP theory and implementation related to the challenges of LLL are already

pro ducing b enecial advances in other sequenceoriented applications of ILP

In addition LLL is starting to develop its own character as a subdiscipline of

AI involving the conuence of computational linguistics machine learning and

logic programming

Acknowledgements

Thanks are due to the funders and researchers who help ed develop the

technology and applications of ILP on the Esprit pro jects ECOLES

ILP I ILPnet ILP II ILPnet ALADIN and the EPSRC Rulebased system pro ject

LogicBased Machine Learning

Exp erimental Application and Developments of ILP

Distributionbased Machine Learning Closed Lo op Machine

Learning The author would also like to acknowledge the p ersonal

supp ort he received in carrying out research into ILP under an SERC Post

do ctoral Fellowship an EPSRC Advanced Research Fellowship

and Research Fellowship from Wolfson College Warm

thanks are oered to the authors wife Thirza and daughter Clare for their continuous cheerful supp ort

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