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<article xmlns:xlink="http://www.w3.org/1999/xlink">
  <front>
    <journal-meta>
      <journal-title-group>
        <journal-title>ASPOCP</journal-title>
      </journal-title-group>
    </journal-meta>
    <article-meta>
      <title-group>
        <article-title>Semantically Guided Scene Generation via Contextual Reasoning and Algebraic Measures</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Loris Bozzato</string-name>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Thomas Eiter</string-name>
          <xref ref-type="aff" rid="aff2">2</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Rafael Kiesel</string-name>
          <xref ref-type="aff" rid="aff2">2</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Daria Stepanova</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>Bosch Center for Artificial Intelligence</institution>
          ,
          <addr-line>Renningen</addr-line>
          ,
          <country country="DE">Germany</country>
        </aff>
        <aff id="aff1">
          <label>1</label>
          <institution>Fondazione Bruno Kessler</institution>
          ,
          <addr-line>Via Sommarive 18, 38123 Trento</addr-line>
          ,
          <country country="IT">Italy</country>
        </aff>
        <aff id="aff2">
          <label>2</label>
          <institution>Institute of Logic and Computation, Technische Universität Wien</institution>
          ,
          <addr-line>Favoritenstraße 9-11, A-1040 Vienna</addr-line>
          ,
          <country country="AT">Austria</country>
        </aff>
      </contrib-group>
      <pub-date>
        <year>2023</year>
      </pub-date>
      <volume>16</volume>
      <fpage>0000</fpage>
      <lpage>0003</lpage>
      <abstract>
        <p>We recently presented the MR-CKR framework to reason with knowledge overriding across contexts organized in multi-relational hierarchies. Reasoning is realized via ASP with Algebraic Measures, allowing for flexible definitions of preferences. In this paper, we show how to apply our theoretical work to autonomous-vehicle scene data: we apply MR-CKR to the problem of generating challenging scenes for autonomous vehicle learning. In practice, most of the scene data for AV learning models common situations, thus it might be dificult to capture cases where a particular situation occurs (e.g. partial occlusions of a crossing pedestrian). The MR-CKR model allows for data organization exploiting the multi-dimensionality of such data (e.g., temporal and spatial dimension). Reasoning over multiple contexts enables the verification and configuration of scenes, using the combination of diferent scene ontologies. We describe a framework for semantically guided data generation, based on a combination of MR-CKR and algebraic measures. The framework is implemented in a proof-of-concept prototype exemplifying some cases of scene generation.</p>
      </abstract>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>1. Introduction</title>
      <p>Testing and evaluation are important steps in the development and deployment of Automated
Vehicles (AVs). To comprehensively evaluate the performance of AVs, it is crucial to test the
AVs’ perception systems in safety-critical scenarios, which rarely happen in naturalistic driving
environment, but still possible in practice. Therefore, the targeted and systematic generation of
such corner cases becomes an important problem.</p>
      <p>
        Most existing studies focus on generating adversarial examples for perception systems of
AVs which are concerned with very simple perturbations in the input (e.g., changing the
color or position of a vehicle). More in general, the generation of adversarial or challenging
examples for neural models is an important problem that gained interest both in industry1
and research [
        <xref ref-type="bibr" rid="ref1 ref2 ref3 ref4">1, 2, 3, 4</xref>
        ]. Generation of inputs is mostly performed by numerical methods.
For example, [
        <xref ref-type="bibr" rid="ref1">1</xref>
        ] uses small numerical perturbations of images, [
        <xref ref-type="bibr" rid="ref2">2</xref>
        ] uses an optimization that
minimizes the numerical change of the input data such that it leads to a diferent prediction of
the network, and [
        <xref ref-type="bibr" rid="ref4">4</xref>
        ] generates adversarial text for natural language processing by performing
minimal replacements of characters.
      </p>
      <p>
        On the other hand, limited eforts have been put on the symbolic generation of complex scenes:
this is the problem we want to consider in this paper, in particular aiming at an ontology-based
and context-specific scene generation (e.g., child walking a dog in the evening in rainy weather).
Specifically, we define our task of interest as follows: given an existing scene (represented by a
scene graph) from a known dataset, we want to generate a new set of scenes that are variations
of the current scene and are:
1. Realistic: consistent with the ontologies describing objects in the scene (e.g., trafic signs
usually do not move);
2. Interesting: they satisfy a semantic restriction, which tells us that the scene is for example,
“dangerous” or challenging for our prediction model (e.g., seeing a cat in the middle of the
street requires special action);
3. Similar: changing the original scene to the generated scenes requires only small variations.
We propose to use symbolic methods to generate valid and challenging scenes on the base
of existing scene graphs and semantic definitions of scenes. In particular, Multi-Relational
Contextualized Knowledge Bases (MR-CKRs) [
        <xref ref-type="bibr" rid="ref5 ref6">5, 6</xref>
        ] are a useful formalism for this: here, ontological
knowledge is contextualized such that in diferent contexts it may have diferent interpretations
(possibly with non-monotonic efects). Thus, MR-CKRs can help us in generating realistic
scenes, since they are capable of handling the background ontologies describing the AV domain.
Additionally, we may have diferent contextualized notions of interestingness. E.g., it may be
that a dog is by default not considered dangerous but in a special context, next to a crowded
street, it is. MR-CKRs also allow us to express this by associating diferent independent semantic
restrictions on scenes within diferent contexts. Another benefit of MR-CKRs is that they come
with a translation to Answer Set Programming (ASP), which can be used to easily express and
eficiently solve hard logical problems.
      </p>
      <p>
        Additionally, we need a way to measure how similar the generated scenes are to the original
scene that we started from: Algebraic Measures [
        <xref ref-type="bibr" rid="ref7">7</xref>
        ] are of great use here. They are a general
framework from the field of ASP that allows us to measure quantities associated with solutions.
As such, they are also capable of expressing a similarity measure of scenes, which we need.
      </p>
      <p>Our main contributions can be summarized as follows:
– We provide a novel framework for semantically guided data generation, which can be
adversarial or training data. An overview of the framework is presented in Section 2. By basing
our framework on a combination of MR-CKRs and Algebraic Measures we obtain a highly
lfexible approach with eficient solving options by employing translations to ASP.
– MR-CKRs allow us (i) to incorporate ontological background knowledge ensuring realism
of the generated data and (ii) to contextualize the notion of what makes a generated input
interesting. The MR-CKR formalism and its use are presented in Section 3.</p>
      <p>MR-CKR</p>
      <sec id="sec-1-1">
        <title>Base Ontology</title>
      </sec>
      <sec id="sec-1-2">
        <title>Possible Scene Modification c1 c2</title>
      </sec>
      <sec id="sec-1-3">
        <title>Diagnosis 1</title>
      </sec>
      <sec id="sec-1-4">
        <title>Diagnosis 2 ASP</title>
      </sec>
      <sec id="sec-1-5">
        <title>Additional ASP Constraints</title>
      </sec>
      <sec id="sec-1-6">
        <title>Weak Constraints:</title>
      </sec>
      <sec id="sec-1-7">
        <title>Similarity Preference</title>
      </sec>
      <sec id="sec-1-8">
        <title>Strong Constraints:</title>
      </sec>
      <sec id="sec-1-9">
        <title>Diagnosis Presence</title>
        <p>– Algebraic Measures enable the maximization of similarity between original and generated data.</p>
        <p>The definition of similarity by Algebraic Measures and its realization via weak constraints is
presented in Section 4.
– We provide a proof of concept implementation of our framework in ASP. Our prototype
(presented in Section 5) for scene generation in the domain of AV is intentionally kept minimal
but shows promise.</p>
      </sec>
    </sec>
    <sec id="sec-2">
      <title>2. Framework Overview</title>
      <p>Before we go into the technical details of how we generate descriptions of new challenging
training scenes, we provide a general structural overview of our framework.</p>
      <p>The architecture of our framework is described in Figure 1. The schema shows that we
use an MR-CKR to define, on the one hand, the possible scene modifications and on the other
hand diferent contexts, here 1 and 2, that specify possibilities for a scene to be challenging
respectively interesting. Ideally, these diferent diagnoses correspond to insights of a neural
network engineer for poor performance of the current neural network. For example, in the AV
context, we might observe that a car does not stop in the correct location when there is not
only a stop sign but also a stop line marking that specifies where the car should stop. Here, we
would therefore want to modify scenes in such a manner that they have both a stop sign and a
stop line marking.</p>
      <p>In general, the goal is to generate more scenes that we suspect the network also performs
badly on, such that we have adversarial examples that we can use to train the neural network
in the hope of improving its performance on these situations that are presumably hard for it,
due to a lack of training data. Given the diagnoses in diferent contexts that may be related via
specialization or otherwise, we can then use the ASP translation of an MR-CKR to obtain an
equivalent ASP encoding to compute models, i.e., representations of generated scenes that are
realistic according to the base ontology included in the MR-CKR.</p>
      <p>Moreover, we add further ASP constraints to ensure that the modifications of the scene make
the resulting scene (a) challenging, i.e., it satisfies a diagnosis (using strong constraints) and (b)
close to a given starting scene (using weak constraints that express the algebraic measure).</p>
      <p>With such combination, we can thus obtain realistic, challenging scenes that are as similar to
the starting scene as possible. On top of that, the diferent contexts allow us to specify diferent
types of target diagnoses resulting in one generated scene that includes it per context.</p>
      <p>In the following, we substantiate our abstract idea by formalizing how we generate scenes
with MR-CKR and measure their similarity with Algebraic Measures.</p>
    </sec>
    <sec id="sec-3">
      <title>3. Formalization of the Scene Generation Problem in MR-CKR</title>
      <p>We begin by briefly introducing the MR-CKR framework and then provide a solution for the
scene generation task making use of MR-CKR.</p>
      <sec id="sec-3-1">
        <title>3.1. MR-CKR: Multi-relational Contextualized Knowledge Bases</title>
        <p>
          We summarize in this subsection the main definitions of the MR-CKR formalism from [
          <xref ref-type="bibr" rid="ref6">6</xref>
          ].
        </p>
        <p>
          We assume the customary definitions for description logics (see, e.g., [
          <xref ref-type="bibr" rid="ref8">8</xref>
          ]), where we consider
a generic description logic language ℒΣ based on a DL signature Σ, which is composed of a set
of concept names NC, role names NR and individual names NI.
        </p>
        <p>
          The contextual structure of a MR-CKR is defined by a nonempty set N ⊆ NI of context names
and a set ℛ of one or more contextual relations ≺  over them, which are strict (partial) orders
≺  ⊆ N × N. A way to define contextual relations is to use contextual dimensions [
          <xref ref-type="bibr" rid="ref10 ref9">9, 10</xref>
          ], that
is a set of contextual “coordinates” associated to each of the contexts: in the case of scene
descriptions, for example, these can represent the time of the day, location type or situation
occurring in a scene.
        </p>
        <p>With each context of N, we associate a contextual language ℒΣ,N as an extension of ℒΣ
representing its local language; in particular, axioms inside contexts can be specified as defeasible
(i.e., they can be overridden in case of exceptions) with respect to one of the contextual relations
composing the contextual structure. Formally, an r-defeasible axiom is any expression of the
form D( ), where  is an axiom of ℒΣ and ≺ ∈ ℛ. Multi-relational CKRs are then composed
by a global structure of context based on the contextual relations in ℛ and a set of DL knowledge
bases associated to each of the local contexts.</p>
        <p>Definition 1 (multi-relational simple CKR). A multi-relational simple CKR (sCKR) over Σ
and N is a structure K = ⟨C, KN⟩ where: (i). C is a structure (N, ≺ 1, . . . , ≺ ) where each ≺ 
is a contextual relation over N; (ii). KN = {Kc}c∈N for each context name c ∈ N, Kc is a DL
knowledge base over ℒΣ,N.</p>
        <p>Example 1. We provide a simple example of MR-CKR to better explain the intended use of
defeasible axioms. Consider the sCKR K = ⟨C, {K1, K2}⟩ composed of the following elements:</p>
        <p>C =
K1 =
{c2 ≺  c1},
{D(Dog ⊑ ¬DangerousAnimal )},
{Dog ⊑ DangerousAnimal , Dog (d )}.</p>
        <p>Intuitively, we want to ensure that in the more specific context c2, dogs are viewed as dangerous
animals, thus the more general defeasible axiom in c1 is not applied to the instance  of Dog .
Interpretations of MR-CKRs I = {ℐ(c)}c∈N are families of DL interpretations associated to
each of the contexts that agree on the interpretation of individuals. Given an axiom  ∈ ℒΣ
with FO-translation ∀x. (x), we say that the instantiation of  with a tuple e of individuals in
NI, written  (e), is the specialization of  to e, i.e.,  (e), depending on the type of  . Given a
relation ⪰ , we denote with ⪰ −  any other relation in ℛ diferent from ⪰ .</p>
        <p>A clashing assumption for a context c and relation  is a pair ⟨, e⟩ such that  (e) is an
axiom instantiation of  , and c′ ⪰ −  c′′ ≻  c. A clashing set for ⟨, e⟩ is a satisfiable set  of
ABox assertions s.t.  ∪ { (e)} is unsatisfiable. Intuitively, clashing assumptions represent
the assumption that e are exceptional individuals of  , clashing sets provide a justification of
such exceptionality. We extend interpretations with clashing assumptions in what we call
CASinterpretations: a CAS-interpretation is a structure ICAS = ⟨I,  ⟩ where I is an interpretation
and  = { 1, . . . ,  } such that each  , for  ∈ {1, . . . , }, maps every c ∈ N to a set  (c)
of clashing assumptions for context c and relation ≺ .</p>
        <p>We say that a CAS-interpretation ICAS = ⟨I,  ⟩ is a CAS-model for K (denoted ICAS |= K),
if it verifies all strict and defeasible axioms of K, i.e., informally: (i) ℐ(c′) |=  for every strict
axiom  in a context c with c′ ⪯ * c; (ii) ℐ(c′) |=  for every -defeasible axiom D( ) in a
context c related by a non- relation, that is c′ ⪯ −  c; (iii) ℐ(c′′) |=  (d) for every -defeasible
axiom D( ) in a context c with c′′ ≺  c′ ⪯ −  c and d not exceptional, that is ⟨, d⟩ ∈/  (c′′).</p>
        <p>We say that ⟨, e⟩ ∈  (c) is justified for a CAS model ICAS , if some clashing set ⟨, e⟩,c
exists such that ℐ′(c) |=  , e⟩,c (and for all I′CAS agreeing on the interpretation of individuals).</p>
        <p>⟨
A CAS model ICAS of a sCKR K is justified , if every ⟨, e⟩ ∈  is justified in K.</p>
        <p>We provide a local preference on clashing assumption sets for each of the relations:
(LP).  1 (c) &gt;  2 (c), if for every ⟨ 1, e⟩ ∈  1 (c) ∖  2 (c) with D( 1) at a context c1 ⪰ − 
c1 ≻  c, some ⟨ 2, f ⟩ ∈  2 (c) ∖  1 (c) exists with D( 2) at context c2 ⪰ −  c2 ≻  c s.t.
c1 ≻  c2.</p>
        <p>Intuitively,  1 (c) is preferred to  2 (c) if  1 (c) exchanges the “more costly” exceptions of  2 (c)
at more specialized contexts with “cheaper” ones at more general contexts. A model preference
is obtained by combining the preferences of the relations: it is a global lexicographical ordering
on models where each ≺  defines the ordering at the -th position.
(MP). I1CAS = ⟨I1,  11, . . . ,  1⟩ is preferred to I2CAS = ⟨I2,  21, . . . ,  2⟩ if:
(i) there exists  ∈ {1, . . . , } and some c ∈ N s.t.  1 (c) &gt;  2 (c) and not  2 (c) &gt;  1 (c),
and for no context c′ ̸= c ∈ N it holds that  1 (c′) &lt;  2 (c′) and not  2 (c′) &lt;  1 (c′).
(ii) for every  &lt;  ∈ {1, . . . , }, it holds  1 ≈  2 (i.e., (i) or its converse do not hold for
≺  ).</p>
        <p>
          Finally, we say that an interpretation I is a CKR model of K (in symbols, I |= K) if: (i) K has
some justified CAS model ICAS ; (ii) there exists no justified I′CAS that is preferred to ICAS .
Example 2. Using the semantics mechanism from above, we can show how to interpret the
sCKR in the previous example. We can consider the CAS-interpretation ICAS = ⟨I,  ⟩ where
 (c2) = {⟨Dog ⊑ ¬DangerousAnimal , ⟩}. This implies that ICAS is a CAS-model if the
defeasible axiom of c1 is not applied to the only Dog in c2, as expected. Note that such CAS-model is also
justified, since the clashing assumption admits the clashing set {Dog (), DangerousAnimal ()}:
thus, considering that no other alternative CAS-model that is minimal with respect to the
preference can be defined, the considered interpretation is also a CKR-model. The preference
deifned above is useful to prefer defeasible axioms in the most specific contexts: for example, if
Dog ⊑ DangerousAnimal in c2 was defined as defeasible (w.r.t. the same contextual relation of
the above defeasible axiom), the context below c2 would have preferred the more specific axiom.
As a method to implement reasoning on MR-CKRs, we provided in [
          <xref ref-type="bibr" rid="ref6">6</xref>
          ] a translation for
MRCKRs to ASP logic programs, which can be used to reason on instance checking and query
answering in a given context. It is based on a uniform encoding of DL knowledge bases
using a materialization calculus, which is extended for defeasible axioms. To give a flavor of
the translation, the following rules define the conditions for application and overriding of a
defeasible inclusion like 1( ⊑  ):
instd(X,F,C,T) :- def_subClass(E,F,C1,REL1), instd(X,E,C,T),
prec(C,C2, REL1), preceq(C2,C1, REL2), REL1 != REL2,
not ovr(subClass,X,E,F,C1,C,REL1).
ovr(subClass,X,E,F,C1,C,REL1) :- def_subClass(E,F,C1,REL1),
prec(C,C2,REL1), preceq(C2,C1,REL2),
REL1 != REL2, instd(X,E,C,"main"),
not test_fails(nlit(X,F,C)).
        </p>
        <p>
          For details and discussion, we refer to [
          <xref ref-type="bibr" rid="ref6">6</xref>
          ].
        </p>
      </sec>
      <sec id="sec-3-2">
        <title>3.2. Scene generation in MR-CKR</title>
        <p>Following the intuitive structure of Figure 1, the role of MR-CKR in our architecture is to define
the logical constraints of the scenes we want to generate, on the basis of a common scene
ontology. Given its multi-contextual structure, the MR-CKR is useful to provide (i) a complex
representation (a contextualization) of the contents of the base scene and (ii) its modifications
towards the diferent diagnoses of interest.</p>
        <p>With respect to the second aspect, the basic organization of contexts can be defined as in
Figure 2. The contexts of this structure are related by a contextual relation ≻ , denoting the
relation of similarity: the upper context Exchange contains, in form of -defeasible axioms,
the axioms that can be modified in the diagnosis scenes. In the Base context, we assume to
have the description of the base scene and the base axioms of the scene description ontology.
The contexts Diagnosis-1 , . . . , Diagnosis-N then provide the diferent modifications to the
base scene that we are interested in modeling. The kind of axioms that are needed to model the
diferent modifications depend on the kind of changes (additions, deletions, etc.) that we want
to admit in scene modifications; more details on such axioms will be provided in the following
sections, where we consider specific modifications.</p>
        <p>With respect to the scene contextualization, we can take advantage of the multi-relational
nature of MR-CKR to further define the properties of the context in which the scene takes place.</p>
        <p>Diagnosis-1</p>
        <p>Diagnosis-N</p>
        <p>Base
City-exch</p>
        <p>City-base
General-d1</p>
        <p>General-dN</p>
        <p>City-d1</p>
        <p>City-dN</p>
        <p>Town-d1</p>
        <p>Town-dN
Example 3. An example of such contextualization is shown in Figure 3. In this contextual structure,
the relation given by the horizontal arrows represents the specialization of scenes with respect to
the specificity of the location: starting from axioms that are verified for general scenes, we can
add further logical constraints that are true for city scenes and then town scenes. Note that such
direction is orthogonal to the base contextual structure described above: location-defeasible axioms
can express knowledge that is, e.g., accepted in general locations, but not valid in town scenes.
After modelling scenes by such framework, we want to use the translation of MR-CKR to ASP in
order to generate the possible models of the diagnoses contexts: these models then correspond
to alternative generated scenes. However, we now need a method to provide a measure for
the similarity of the generated scenes with respect to the scenes of interest: as we detail in the
following sections, this can be easily defined by means of algebraic measures.</p>
      </sec>
    </sec>
    <sec id="sec-4">
      <title>4. Formalization of Similarity using Algebraic Measures</title>
      <p>
        If we generate a new scene based on a starting scene, we want to optimize a measure of similarity.
Here, we use algebraic measures [
        <xref ref-type="bibr" rid="ref7">7</xref>
        ], which measure and aggregate quantities associated with
models by evaluating a formula over a semiring.
      </p>
      <p>Definition 2 (Semiring). A commutative semiring  = (, ⊕ , ⊗ , ⊕ , ⊗ ) is an algebraic
structure with binary infix operations ⊕ , ⊗ such that
1. ⊕ and ⊗ are associative and commutative,
2. ⊗ right and left distributes over ⊕ ,
3. ⊕ (resp. ⊗ ) is a neutral element for ⊕ (resp. ⊗ ), and
4. ⊕ annihilates , i.e., ∀ ∈  : ⊗ ⊕ = ⊕ = ⊕ ⊗ .</p>
      <p>
        Examples of well-known commutative semirings are
– F = (F, +, · , 0, 1), where F ∈ {N, Z, Q, R}, the semiring over the numbers in F with addition
and multiplication,
–  = ([
        <xref ref-type="bibr" rid="ref1">0, 1</xref>
        ], +, · , 0, 1), the probability semiring,
– ℛmin,+ = (R ∪ {∞}, min, +, ∞, 0), the min-plus semiring.
      </p>
      <p>
        Another list of semirings, which is annotated with applications, can be found in [
        <xref ref-type="bibr" rid="ref11">11</xref>
        ].
      </p>
      <p>
        In order to connect the quantitative aspects of semirings and the qualitative ones of logics
we use weighted logics [
        <xref ref-type="bibr" rid="ref12">12</xref>
        ].
      </p>
      <p>Definition 3 (Weighted Logic). Let  be a set of propositional variables and let ℛ = (, ⊕ , ⊗ , ⊕ , ⊗ )
be a semiring. A weighted (propositional) formula over ℛ is of the form  given by the grammar
 ::=  |  | ¬ |  +  |  * 
where  ∈  and  ∈ . The value J Kℛ(ℐ) of  w.r.t. an interpretation ℐ ⊆  is defined as:
JKℛ(ℐ) = 
JKℛ(ℐ) = ︂{ ⊕⊗
︂{ ⊕</p>
      <p>⊗
J¬Kℛ(ℐ) =</p>
      <p>∈ ℐ
otherwise.</p>
      <p>∈ ℐ
otherwise.</p>
      <p>( ∈ )
( ∈ )
J 1 +  2Kℛ(ℐ) = J 1Kℛ(ℐ)⊕ J 2Kℛ(ℐ)</p>
      <p>J 1 *  2Kℛ(ℐ) = J 1Kℛ(ℐ)⊗ J 2Kℛ(ℐ).</p>
      <p>Algebraic measures combine the qualitative language of ASP with the quantitative one of
weighted logic.</p>
      <p>Definition 4 (Algebraic Measure). An algebraic measure  = ⟨Π, , ℛ⟩ consists of an answer
set program Π, a weighted formula  , and a semiring ℛ. Then, the weight of an answer set
ℐ ∈ (Π) under  is defined by
 (ℐ) =</p>
      <p>J Kℛ(ℐ).</p>
      <p>
        Intuitively, Π determines the solutions and  assigns them weights. Algebraic measures ofer
further queries that aggregate the weights of (some) solutions [
        <xref ref-type="bibr" rid="ref7">7</xref>
        ] that we however do not
require here.
      </p>
      <sec id="sec-4-1">
        <title>4.1. Similarity of Scenes</title>
        <p>We measure the similarity of two scenes as the minimum cost required to modify one scene to
be equal to another one. There are many ways to modify a scene. For simplicity, we restrict
ourselves to deletion of object  from class  and addition of object  to class , denoted deletion(, )
and addition(, ), with fixed costs 2 cost() and cost() respectively. Advanced options
would be class variation, displacement, or property variation.</p>
        <p>We use the weighted formula  
Πclass ,individual (addition(, ) * cost() + ¬addition(, ))
* Πclass ,individual (deletion(, ) * cost() + ¬deletion(, ))
over the semiring ℛmin,+, which takes the minimum of diferent options and sums up the costs
of atomic modifications in one option.</p>
        <p>Example 4. For example, consider the interpretation</p>
        <p>ℐ = {addition(RollingContainer , 1), deletion(Child , 2), deletion(Child , 3)}.
Intuitively, this means that we add the object 1 to the concept RollingContainer and remove the
objects 2 and 3 from the concept Child . Thus, we expect a cost of cost() + 2 · cost().</p>
        <p>Since the interpretation ℐ contains addition(RollingContainer , 1) the first row of  
evaluates to cost() and the second row evaluates to cost()⊗ cost(). Since we use ℛmin,+
the operation ⊗ is + and we obtain cost() + 2 · cost() as the final cost, as expected.</p>
        <p>
          While algebraic measures are a useful and highly general tool, to specify quantitative measures
for the answer sets of logic programs, most solvers for ASP currently do not support optimization
of the weight of an algebraic measure. However, algebraic measures over the semiring ℛmin,+
can be translated to weak constraints [
          <xref ref-type="bibr" rid="ref13">13</xref>
          ].
        </p>
        <p>Since we intentionally kept the measure simple, it is suficient to use the weak constraints
:∼
addition(,  ).[cost(), , ,  ]
:∼
deletion(,  ).[cost(), , ,  ]
which add a cost of cost() for each individual  and concept  such that we add  to
concept  (and anologously for deletion). In general, this is not as simple since measures can
specify complex algebraic expression, which is why we prefer the specifiation via measures.</p>
      </sec>
    </sec>
    <sec id="sec-5">
      <title>5. Implementation Prototype for Scene Generation in</title>
    </sec>
    <sec id="sec-6">
      <title>Autonomous Driving</title>
      <p>We have implemented and tested our approach using an example from Autonomous Driving.3
Here, we reconstructed and slightly extended the base ontology from [14, 15].4 It features
2i.e., costs do not depend on the class or individual.
3https://github.com/raki123/MR-CKR
4https://github.com/boschresearch/ad_cskg</p>
      <p>D(  ⊑  )
D(  ⊑  )
( ⊓   ) ⊔  ⊑</p>
      <p>D(  ⊑   )</p>
      <p>D(  ⊑   )
ℎ

ℎ</p>
      <p>⊓   ⊑ ⊥
 ⊓   ⊑ ⊥
:∼ instd(X, ,Context,"main"). [1,X, ,Context]
:∼ instd(X, ,Context,"main"). [1,X, ,Context]
diferent scenes, each annotated with the objects included in it. The included objects are
annotated with information about them, such as their type. Furthermore, the ontology includes
axioms that add knowledge about the relationship between diferent concepts in the ontology.
Overall, the base ontology has more than 3 million axioms, concerning knowledge of 41 concepts,
more than 100 scenes, and more than 50,000 objects.</p>
      <p>We provide an overall sketch of the construction of the MR-CKR and its interplay with ASP
constraints in Figure 4. We go over the diferent parts step by step.</p>
      <p>MR-CKR Encoding. Here, we describe how scenes can be modified (annoted via solid black
boxes in Figure 4). Namely, we state that every named object should either be added or not added
(resp. deleted) to each modifiable concept. Additionally, we ensure that the modification takes
efect by stating that a concept contains exactly those objects (i) which it originally contained
before modification and that were not deleted, or (ii) that were added.</p>
      <p>
        Apart from that, the MR-CKR contains the axioms from the base ontology and one context
 for each diagnosis . We use the following diagnoses:
1. ℎ: the scene contains an object that is in the class ℎ. It is dangerous due to
unpredictable behaviour compared to other humans.
2. : the scene contains an object that is in the class  but no object in
the class  . It is dangerous due to unpredictable behaviour of the rolling container.
We then translate the resulting encoding to ASP using the CKRew software5 from [
        <xref ref-type="bibr" rid="ref6">6</xref>
        ].
Additional ASP Constraints. To ensure that in context  the diagnosis  is derived, we add
strong constraints (annoted via solid gray boxes in Figure 4). For example, for the first diagnosis
in context 1, we ensure the presence of a child using the rules
      </p>
      <p>To ensure similarity, we add weak constraints (annoted via the dashed gray box in Figure 4).
This ensures that a penalty of 1 is added every time we add or delete an individual  to .
Note that the penalty is applied for every context.</p>
      <p>The ASP translation of the MR-CKR and the additional constraints constitute the encoding of
the problem in ASP. To obtain solutions, we then used a standard ASP solver, namely clingo [16].
Example 5. Assume our input scene contains four objects 1, . . . , 4 and Child (i2 ), Child (i3 ),
Car (i4 ) hold. Due to the ontology axiom Child ⊑ Human, we could derive Human(i2 ) and
Human(i3 ).</p>
      <p>Thus, in context 2, where we need a rolling container but no human, we need to remove 2 and
3 from the Child concept and add an object to the RollingContainer concept. Thus, a potential
modification (restricted to context 3) is represented by the interpretation
ℐ = {instd(1, , 3, “”), instd(2, ℎ, 3“”),
instd(3, ℎ, 3, “”)}.</p>
      <p>As discussed in the previous example, it has cost cost() + 2 · cost(), which is 3 since we
assign cost 1 to addition and deletion respectively.</p>
      <p>As there is no modification of a lower cost, one of the possible generated scenes for 3 consists of
(1), (4), i.e., it contains a rolling container 1, no humans, but a car 4.</p>
      <p>On the other hand, in the context 1 we do not need to perform any modifications, since the
original scene already contains a child.</p>
      <sec id="sec-6-1">
        <title>5.1. Specialized Translation</title>
        <p>The original MR-CKR to ASP translation is capable of handling highly complex relations
between contexts and supports arbitrary defaults and flexible ontological background knowledge.
However, this comes at the cost of an encoding in ASP that is not suitable for our purposes,
using large scene graphs with many contexts and concepts.</p>
        <p>To circumvent this, we specialized the encoding to our setting. Recall that the (defeasible)
axioms of the MR-CKR (see Figure 4, annoted in green) tell us that we guess either the addition
or the non-addition of any named individual  to , as long as there is no other reason in the
ontology that prevents both. As our base ontology is consistent, there can never be a reason in
our ontology that prevents the non-addition. Hence the either-or really holds in our setting.</p>
        <p>This allows us to use the following rules to encode the (defeasible) axioms above:
instd(X, ,Con,"main") :- instd(X,"Named",Con,"main"),
not instd(X,  ,Con,"main").
instd(X,  ,Con,"main") :- instd(X,"Named",Con,"main"),
not instd(X, ,Con,"main").</p>
        <p>Clearly, the same can be done for deletion and non-deletion.</p>
        <p>This specialized translation for our setting leads to a significant performance improvement.
While the original encoding only allows us to generate new scenes using tiny starting scenes, the
improved strategy allows inference of the real world scenes from the ontology within seconds.
100
s
cond 80
e
isn 60
e
itnm40
u
r
20
0</p>
        <p>1</p>
      </sec>
      <sec id="sec-6-2">
        <title>5.2. Scalability</title>
        <p>We briefly investigate how large the instances that we can solve can become, while maintaining
a low runtime. Here, we compare the original translation, denoted General, and the specialized
one, denoted Specialized.</p>
        <p>Secondly, we investigate how much the solving time depends on (i) the number of objects in
the scene and (ii) the number of contexts. We vary (i) between 1 and 20 and (ii) between 1 and 5
on a randomly chosen example scene from the ontology.</p>
        <p>Here, we use clingo [16] on the generated programs with input option “-t 3” to specify that
three threads in parallel should be used to solve the problem. We apply a time limit of 120
seconds and assign runs that do not finish during this time a runtime of 120 seconds.</p>
        <p>The results of our investigation are given in Figure 5. We see that even if only one context
is used, the runtime after General grows quickly. While it still remains in a feasible range
when using one context and up to 20 objects in the scene, the same cannot be said when more
contexts are used. For five contexts, solving already becomes slow when ten or more objects
are included in the scene. Additionally, the original scene has many more objects (more than
300), thus, this translation can only be employed to restricted examples, even if there is only
one context.</p>
        <p>On the other hand, for Specialized we see that the solving time is consistently far below one
second, even when using all five contexts and 20 objects in the scene. Note here the diferent
limits of the Y-axis, which we adapted to make the runtimes visible. Even using the full scene,
which constitutes a realistic industry size example (including more than 300 objects) the solving
time remains at around 0.67 seconds. We observed a similar efect in the grounding size, which
went to around 80 thousand rules and did not finish with more than half a million rules already
produced for the specialized and general encoding, respectively.</p>
        <p>We see that while the original translation General is able to handle a broader range of
MRCKRs, it pays of to use the specialized translation Specialized in our setting. With Specialized
we can generate new scenes in subsecond times, even if the full scene (i.e., all its objects) and
all contexts are used. This suggests that with Specialized we can also generate new inputs for
more complex semantic conditions and base ontologies than the ones provided in our prototype,
giving us interesting opportunities to extend our work in the future.</p>
      </sec>
    </sec>
    <sec id="sec-7">
      <title>6. Conclusion</title>
      <p>We have introduced a new framework to generate new interesting inputs for neural models
based on existing ones, in particular the setting of scene generation for AV scene data. Notably,
our framework does so based on symbolic reasoning methods. This allows us, on the one hand,
to incorporate real world knowledge (in the form of contextual knowledge) that ensures that
the generated inputs are realistic, and, on the other hand, to formulate a semantic criterion that
should be satisfied by the new input. We saw that all components that we incorporated in our
framework add their respective benefits:
– MR-CKR allows us (i) to incorporate ontological knowledge easily and (ii) to perform
diferent modifications in diferent contexts.
– Algebraic Measures allow us to easily specify a cost value to optimize.
– ASP, as a declarative backend programming language, allows us to perform reasoning/scene
generation eficiently using standard solvers.</p>
      <p>While we only considered a small example in our prototype, it successfully generates new scene
descriptions. Furthermore, as it can be easily generalized to the generation of diferent types of
scenes, it provides a proof of concept of our approach.</p>
      <p>In future work, it will be interesting to extend this example with more complicated semantic
descriptions of interesting scenes gathered by inspecting poor performing inputs for a prediction
task with a neural model: in particular, it would be interesting to use more complex contextual
structures to represent diferent variations of the scenes, but also use inputs performances to
give a quantification of the more interesting cases to be generated. Another open challenge
is to use the symbolic description of the new scene to generate images that can be fed to the
neural model and assess how much training with these new examples improves the network
performance.</p>
      <p>Acknowledgments. We would like to thank Michael Pfeifer, Nicole Finnie, Grace Hua and
Jan-Hendrik Metzen from Bosch Center for AI for interesting discussions on the topic of scene
generation. This work was partially supported by the European Commission funded projects
“Humane AI: Toward AI Systems That Augment and Empower Humans by Understanding
Us, our Society and the World Around Us” (grant #820437) and “AI4EU: A European AI on
Demand Platform and Ecosystem” (grant #825619), and the Austrian Science Fund (FWF) project
W1255-N23. The support is gratefully acknowledged.
Proceedings, volume 1265 of Lecture Notes in Computer Science, Springer, 1997, pp. 2–17.</p>
      <p>URL: https://doi.org/10.1007/3-540-63255-7_2. doi:10.1007/3-540-63255-7∖_2.
[14] S. N. Chowdhury, R. Wickramarachchi, M. H. Gad-Elrab, D. Stepanova, C. A.
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[15] R. Wickramarachchi, C. Henson, A. Sheth, Knowledge-infused learning for entity
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[16] M. Gebser, R. Kaminski, B. Kaufmann, T. Schaub, Clingo = ASP + control: Preliminary
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