A Case for Embedded Natural Logic for Ontological Knowledge Bases

Troels Andreasen

and Jørgen Fischer Nilsson

Computer Science, Roskilde University, Roskilde, Denmark

Department of Mathematics and Computer Science, Technical University of Denmark, Lyngby, Denmark

Keywords:

Ontological Engineering, Natural Language Processing, Natural Logic, Domain Modeling.

Abstract:

We argue in favour of adopting a form of natural logic for ontology-structured knowledge bases as an al-

ternative to description logic and rule based languages. Natural logic is a form of logic resembling natural

language assertions, unlike description logic. This is essential e.g. in life sciences, where the large and evolv-

ing knowledge speciﬁcations should be directly accessible to domain experts. Moreover, natural logic comes

with intuitive inference rules. The considered version of natural logic leans toward the closed world assump-

tion (CWA) unlike the open world assumption with classical negation in description logic. We embed the

natural logic in DATALOG clauses which is to take care of the computational inference in connection with

querying.

1 INTRODUCTION

This position paper discusses a novel speciﬁcation

language framework for logical knowledge bases. We

have in mind in particular but not exclusively the life

science application domains.

We take as departure the following desiderata for

ontological knowledge base languages:

• Readability of the knowledge base for domain ex-

perts

• Appropriate level and range of expressivity bal-

anced against computational complexity concerns

• Semantic rigor: a precise logical semantics, af-

fording intuitive and computationally manageable

reasoning rules

• Ability to cope with classes and relationships in-

tensionally in querying, that is not just as exten-

sional sets.

We argue that these desiderata may be met with

the following set-up: A form of natural logic embed-

ded in clausal logic, the latter as known from logic

programming. The natural logic endorses arbitrarily

complex formulations by recursive forms reﬂecting

natural language phrase forms.

In this set-up the innermost level of natural logic

serves to represent domain assertions, whereas the

outermost logic provide the means of formulating log-

ical inference rules as well as ad hoc domain rules.

In other words we advocate a metalogic framework,

where the interaction between the two language lay-

ers is facilitated by the variable free form of natural

logic. Thus there is no confusion between quantiﬁed

variables at the metalevel and the natural logic level.

It should be mentioned that the proposal is not an at-

tempt to merge the two mentioned logical languages

into one language, cf. (Grosof et al., 2003).

As a key point in our approach the compound

natural logic assertions are broken down into atomic

assertions in the form of triples admitting a labeled

graph representation conducive to pathway computa-

tions in the entire semantic graph.

The ideas in our approach appeared in seminal

form in (Andreasen and Fischer Nilsson, 2004; Nils-

son, 2011; Andreasen et al., 2013). The brief presen-

tation here draws on and reﬂects on our (Andreasen

et al., 2014a), which focusses on life science appli-

cation domains and (Andreasen et al., 2014b), which

describes the natural logic forms, and the semantic

net internal representation for pathway computations

in the knowledge base.

We consider knowledge bases as conventionally

conceived as classes of entities and relationships ex-

pressed as logical assertions. As usual the backbone

ontology is formed by the class inclusion relationship

conventionally known as isa. The inclusion relation

comes with inheritance of attached properties.

In addition there may be introduced domain spe-

ciﬁc relationships such as locative, causative, prop-

423

Andreasen T. and Fischer Nilsson J..

A Case for Embedded Natural Logic for Ontological Knowledge Bases.

DOI: 10.5220/0005156504230427

In Proceedings of the International Conference on Knowledge Engineering and Ontology Development (KEOD-2014), pages 423-427

ISBN: 978-989-758-049-9

 2014 SCITEPRESS (Science and Technology Publications, Lda.)

erty ascribing, and partonomic as well as more do-

main speciﬁc relationships.

2 A NATURAL LOGIC

Natural logic is a common term for logics which re-

semble natural language and which are further sup-

posed to apply more intuitive reasoning rules than

mathematical logics (van Benthem, 1986; van Ben-

them, 2011; Muskens, 2011; Sanchez Valencia, 2004,

MacCartney and Manning, 2009). The price paid is

limited expressivity compared, say, with ﬁrst order

logic.

The general linguistic form of assertions in the

natural logic considered here, called NATURALOG, is

CNterm

Verb Q

CNterm

where Q

is either of the determiners every and some,

CNterm

are common noun terms, and Verb is a tran-

sitive verb. In the simplest case CNterm

is a class

name.

As an example, in the context of a knowledge base

for biological cells we have

every eukariot has-part some nucleus

where the verb form ”has part” is stylized into has-

part, cf. the handling of partonomies in (Smith and

Rosse, 2004).

In compound noun terms a class name forming

the head noun is attached modiﬁers corresponding to

adjectives, compound nouns, adnominal prepositional

phrases, and restrictive relative clauses. The latter two

modiﬁers have recursive syntactic structure. Individ-

ual class entities are handled by being re-conceived as

singleton classes. This complies with scientiﬁc terms

such as substance names being considered as class

names.

In the logical conception the above NATURALOG

assertion becomes

Cterm

Rterm Q

Cterm

where Cterm

are class or concept terms and Rterm

is a binary relation name coming from the transitive

verb. In compound concept terms a class name is at-

tached modiﬁers. Here we consider the form [that]

Rterm some Cterm, where that is an optional key-

word, serving to improve readability, only. Modiﬁers

are supposed always to restrict a class to a subclass.

Presence of multiple modiﬁers in a class term forms a

conjunction.

The above propositional form yields four quanti-

ﬁer cases:

every c r some d

every c r every d

some c r some d

some c r every d

The ﬁrst one covers most cases in knowledge base

practice. By appropriate default rules for quantiﬁers

the sample

alphacell secrete glucagon

is interpreted logically as the proposition

every alphacell secrete some glucagon

that is, in the predicate logic explication

∀x(al phacell(x) → ∃y(secrete(x, y) ∧ glucagon(y)))

As a slightly more complex example, let us con-

sider the natural language sentence

cells that produce glucagon reside in pancreas

In predicate logic it would be

∀x(cell(x) ∧ ∃y(glucagon(y) ∧ produce(x, y)) →

∃z(pancreas(z) ∧ residein(x, z))

In description logic:

cell u ∃produce.glucagon v ∃residein.pancreas

In natural logic

(cell that produce glucagon) reside-in pancreas

or simply

cell that produce glucagon reside-in pancreas

Our ∀∀ natural logic sentence every c r every d

should not be confused with the description logic sen-

tence c v ∀r.d.

2.1 Class Inclusion

The key relationship of class inclusion, convention-

ally denoted isa, actually comes about as a special

case of the natural logic forms every c r some d,

namely with the relation r being equality. However,

we use c isa d for every c equals some d.

As an example of class inclusion we can state

alphacell isa cell

By contrast we need not state that pancreatic cell isa a

cell explicitly because pancreatic acts as a restrictive

modiﬁer.

By default two classes (simple or compound) are

conceived to be disjoint unless either

• one is a subclass of the other, or

• they have a common subclass.

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Unlike description logic classes are formally consid-

ered nonempty: ∃xc(x) for all classes c. A common

subclass cd is readily obtained by stating the two as-

sertions cd isa c and cd isa d.

Unlike (Smith and Rosse, 2004) we accept taxo-

nomic cross categories (common subclasses). For in-

stance in our ontology the blood (cf. bloodstream) is

conceived of as a bodily organ as well as an substance

coming in quantities (ﬁgure 1).

organ

blood

isa

substance

isa

Figure 1: Blood as cross categories in the ontology.

Another example, there is presumably peptide

hormone, where there are peptides which are not hor-

mones and hormones which are not peptides. The

common noun peptide hormone is an example of a

compound noun formed by two class names where

peptide acts as a restrictive modiﬁer.

2.2 Reduction to Predicate Logic

Let us consider the above main quantiﬁer case ∀∃, that

every c r some d

where c is the class name c

possibly with modiﬁers

and analogously for d.

This case has the following backtranslation to

predicate logic:

∀x(c

comp

(x) → ∃y(r

(x, y) ∧ d

comp

(y)))

with

∀x(c

comp

(x) ↔ c

∧

i=1

∃y

(x, y

) ∧ c

)))

∀x(d

comp

(x) → d

∧

i=1

∃y

(x, y

)∧ d

)))

where c

and d

simple or complex with recursively

the same structure

The special class inclusion case:

∀x(c(x) → ∃y(x = y) ∧ d(y)))

reduces to

∀x(c(x) → d(x))

It should be stressed that this reduction to pred-

icate logic is for explicatory reasons, only. The ap-

plied variable-free forms are subject to reasoning at

the metalogic level as to be explained next.

3 META LEVEL

We now turn to the clausal logic level into which the

natural logic assertions are embedded. At the meta

level NATURALOG knowledge base assertions appear

encoded as data. The applied meta level logic consist

of the well known DATALOG clauses

, ..., t

) ←

i=1

, ..., t

)

where the logical terms t are either constants or uni-

versally quantiﬁed variables. The variables are distin-

guished by upper case initial letter. The case of k be-

ing 0 yields an atomic fact p(t

, ..., t

). These clauses

are occasionally enriched with use of stratiﬁed nega-

tion by non-provability for which is used the symbol

6` referred to as DATALOG

A NATURALOG assertion with simple classes, ev-

ery c r some d, may then be represented straightfor-

wardly at the meta level, say, in principle with the

ground atomic

assert∀∃(c, r, d)

We remind that this framework is not an attempt

to extend the natural logic with the rule language cf.

(Grosof et al., 2012), since the two languages are kept

at two different levels.

3.1 Decomposition of Natural Logic

Assertions

Compound class terms (class names with modiﬁers)

call for encoding with the functional logic terms be-

ing available in the general form of deﬁnite clauses.

However, since we stick to DATALOG we have to de-

compose compound class terms.

Consider again the assertion

cell that produce glucagon reside-in pancreas

This assertion is decomposed into the DATALOG

fact

assert∀∃(cell-that-produce-glucagon,

reside-in, pancreas)

where cell-that-produce-glucagon is conceived of as a

new, auxiliary class name, which is in turn deﬁned by

the ground atomic facts

isa(cell-that-produce-glucagon, cell)

de f (cell-that-produce-glucagon,

produces, glucagon)

This decomposition principle admits representa-

tion of unlimited complex assertions as labeled graphs

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as illustrated in ﬁgure 2, where the adjoined arc tells

that the two edges form a deﬁnition. The graph for

one NATURALOG assertion forms part of the graph

conception for the entire knowledge base, cf. seman-

tic nets (Sowa, 1991; Sowa, 2000).

pancreas

cell-that-produce-glucagon

cell glucagon

isa producesreside_in

Figure 2: Complex assertions represented as labeled graphs.

3.2 Logical Inference Rules

The natural logic is supported by the logic inference

rules stated in DATALOG and comprising

• partial order rules for class inclusion isa

• monotonicity rules (van Benthem, 1986, 2011)

e.g.

assert∀∃(C

sub

, R, D) ←

isa(C

sub

, C) ∧ assert∀∃(C, R, D)

assert∀∃(C, R, D

sup

) ←

isa(D, D

sup

) ∧ assert∀∃(C, R, D)

• a subsumption rule which adds isa relationships

following logically from the given assertions.

For instance alphacell is subsumed by cell-that-

produce-glucagon, cf. ﬁgure 3, because alphacell

isa cell and alphacell produces glucagon

• ad hoc domain rules e.g. quasi-transitivity for

causation and partonomy

• integrity constraints e.g. for location (it being a

functional relation)

The disjointness of two classes is veriﬁed with

dis joint(C, D) ← 6` overlap(C, D)

overlap(C, D) ← isa(CD, C) ∧ isa(CD, D)

where the variable CD ranging over applied class

names may be conceived to be existentially quantiﬁed

to the right of the inverse implication.

From the point of view of ontology development

the non-monotonic negation by non-provability im-

plies that addition of new overlapping classes to the

knowledge base incurs retraction of previous disjoint-

ness.

pancreas

cell-that-produce-glucagon

cell glucagon

isa producesreside_in

alphacell

reside_in

isa

Figure 3: Inferred relationship alphacell reside-in pancreas.

3.3 Intensional Querying and

Pathﬁnding

The NATURALOG knowledge base may now be

queried deductively via the clause language appeal-

ing to the above-mentioned inference rules. The given

class names are introduced by

class(c)

The concepts (simple or complex) may be queried,

say, with

← isa(X, c)

giving for variable X all concept terms below c, – or

more restrictively with

← class(X) ∧ isa(X, c)

giving all applied subordinate class names.

Figure 3 illustrates derivation of the assertion al-

phacell reside-in pancreas using a monotonicity in-

ference rule.

Furthermore, the framework affords conceptual

pathﬁnding between a pair of stated terms to be an-

swered by computing shortest paths in the graph be-

tween the two terms, see further (Andreasen et al.,

2014). In the graph conception derived assertions

may act as shortcuts in the pathways. For instance,

giving the pair of terms pancreas and alphacell, the

inferred sentence forms a shortcut.

4 POSITION SUMMARY

We summarise our position as follows:

• Natural logic is like a stylized form of natural lan-

guage and thus easy to read for domain experts.

• Predicate logic is ”unreadable” and complex for

practical reasoning tasks.

• Natural logic possesses intuitive reasoning rules.

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• Description logics is ”unnatural” from a knowl-

edge engineering point of view by enforcing cop-

ula form (c

ISA c

) As an alternative to our natu-

ral logic approach, (de Azevedo, 2014) generates

internal description logic representations.

• We wish to distinguish deﬁnitional (analytic) and

empirical (synthetic) facts.

• We prefer CWA in favour of classical negation

e.g. for class disjointness.

• Our natural logic comes with a semantic graph

form facilitating computational pathﬁnding and

intensional querying.

5 CONCLUDING REMARKS

We have advocated use of natural logic embedded in

clausal logic for ontology structured knowledge bases

as an alternative to the prevailing use of description

logic dialects and derivatives. Our approach differs

from description logic approaches primarily in that

it recognizes and supports the role of the main verb

in knowledge base assertions. Moreover, the two

level set-up affords an intensional view in which class

terms appear in query answers.

We are in the process of building a prototype sys-

tem as a test bed for domain speciﬁcations within

selected bio- and medico-domains for ascertaining

whether this is a viable approach meeting the desider-

ata in the introduction. The DATALOG level in a scal-

ing up of the prototype may readily be realized by

appealing to state-of-the-art relational database tech-

nology offering efﬁcient access to massive data.

An open issue in knowledge bases is the handling

of denials. The use of CWA seems appealing since it

departures with classes being born disjoint in accor-

dance with scientiﬁc practice in classiﬁcation. More-

over, it opens for means of dealing with exceptions in

the non-monotonic fashion.

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