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  <front>
    <journal-meta />
    <article-meta>
      <title-group>
        <article-title>The GraphBRAIN Knowledge Graph Framework for XAI through Multistrategy Reasoning</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Stefano Ferilli</string-name>
          <email>stefano.ferilli@uniba.it</email>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Eleonora Bernasconi</string-name>
          <email>eleonora.bernasconi@uniba.it</email>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Domenico Redavid</string-name>
          <email>domenico.redavid1@uniba.it</email>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>University of Bari</institution>
          ,
          <addr-line>Bari</addr-line>
          ,
          <country country="IT">Italy</country>
        </aff>
      </contrib-group>
      <pub-date>
        <year>2026</year>
      </pub-date>
      <abstract>
        <p>As long as Artificial Intelligence is pervading all aspects of our lives, it is becoming instrumental also for crucial aspects, impacting directly our existence and well-being. This means that some of its decisions must be checked and validated, which in turn requires them to be explainable. The explainable-by-design approach in Artificial Intelligence is the symbolic one, based on formal logics. It applies human-like automated reasoning and relies on suitable knowledge representations. The most widely known and adopted knowledge representation approach nowadays comes from the Semantic Web community, but due to its peculiarities it has some limitations and shortcomings. In this paper we propose an alternate framework that significantly expands the range of applicable automated reasoning strategies.</p>
      </abstract>
      <kwd-group>
        <kwd>eol&gt;Knowledge Graphs</kwd>
        <kwd>Semantic Web</kwd>
        <kwd>Multistrategy Reasoning</kwd>
        <kwd>Labeled Property Graphs</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>-</title>
      <p>
        AI approaches can be distinguished into sub-symbolic ones [
        <xref ref-type="bibr" rid="ref3">3</xref>
        ], based on numbers for representation
and on mathematical-statistical tools for processing, and symbolic ones [
        <xref ref-type="bibr" rid="ref4">4</xref>
        ], based on explicit concepts
and on formal logic-based tools for processing [
        <xref ref-type="bibr" rid="ref5">5</xref>
        ]. The former simulate the brain; they are eficient, fit
for reproducing perception or intuition, and Kahneman’s ‘fast thinking’ [
        <xref ref-type="bibr" rid="ref6">6</xref>
        ]. The latter simulate human
mind; they are quite efective, fit for reproducing reasoning, and ‘slow thinking’ (in terms of Kahneman’s
theory). The pros and cons of these two approaches are clearly complementary [
        <xref ref-type="bibr" rid="ref7">7</xref>
        ], and in humans they
harmoniously cooperate to support the everyday behavior of single agents and of multi-agent systems.
While the latter approach is explainable by design (i.e., its outcomes are inherently explainable), being
based on a close reproduction of the conscious mechanisms in humans, the kind of AI that is nowadays
becoming pervasive belongs to the sub-symbolic type, which is inherently non-explainable. Even worse,
the complexity of the systems in wide adoption today is such that they can also barely be considered
transparent. Due to the need for explainability, which in some countries is required by law for some
applications (e.g., the AI Act in the EU [
        <xref ref-type="bibr" rid="ref8">8</xref>
        ]), much efort is being spent in research on such systems to
make them explainable. However, our position is that, unfortunately, research in eXplainable Artificial
Intelligence (XAI) [
        <xref ref-type="bibr" rid="ref10 ref9">9, 10</xref>
        ] is mostly proposing approaches that are just interpretable, not explainable. A
true explainability should be obtained by a cooperation of the two approaches, just like it happens in
humans: after perception happens from the outside world, and intuition immediately takes place, a
process of rationalization and reasoning allows us to compensate for the biases and errors of intuition,
and to get to a more conscious and controlled, possibly even shared, understanding and decision. Again,
attempts in this direction (e.g., NeSy, the stream of research aimed at joining Neural with Symbolic
approahes [
        <xref ref-type="bibr" rid="ref11">11</xref>
        ]) are often flawed: instead of striving for a true cooperation, they tend to overcharge the
neural part so that it can also carry out something that can resemble reasoning. On the contrary, we
strongly believe that a true cooperation must take place, and in this paper we propose a framework for
Knowledge Representation and Reasoning (KRR) and associated tools.
      </p>
      <p>Knowledge is the complex inter-relation of information items, where an information is an interpreted
datum. By definition knowledge is explicit, so that it can be shared and communicated among diferent
subjects. This was the basis of all human growth so far, and the way in which reliable theories were
recognized, validated and adopted, by reaching consensus and superseding wrong ones. The current
state-of-the-art for knowledge representation is based on the representation of knowledge bases (KBs)
as graphs so-called Knowledge Graphs (KGs). Two parts can be distinguished in the content of a KG: the
ontology and the instances. The former determines what can be described (entities, relationships and
their attributes), how it can be described (the terminology for expressing the entities, relationships and
attributes), and what properties or constraints must hold in the world that is being described; ontologies
are important because they provide meaning and context to the symbols used in the KB. The latter are
the specific objects of interest in the world that is being described, connected to the corresponding
ontological elements and described by suitable values for their attributes).</p>
      <p>
        The most widespread approach to KGs in the current research landscape is the Semantic Web (SW)
one. Born for specific purposes (allowings machines —and humans— to share data by associating them
with the very same interpretation, in order to support interoperability), it set its own standards for
representation and reasoning, now adopted in a wide range of application fields. In the SW, both the
ontology and the instances co-exist in the same graph, which is represented according to the RDF graph
model, where a graph consists of a set of triples &lt; , ,  &gt; whose constituents
are atomic (i.e., simple values). The subject and object correspond to nodes in the graph, and the
predicate corresponds to an arc. We believe that, while being a precious starting point for our work on
XAI, the SW approach and standard are not fully satisfactory, for a number of reasons, and notably:
• the RDF representation is too scattered [
        <xref ref-type="bibr" rid="ref12">12</xref>
        ]: the description of an instance in the world
corresponds to a subgraph, and it is not immediate to collect all the components of such a subgraph;
• even the representation of common knowledge items, such as attributes of relationships or the
existence of several instances of one relationship between the same pair of objects, may be
impossible or overly complex;
• the kind of reasoning that can be applied in the SW is mostly ontological (inheritance of properties,
completeness or consistency checks on the instances, etc.), leaving out the bulk of inference
strategies that humans use everyday to carry out our practical activities.
      </p>
      <p>This paper focuses on the latter limitation. Humans solve problems using combinations of inference
strategies, and our thesis is that, to be fully explainable, also the AI approaches must support a similar
behavior. To tackle this limitation, we also deal with the former one, adopting the LPG graph model.
In addition to be more compact and readable than the RDF model, it is also less coupled with SW
approaches, and thus amenable to broaden the set of inference strategies applicable to the knowledge,
and is implemented by very eficient state-of-the-art DBMS adopted by big players in the industry.</p>
      <p>In the following we will propose a framework for KRR that is aimed at overcoming these limitations,
in order to provide a more extensive and useful approach to XAI. We will discuss its representation and
reasoning strategies and formalisms, and its current implementation status and applications. Finally,
we will conclude the paper and outline future work issues.</p>
    </sec>
    <sec id="sec-2">
      <title>2. The GraphBRAIN Framework</title>
      <p>
        GraphBRAIN is a general-purpose KRR framework, and a knowledge base management system aimed
at covering all stages and tasks in the lifecycle of a KB, including knowledge acquisition, organization,
and (personalized) fruition. It adopts the Labeled Property Graph (LPG) data model, where nodes
(representing individuals) and arcs (representing relationships) may have labels (usually expressing
their type) and associated attribute-value pairs, and uses the Neo4j [
        <xref ref-type="bibr" rid="ref13">13</xref>
        ] DBMS. Neo4j is schema-less,
which ensures great flexibility but does not allow to associate a clear semantics to the graph items. For
this reason, GraphBRAIN requires its users to work according to pre-specified data schemes, expressed
in the form of ontologies. Thus, a characterizing feature of GraphBRAIN is its bringing to cooperation
a database management system for eficiently handling, mining and browsing the individuals, with an
ontology level that allows it to carry out formal reasoning on the knowledge.
      </p>
      <p>
        The ontologies are expressed in a proprietary format1, specifically tailored for LPGs [
        <xref ref-type="bibr" rid="ref14">14</xref>
        ]. It allows to
define:
• data types (whose names start with a lowercase letter), as enumerations or tree-structured
organization of values (whose names start with an uppercase letter);
• entities (whose names start with an uppercase letter);
• entity properties (e.g., being abstract, i.e. not allowing instances in the KB);
• relationships (whose names start with a lowercase letter);
• relationship properties (e.g., symmetricity, transitivity, etc.);
• entity or relationship attributes (whose names start with a lowercase letter – note that relationship
attributes are not available in RDF);
• attribute properties (e.g., being mandatory or not);
• axioms (logic formulas or constraints that must be verified by the instances in the KB).
GraphBRAIN can apply several ontologies on the same graph, describing diferent domains and
representing diferent perspectives on the same knowledge. The classes shared by diferent ontologies
allow the system to connect knowledge across domains: their individuals act as bridges, allowing
the users of a domain to reach information coming from other domains. In particular, GraphBRAIN
comes with a top-level ontology defining very general and highly reusable concepts (e.g., Person, Place;
Person.wasIn.Place; etc.). This top-level ontology plays a crucial role to interconnect the domain-specific
ontologies, ensuring an overall connected KG. Using a suitable tool, GraphBRAIN administrators may
create, build and maintain additional ontologies.
      </p>
      <p>
        Information (instances) can be fed into, or retrieved from, the KB only according to the ontologies.
Specifically, the following correspondence is established between the ontology and the LPG elements:
1Most other works tried to merge research on RDF and LPG knowledge representations, but always giving the RDF perspective
priority and predominance. GraphBRAIN was the first to push for a native LPG-oriented approach [
        <xref ref-type="bibr" rid="ref14">14</xref>
        ]. After the publication
of GraphBRAIN, other initiatives investigated the possibility of developing suitable schemas for LPGs specifically [
        <xref ref-type="bibr" rid="ref15">15</xref>
        ].
• nodes in the graph are entity instances (each node has a unique identifier, so that two nodes
carrying exactly the same information can co-exist in the graph);
• each node is labeled with the name of the most specific entity it belongs to in the ontology; it is
also labeled with all the domain names for which it is relevant;
• nodes include attribute-value maps expressing the values of the properties associated to their
entity and to all of its superclasses (by inheritance);
• arcs in the graph are relationship instances (each arc has a unique identifier as well, so that two
arcs carrying exactly the same information can co-exist in the graph);
• each arc is labeled with the name of the most specific relationship it belongs to in the ontology; it
is also labeled with all the domain names for which it is relevant;
• arcs include attribute-value maps expressing the values of the properties associated to their
relationship and to all of its generaizations (by inheritance).
      </p>
      <p>Note that graphs can only represent binary relationships through arcs. For -ary relationships ( &gt; 2),
reification is needed: the relationship is represented as an entity and its instances as nodes, and the
arguments of the original relationship are connected by arcs to the node. -ary relationships are
expressed in the ontology as relationships that, in addition to the subject and object, also have additional
attributes that are entity instances. Nodes representing reified relationships can be easily distinguished
in GraphBRAIN since they get a label with the relationship name, which starts with a lowercase letter.</p>
      <p>To make the KB self-contained, also the ontological items are described as instances in the KB, just
like for the SW. Instances may also have attachments, making GraphBRAIN a digital library, whose
content is organized according to formal ontologies, fostering interoperability with other systems. Users
may add, display, or delete attachments.</p>
      <p>In addition to basic KBMS functions, GraphBRAIN also provides its users with several advanced
functionalities they can apply to the available knowledge. Currently included functions are:
• assess relevance of nodes and arcs in the graph, and extract the most relevant ones, using Network</p>
      <p>Analysis algorithms;
• extract a portion of the graph that is relevant to some specified starting nodes, using graph
traversal algorithms;
• extract frequent patterns and associated sub-graphs, using Graph Mining algorithms;
• predict possible links between nodes;
• retrieve relevant knowledge using Information Retrieval and Extraction techniques;
• recommend relevant knowledge items;
• carry out high-level automated reasoning on the available knowledge (the main focus of this
paper, see next section);
• interact bidirectionally with SW resources;
• express into natural language the information content of a portion of the graph.
If available, a user profile can be used to personalize the results of all these algorithms. This would
ensure that each user obtains tailored information. The user profile takes the form of a set of weights,
associated to the ontological elements (entity, relationship or attribute) or to specific nodes or arcs (i.e.,
entity or relationship instances). The weights are formed and continuously updated by taking into
account both explicit preference indications by the users and implicit preferences computed on usage.</p>
      <p>As said, both ontologies and instances may be imported from, or exported to, the standard SW format
Ontology Web Language (OWL)2, in order to support their interoperability and reuse as Linked Open
Data (LOD) [16]. Still, the GraphBRAIN KG is not available in its entirety as LOD. Privacy is obtained
by associating with each ontological element a privacy attribute, which can be set to True or False.
When True, the owner of a knowledge item (an entity or relationship instance, i.e., a node or arc in the
graph) can set its privacy value to Private (visible only to its owner), Restricted (only selected users
can access it), or Public (visible to all users and publishable as open data). When Restricted, he may
specify, for each node or arc as a whole, or for its labels and attributes, which users may access it, and
the specific kinds of access allowed.</p>
      <p>Personalization and Privacy are handled in GraphBRAIN with a system of registered users. In
a collaborative spirit, users may add comments on (to provide suggestions or add information), or
approve/disapprove, each entity or relationship instance, each single attribute value thereof, and even
the ontological items. This feedback is used to assign a trust value to the users which in turn may reflect
the reliability of the knowledge they provide.</p>
      <p>GraphBRAIN comes in the form of an API, that any interested application must use. Each function
in the platform is exposed as a service by the API, and the API wraps the KG ensuring that every
interaction is controlled and compliant with the specified ontology.</p>
      <p>A general-purpose KG management interface for using the various features of GraphBRAIN was
also developed3. It includes a form-based interface that allows users to manually insert/update/remove
instances or to query the knowledge base for instances of entities and relationships: they must select
one of the available domains/schemas, and the forms are automatically generated by the system starting
from the corresponding ontologies. The knowledge base can also be fed by automatic knowledge
extraction from documents and other kinds of resources (e.g., books or the Internet). It also includes
another interface that allows users to display a portion of the graph, browse it interactively and display
detailed information about entity and relationship instances. This allows the user to continue his search
in a less structured way, by exploring the available knowledge without a predefined goal in mind, letting
the data themselves drive the search, possibly finding relevant information in a serendipitous way.</p>
    </sec>
    <sec id="sec-3">
      <title>3. Related Work: Automated Reasoning in Logic Programming</title>
      <p>Research in AI investigated many approaches to simulate the inference strategies used by humans,
proposing automated procedures that implement them, especially within the Logic Programming (LP)
framework4. This makes LP a good candidate for their integration in an overall framework. Here we
provide an overview of various inference strategies that have been investigated in connection with the
LP framework (and thus are amenable for integration), and on their implementation.
Deduction Deduction is aimed at making explicit knowledge that is only implicit in the available
knowledge, but is a strict consequence thereof. Deductive inference can be carried out using two
strategies: backward (goal-driven) or forward (data-driven) . For the backward approach, we use the
refutation procedure.</p>
      <p>If the body of clauses may contain negated literals, the resulting programs are called general logic
programs. In the backward approach, such negated literals are proved using the Negation as Failure
(NAF) rule [17], that stems from the Closed World Assumption (only what is reported in the program is
true; whatever is not reported in the program is considered as false).</p>
      <p>Abstraction Abstraction reduces the amount of information conveyed by a set of facts, called the
reference set [18]. This reduces the computational load needed to process the set of facts, provided that
the information that is relevant to the achievement of a goal is preserved. we adopt the framework
proposed in [19], where abstraction happens by means of a set of operators.</p>
      <p>Abduction Abduction is devoted to cope with missing information, by guessing unknown facts when
they are needed for a given purpose. The Abductive Logic Programming (ALP) [20, 21] framework
extends deduction by allowing to guess some ‘abducible’ facts (abductive hypotheses) that are not
stated in the available knowledge but are needed to explain given observations, provided that they
3A demo can be found at http://193.204.187.73:8088/GraphBRAIN/
4LP is a fragment of First-Order Logic based on clauses, i.e., implications of the form  ⇐ 1 ∧ · · · ∧ . Full implications
are called rules, clauses with no preconditions are called facts, and clauses with no conclusion are called goals.
are consistent with given Integrity Constraints (formulas that that must be satisfied by the abductive
hypotheses). The set of guessed facts is called an ‘explanation’. Of course, there may be many plausible
explanations for a given observation, and thus abductive explanations are not conclusive, requiring
strategies to filter and rank explanations. Among the various procedures proposed in the literature to
obtain abductive explanations for abductive logic programs, also when negated literals are used in the
body [22], we use the one proposed by [23]. We adopt Expressive ALP (EALP), an extended version of
ALP allowing a wider variety of operators, proposed in [24].</p>
      <p>Uncertain Reasoning Much research investigated how to combine logical and statistical inference,
so that the former supports high-level reasoning strategies, and the latter improves flexibility and
robustness. From an LP perspective, they resulted in the Probabilistic Logic Programming (PLP)
setting [25]. A probabilistic logic program defines a probability distribution over a set of normal logic
programs (called worlds). Diferent languages have been proposed, that difer in the way they define
the distribution. Some allow to set probabilities only on facts; some allow two alternatives only (true or
false)some ofer a more general syntax than others. We use LPADs [26].</p>
      <p>A diferent approach to uncertainty is based on an informal but quick ways of estimating the certainty
of the information they handle. We opt for the approach aimed at simulating this behavior implemented
in the famous expert system MYCIN [27], inspired by fuzzy set theory [28].</p>
      <p>Argumentation Argumentation aims at dealing with inconsistent knowledge, in order to distinguish
which of several contrasting positions in a dispute are justified. In a dispute, the participants make claims
(the arguments) to support their own position, to attack the arguments for competing positions of the
other participants, and to defend their position from the attacks of the others. Abstract argumentation,
stemmed from ALP, focuses only on the inter-relationships among the arguments, neglecting their
internal structure or interpretation.</p>
      <p>Abstract Argumentation Frameworks (AFs) [29] can be represented as graphs, where nodes are the
arguments and arcs represent the relationships between pairs of arguments. We adopt the Generalized
Argumentation Framework (GAF) [30] extension of traditional AFs, a much more powerful model which
provides bipolarity (the possibility of expressing both attacks and supports between pairs of arguments)
and weights on both the arguments and the attack/support relationships (denoting their strength), and
is compatible with the most prominent extensions proposed in the literature. In particular, the T-GAFs
specialization of the GAF model introduces community and topics as a context of the arguments that
can afect their reliability.</p>
      <p>Induction The term induction refers to the inference of general rules or theories starting from specific
instances. Observations are descriptions of objects or situations as ‘perceived’ from the world. Examples
are labels assigned to observations to explicitly specify what are the concepts of interest (to be learned)
in the observations. Examples can be positive (representing instances of the concepts) or negative
(representing instances that do not belong to a concept). Inductive Learning aims, given a set of examples
concerning some concept, at extracting a model (i.e., a characterization) of that concept.</p>
      <p>Inductive Logic Programming (ILP) [31] is a branch of Machine Learning exploiting LP as a
representation language. Some ILP systems work in a batch way: they start from an empty theory and stop
the inductive process when the current set of hypotheses is able to explain all the available examples.
When new evidence contradicts the learned theory, the whole process must be restarted from scratch,
taking no advantage of the previously learned hypotheses. Other systems can revise and refine a theory
in an incremental way: they try to change the previously generated hypotheses in such a way that
the changed hypotheses explain both the old and the new examples. We perform induction using the
incremental ILP system InTheLEx [32].</p>
      <p>Ontological Typical ontology-based reasoning tasks of interest are satisfiability (checking if the
described world may exist), instance checking (checking whether an instance belongs to a certain
concept), concept satisfiability (checking if a concept may exist in the described world), subsumption
(checking if a concept is a subclass of another concept), equivalence (checking if two classes are the
same), retrieval (of the set of instances that belong to a certain concept), extraction of
super-/subclasses, relationships and properties of a given concept. Particularly relevant is the relationship of
generalization/specialization, on which inheritance can be applied.</p>
      <p>The research on ontologies evolved separately from LP, and relied on the Description Logics [33]
fragment of FOL. Diferent description logics can be defined, depending on the available operators.
Adding more and diferent operators extends the expressive power of a DL, but may lead to indecidability.
Unfortunately, DLs are only partially overlapping to LP, and the non-overlapping parts are incompatible,
mainly due to the diferent fundamental assumption they make on unknown information (Open World
Assumption in DLs vs Closed World Assumption in LP). Ontologies can be translated to default logic [34],
one of the most famous formalisms for non-monotonic reasoning.</p>
      <p>Similarity Similarity computation between FOL descriptions is complex due to indeterminacy (the
possibility of mapping various portions of one description in many ways onto another description). For
this reason, very few works in the literature tackled this problem. We adopt the approach proposed
in [35]. It considers a set of parameters and defines a similarity function based on them, plus a set of
criteria to assess the similarity for diferent clause components. The parameters it uses for comparing
two objects ′ and ′′ are widely accepted in the literature [36]. The similarity criteria deal with
increasingly complex clause components: terms, atoms, groups of atoms, clauses. The similarity of
more complex components is based on the similarity of simpler components. In FOL formulae, terms
represent specific objects, while predicates express their properties and relationships. Accordingly, two
levels of similarity can be defined for pairs of FOL descriptions: the object level, concerning similarities
between the terms referred to in the descriptions, and the structure one, referring to how the nets of
relationships in the descriptions overlap.</p>
      <p>Analogy Analogy is the cognitive process of matching the characterizing features of two items
(subjects, objects, situations, etc.). It allows one to reuse knowledge from a known item or domain
(called the base) to an unknown one (called the target). While similarity is a syntactic task that looks
for exactly the same features in two items, analogy maps ‘roles’, which has to do with semantics (i.e.,
the meaning). The mapping is bi-directional, while in metaphors it only holds in one direction. After
ifnding an analogy on some roles, the association can be extended to further missing features. The
analogy may depend on the context, goal or perspective, and its outcome might be inconsistent with
previous knowledge [37].</p>
      <p>Analogical reasoning consists of 5 steps [38]: (1) Retrieval finds the best base domain that may help
to solve the problem in the target domain; (2) Mapping looks for a mapping between base and target
domains; (3) Evaluation provides criteria to evaluate candidate mappings; (4) Abstraction shifts the
representation of both domains to their roles’ schema, converging to the same analogical pattern; (5)
Re-representation adapts one or more pieces of the representation to improve the matching. A procedure
that, applied to two descriptions, returns possible analogies between them is called an analogy operator.
The analogy setting we adopt, specifically based on LP formalisms, was provided in [39].</p>
    </sec>
    <sec id="sec-4">
      <title>4. Multistrategy Reasoning for Explainability in GraphBRAIN</title>
      <p>As noted, single inference strategies have been typically studied in isolation or in combinations of
very small sets (most often just pairs). This limitation motivated a new research direction, named
Multistrategy Reasoning (MSR), as an extension of the Inferential Theory of Learning (ITL) [18] theoretical
framework (developed from the specific perspective of learning agents) specifically aimed at combining
as many approaches as possible, without giving priority to any of them. We now describe the MSR
framework underlying GraphBRAIN’s automated reasoning capabilities.</p>
      <sec id="sec-4-1">
        <title>4.1. Combination of Inference Strategies</title>
        <p>There are many interconnections among the inference strategies proposed above so that they can
help each other in accomplishing their tasks. Here we describe the integration approaches and their
implementations adopted by in GraphBRAIN.</p>
        <p>Ontologies and Logic Programming While the realms of Logic Programming and Description
Logics, used to specify ontologies, are partly incompatible, attempts to merge them have been made in
the literature. We adopt ℒ + log [40], as the most powerful decidable combination of Description
Logics and disjunctive Datalog rules (i.e., Datalog rules whose head may consist of a disjunction of
atoms). This language allows to mix ‘Datalog predicates’, coming from the LP perspective, from ‘DL
predicates’, coming from the ontological perspective, in a clause, but DL predicates cannot be negated.
Abduction and Deduction The integration of abduction and deduction has been defined in [ 20, 41],
to allow reaching conclusions or making prediction when the available information is insuficient.
Similarity for Deduction Similarity can be used both to help a subsumption procedure to converge
quickly towards the correct associations [35], and to weaken subsumption and obtain a flexible matching
procedure that returns a degree of matching instead of a boolean decision.</p>
      </sec>
      <sec id="sec-4-2">
        <title>Abstraction, Deduction, Similarity, Abduction and Argumentation for Induction A very</title>
        <p>interesting case of the use of several strategies in support of induction is provided by the incremental
ILP system InTheLEx [32, 42].</p>
        <p>Abstraction is carried out as a pre-processing step that removes useless information according to the
framework in [19]. This is obtained by expressing abstraction operators as clauses, such that whenever
the body is recognized in an observation, the involved facts are replaced by those in the head, suitably
defined to hide the useless information.</p>
        <p>Deduction is used in a saturation step that makes explicit facts that are implicit in the available
description of the observations and that may be useful to correctly grasp the concept that is being
learnt. To do this, deduction exploits the rules in the KB. Whenever the body of a clause in the theory
is recognized in an observation, the head of the clause is added to the observation itself.</p>
        <p>Abduction is used to check if an unexplained example/observation can be explained by assuming
additional unseen information that is not present in the observations. In such a case, the guessed
information is added to the example description. This prevents the refinement operators from being
applied, and the theory from being changed.</p>
        <p>Similarity is used to guide the generalization operator, by taking the paths univoquely determined
according to the technique proposed in [35], and using a greedy techinque that adds the generalization
of these paths by decreasing similarity, as long as they are compatible. Further generalizations can then
be obtained through backtracking [43].</p>
        <p>Recently, argumentation has been integrated to identify consistent portions of inconsistent
observations and to choose the one to rely on, exploiting the same integrity constraints defined for abduction
to identify attacks and supports (an example of a further integration of diferent strategies) [44].</p>
      </sec>
      <sec id="sec-4-3">
        <title>Induction for Abduction, Abstraction and Deduction Abstraction operators, integrity constraints</title>
        <p>for abduction (and argumentation), and rules for saturation can be inductively learned from observations,
as shown in [45, 46]. Combinations of facts that never occur generate integrity constraints for abduction
(that can be used also for generating abstract argumentation frameworks [44]). Combinations that
always occur generate abstraction operators. Concept definitions learned by an ILP system can be used
to identify known concepts in observations when learning other concepts.</p>
        <p>Argumentation and Induction for Analogy The analogy operator defined in [ 39] leverages
argumentation to overcome the constraint that using the same descriptors in the two domains means
that they necessarily denote the same roles. All possible analogical mappings between descriptors are
considered, and mappings are inconsistent if they map one feature in one domain onto many features in
the other. These inconsistencies are expressed as attacks in an argumentation framework, and abstract
argumentation strategies are used to select only consistent associations.</p>
        <p>In the same paper, the use of an inductive (generalization) operator to obtain more general knowledge
structures that can be mapped onto several domains is also proposed.</p>
        <p>Abduction and Probabilistic Reasoning While, from a logical standpoint, all consistent abductive
explanations are equally good, in a probabilistic setting diferent explanations of a goal are associated
to diferent possible worlds, and their validity depends on the validity of the rules, facts and integrity
constraints used to obtain those worlds. PEALP takes into account all these items [24, 47].</p>
        <p>A world that violates a probabilistic integrity constraint is not impossible, just diferently probable.
So, all (minimal) abductive explanations must be obtained to identify the most likely one, and whenever
the abductive procedure has a choice, it must explore the worlds associated to all diferent options.
Cues for Further Cooperations As observed in the ITL, analogy is strictly connected to abstraction
and deduction, since these two strategies are needed to go from a specific domain to its abstract structure
and then from the latter to a new specific domain. It also has strict connections to abduction, that can
be used to guess information in the target domain that is not observed but is analogous to information
available in the source domain.</p>
        <p>Argumentation can help deduction to resolve inconsistencies and determine (possibly diferent
settings of) consistent information on which deduction can be carried out.</p>
        <p>Uncertain reasoning allows to add flexibiity to all the others. Especially interesting is combining it
with argumentation (to determine how reliable each consistent setting is and rank diferent settings)
and induction (to assign a degree of reliability to the learned knowledge).</p>
      </sec>
      <sec id="sec-4-4">
        <title>4.2. Implementation of Explainable Multistrategy Reasoning in GraphBRAIN</title>
        <p>
          An implementation of the MSL framework has been started, resulting in the GEAR (acronym for
‘General Engine for Automated Reasoning’) inference engine [48]. GEAR tracks all reasoning steps,
and can provide a full account/explanation of its outcomes, that can be analyzed and browsed by the
users. GEAR is written in Prolog language, because it provides native support to deduction, unification,
manipulation of logic representations, and Logic Programming. Knowledge bases handled by GEAR
may include various kinds of knowledge items, including Facts, Rules, Integrity Constraints, Abstraction
Operators, and Argumentative relationships. Uncertainty is expressed by values in [
          <xref ref-type="bibr" rid="ref1">0, 1</xref>
          ], inspired by
mathematical probability theory.
        </p>
        <p>The main components of a KB are facts and rules. Facts are formalized as
while rules are formalized as</p>
        <p>fact([ ,],  , ).</p>
        <p>rule([ ,], , ,  , ).
where  is the unique identifier of the fact or rule, and  ∈]0, 1] is the certainty value (1 meaning
‘absolutely’ true and 0 meaning ‘absolutely’ false).  is an atom, while  and  are the rule’s head and
body, respectively, and  is its priority (a number used to determine which rule should be executed
ifrst in case of conflicts).</p>
        <p>is a logistic expression built on the following operators:
and([1,...,]) representing the conjunction (AND) of the ’s;
or([1,...,]) representing the disjunction (OR) of the ’s;
no() representing a ‘probabilistic’ negation (NOT) of ;
not_exists() representing an ‘existential’ negation of ;
where the ’s are atoms or nested operator applications, to express complex conditions.  is one of
the following:
and([1,...,]) representing the conjunction (AND) of the atoms ;
or([1,...,]) representing the disjunction (OR) of the atoms ;
no() representing a ‘probabilistic’ negation (NOT) of the atom .</p>
        <p>Abducibles are formalized as
abducible(/ ).</p>
        <p>ic(, , ).
where  is the predicate name and  is its arity, while integrity constraints for abduction and
argumentation are formalized as
where  is the unique identifier of the constraint,  is its certainty value, and  is one of the following:
nand([1,...,]) at least one among literals 1,. . . , must be false;
xor([1,...,]) exactly one among literals 1,. . . , must be true;
or([1,...,]) at least one among literals 1,. . . , must be true;
if([1′,...,′],[1′′,...,′′]) if all literals 1′,. . . ,′ are true, then all literals 1′′,. . . ,′′ must also be
true (modus ponens); alternatively, if all literals 1′′,. . . ,′′ are false, then all literals 1′,. . . ,′ must
also be false (modus tollens);
iff([1′,...,′],[1′′,...,′′]) either all literals 1′,. . . ,′ and 1′′,. . . ,′′ are true, or all literals 1′,. . . ,′
and ′′,. . . ,′′ are false;</p>
        <p>1
and([1,...,]) all literals 1,. . . , must be true;
nor([1,...,]) all literals 1,. . . , must be false.</p>
        <sec id="sec-4-4-1">
          <title>Abstraction operators are formalized as</title>
          <p>where  is the unique identifier of the operator, and  is the abstracted set of atoms that replaces the
ground set of atoms  whenever it is found in an observation.</p>
          <p>Identifiers of knowledge items are in either of the following forms:
 a general unique identifier for the item in the overall KB;
[ ,]  is the unique identifier of the item within knowledge module  .</p>
        </sec>
        <sec id="sec-4-4-2">
          <title>Finally, argumentation works on the following predicate:</title>
          <p>arg(, ).</p>
          <p>
            arg_rel(′, ′′, ′).
where , ′ and ′′ are fact identifiers,  ∈ [
            <xref ref-type="bibr" rid="ref1">0, 1</xref>
            ] is the strength of the argument and ′ ∈ [− 1, +1]
expresses the type (attack or support, based on the sign) and strength of the argumentative relationship.
          </p>
          <p>Other predicates can be used to specify system settings (e.g., gear_flag allows to set flags that direct
the system’s behavior), information related to user interaction (e.g., askable specifies information
that can be asked to the user if missing in the KB), calls to pre-defined procedures (e.g., call may call
Prolog to carry out some computations), and others, but they are beyond the scope of this paper.</p>
          <p>GEAR has been connected to GraphBRAIN via an export procedure of GraphBRAIN that generates
facts from the instances in the graph and other knowledge items (rules, integrity constraints, etc.) from
the axioms specified in the ontologies and from the ontological properties expressed in the definition of
the ontological elements.</p>
          <p>The predicates of the language are derived directly from the ontology, as follows:
• an instance with identifier  of entity , which is associated with attributes 1, . . . , , is
expressed using a predicate (, 1, . . . , );
• an instance with identifier  of relationship , which is associated with attributes 1, . . . , ,
connecting subject instance (node)  to object instance (node)  is expressed using a predicate
(, , , 1, . . . , );
• an instance with identifier  of an entity representing a reified relationship , which connects
entity instances 1, . . . ,  and is associated with attributes 1, . . . , , is expressed using a
predicate (, 1, . . . , , 1, . . . , ).
where the order of the instances and attributes in the arguments is as specified in the ontology.</p>
          <p>GraphBRAIN can provide the facts to GEAR both in batches, by translating a relevant portion of the
KG determined according to suitable algorithms, or on-demand, by generating single facts needed by
the inference engine to carry on the current reasoning task.</p>
          <p>Figure 1 shows two steps in the use of GEAR inside GraphBRAIN: on the top, the knowledge extraction
algorithms have selected a (possibly personalized) subgraph of the KG starting from the nodes listed in
the table on the left and with thicker borders in the graph displayed in the middle. After exporting this
knowledge in GEAR format, GEAR can be applied. The bottom screenshot shows the interface from
which the user may carry out several functions and get the results. Of interest here is the section on
the top left of the window, where the explanation for the obtained outcome is displayed and can be
interactively browsed by the user.</p>
          <p>The proposed approach has been used so far in two application domains. The former is a porting to
GEAR of an older version of the inference engine, called ReLay, and of the associated KB to GraphBRAIN
representation. It was about the diagnosis of eating disorders (Figure 1 refers to this domain). Another,
more recent application, is about Cultural Heritage (CH), for which GraphBRAIN is very suitable
because it can enforce privacy, which is very important for some collections (especially private ones),
and personalization, useful to support the needs of very diferent stakeholders (professionals, researchers,
scholars, hobbyists, enthusiasts, tourists, curious people) with diferent background, culture, interests,
aims, contexts, expectations, etc.</p>
        </sec>
      </sec>
    </sec>
    <sec id="sec-5">
      <title>5. Conclusions and Future Work</title>
      <p>Artificial Intelligence is nowadays pervading all aspects of our lives, starting to cover also applications
that involve crucial aspects of human lives or well-being. In these cases, impacting directly our
existence, we the humans need to stay in control, checking and validating its decisions. In turn, this
requires them to be explainable. In spite of many attempts to simulate explainaility in sub-symbolic
AI approaches, only the symbolic one, based on formal logics, is explainable-by-design. It applies
human-like automated reasoning and relies on suitable knowledge representations, ensuring semantic
and procedural interoperability with humans and human thought. The most widely known and adopted
knowledge representation approach in the current research landscape is Knowledge Graphs, mostly
investigated by the Semantic Web community, but due to its peculiarities the Semantic Web perspective
and standards are afected by some limitations and shortcomings.</p>
      <p>In this paper we proposed GraphBRAIN, an alternate KG framework, based on state-of-the-art DB
technology and on a diferent graph model, allowing richer representations. By not being tightly coupled
to the Semantic Web representations, this framework also expands the range of possible inference
strategies to be used in automated reasoning, which in turn may better support explainability of the
AI outcomes. In particular, we described how a Multistrategy Reasoning framework can be applied
to GraphBRAIN, through the GEAR inference engine, that is specifically designed for supporting
explainability of its outcomes.</p>
      <p>Ongoing and future work is aimed at enriching the knowledge representation in GraphBRAIN, in
order to support more advanced approaches to automated reasoning. Development of GEAR is also
being carried on, to better integrate the diferent inference strategies and expand them. Finally, the
theoretical and practical results of this efort are being applied to real-world tasks.</p>
    </sec>
    <sec id="sec-6">
      <title>Acknowledgments</title>
      <p>This research was partially supported by projects CHANGES “Cultural Heritage Active Innovation
for Sustainable Society” (PE00000020), Spoke 3 “Digital Libraries, Archives and Philology” and FAIR
“Future AI Research” (PE00000013), spoke 6 “Symbiotic AI”, funded by the Italian Ministry of University
and Research NRRP initiatives under the NextGenerationEU program.</p>
    </sec>
    <sec id="sec-7">
      <title>Declaration on Generative AI</title>
      <sec id="sec-7-1">
        <title>The author(s) have not employed any Generative AI tools.</title>
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