On the Artificial Reasoning with Chess: A CBR vs PBR View

Zahira Ghalem

1,2 a

, Karima Berramla

3,4 b

, Thouraya Bouabana-Tebibel

and

Djamel Eddine Zegour

Laboratoire de la Communication dans les Systèmes Informatiques (LCSI),

Ecole Nationale Supérieure d’Informatique (ESI), BP, 68M Oued-Smar,16270 Alger, Algeria

Oran 2 University Ahmed Ben Ahmed, Algeria

LAPECI Laboratory, Oran 1 University Ahmed Ben Bella, Algeria

University of Science and Technology Mohamed Boudiaf, Algeria

Keywords: Artificial Reasoning, Game Playing, Knowledge Generalization, Knowledge Representation.

Abstract: In the quest to advance artificial reasoning, this article delves into the contrasting realms of Case-Based

Reasoning (CBR) and Pattern-Based Reasoning (PBR). Drawing inspiration from human thinking behavior

in tackling novel problems. The study centers on the chess domain, exploring the intricacies of representation,

generalization, and reasoning processes. It illuminates the fundamental trade-off between computational

efficiency and decision quality in (PBR) systems. This comprehensive examination provides valuable insights

into the adaptability of reasoning systems and the role of abstract knowledge bases in enhancing performance.

1 INTRODUCTION

Chess, often referred to as the touchstone of artificial

intelligence (Ensmenger, 2012), has been extensively

examined due to its accessibility and

comprehensibility. From the historical tale of the

Turk (Sajo et al., 2008), through the monumental

clash between Deep Blue and Kasparov (Campbell et

al., 2002), to the superhuman performance of

Alphazero (Silver et al., 2017), machine mastery of

the game has seen significant advancements.

However, these achievements have predominantly

relied on resource-intensive brute-force search

techniques (Chaslot et al., 2008), complemented by

heuristics like Alpha-beta pruning (Sato and Ikeda,

2016).

Intelligence, in a general sense, can be defined as

the capacity to take actions that enhance the

likelihood of problem-solving (Russell & Norvig,

2003). Given the computational speed of machines,

this capability can be artificially replicated through

brute-force computation, involving a systematic

exploration of potential solutions. However, it is

https://orcid.org/0000-0002-4070-1237

https://orcid.org/0000-0002-2847-4895

https://orcid.org/0000-0002-9944-3738

https://orcid.org/0000-0001-9538-5895

crucial to note that explainable artificial intelligence

(AI)extends beyond mere computational power. It

encompasses the ability to emulate the cognitive

processes of human thinking in machines, enabling

them to acquire knowledge, tackle complex problems

(Ongsulee, 2017), and provide understandable,

interpretable, and transparent explanations for their

decisions and actions (Keane and Kenny, 2019). This

paper is targeted at distinguished disciplines of

existing artificial reasoning methods.

Since the pioneering work of Robert Shank

(Shank,1982), case-based reasoning (CBR) has found

its way into numerous computer applications leading

to the development of successful CBR systems. Often

touted for its ability to closely mimic human thought

processes (Aamodt and Plaza, 1994), this approach

hinges on the idea that solutions to new problems can

be derived from the problem-solving experiences of

similar, previously encountered issues. Likewise,

pattern-based reasoning (PBR) involves eager

generalization to extract patterns from a set of prior

problems and construct a set of solutions-indicating

rules.

378

Ghalem, Z., Berramla, K., Bouabana-Tebibel, T. and Zegour, D.

On the Artiﬁcial Reasoning with Chess: A CBR vs PBR View.

DOI: 10.5220/0012624000003645

Paper published under CC license (CC BY-NC-ND 4.0)

In Proceedings of the 12th International Conference on Model-Based Software and Systems Engineering (MODELSWARD 2024), pages 378-385

ISBN: 978-989-758-682-8; ISSN: 2184-4348

RBR and CBR represent two complementary

paradigms for constructing artificially intelligent

systems (Sun, 1995). This paper delves into their

respective applications in the context of chess,

emphasizing their distinct knowledge representation

techniques and approaches to case generalization. It

engages in a discussion of the research findings and

conclusions in this area and underlines the potential

value in adopting a combined perspective that

leverages the strengths of both methods.

2 BACKGROUND AND

PROBLEM STATEMENT

In addressing everyday problems, our natural

inclination is to draw upon past experiences, compare

them with new situations, and develop customized

solutions. In turn, this process generates fresh

knowledge that we can later recall and apply. As

illustrated in Figure 1 (CBR) serves as a simulation of

this human thinking behavior when tackling new

problems.

Figure1: CBR reasoning process.

PBR, on the other hand, relies on explicit pre-

generalization and employs a more abstract

knowledge representation through rules. When faced

with a new problem, it selects relevant rules that have

premises consistent with the problem description (see

Figure 2). In larger domains, summarizing all the

knowledge becomes increasingly challenging, and

exact matching is seldom achievable. Consequently,

rule selection is based on various contextual

adaptations. This leads to the interchangeability of the

terms "rule" and "pattern" (Reason, 1990).

In a fully automated environment, both CBR and

PBR rely on a set of training examples to create

generalizations. The key distinction between the two

systems is that CBR generates (implicit)

generalizations during the search and retrieval

process by identifying similarities between base cases

and target problems. In contrast, PBR systems make

eager explicit generalizations by identifying shared

characteristics with the same solution, which are then

turned into rules applied to solve future problems.

Figure 2: PBR process.

The performance of an artificial reasoning approach

relies heavily on the quality of its knowledge base.

But can it be influenced by its generalization method?

To address this problem, we formulate the following

questions:

RQ1: what are the advantages of each of the PBR

and CBR approaches?

RQ2: how could their shortcomings be mitigated?

RQ3: could this lead to a new generalization

approach?

3 CHESS GAME: CBR VS PBR

The fundamental challenge in knowledge-based

approaches is to extract and present relevant

knowledge in a usable form. In this paper, the

surveyed research can be categorized into two

primary directions: the first utilizes pattern-based,

expert-level advice in the form of constraint rules,

while the second involves creating case bases from

expert-level gameplay.

3.1 Representation

From a CBR perspective, the knowledge base

comprises games played at the expert level. In this

view, a game can be seen as a series of distinct

problems, each with its own solution. These problems

involve the remaining pieces and their respective

positions, referred to as the board position throughout

this article. Due to the complexity of the game

(approximately 10

120

possible positions), the search

function must be thoughtfully designed to balance

search specificity and accuracy of selected solutions.

Case base

Similar cases'

retrieval and adaptation

New case

Problem

description

Validation

and

learning

Case base

Pattern extraction

and validation

Solution

Problem

description

Pattern bases

Pattern selection

On the Artiﬁcial Reasoning with Chess: A CBR vs PBR View

379

To address this challenge, various researchers

have explored different approaches for the

representation of chess board positions. For instance,

(BRATKO et al., 1978) focused on studying

endgames with pattern descriptions. Their

representation includes a listing of the remaining

pieces, their relative positions, and attack/defense

relationships, along with defined goals. the

educational system ICONCHESS (Lazzari, 1996)

combines CBR with fuzzy logic to offer high-level

playing advice. This system utilizes cases, drawn

from games played by various experts and masters,

along with their corresponding analyses, see (Figure

3). David Sinclair (Sinclair, 1998) employed

Principal Component Analysis to condense 56

predictive features into 11. Another approach, as seen

in (Ganguly et al., 2014) and, represents cases in a

textual format, including precise piece positions and

their potential interactions (attacks, defenses,

counterattacks). Similarly, (Hesham et al., 2021)

represent the board position in a simple textual

format.

Figure 3: Board representation for CBR systems.

In contrast, knowledge can also be represented as

a collection of conditional recommendations based on

pattern extraction, suggesting potential winning

moves. This approach is exemplified in (Kass, 1990)

and (Kerner, 1995), where the concept of Explanation

Models (XP) is introduced. An XP serves as a

parametric explanation that can be adapted to

elucidate new cases. A Multiple Explanation Model

(MXP) comprises a collection of XPs, each

representing a unique perspective on a given case.

These XPs are assigned weights and assessments,

contributing to the overall evaluation of the position.

CHUNKER (Berliner & Campbell 1984) employs

abstract patterns stored in predefined libraries to

assess pawn endgame positions. This approach has

been further explored in SUPREM (Berliner &

Ebeling, 1984) (Berliner & Ebeling, 1990), a pattern-

based program implemented in the specialized

machine/program HITECH. In this system, a board

position is interpreted as a collection of patterns.

Clamp (Cook, 2008), analyses middle-game positions

to construct decisive piece groupings for move

selection. Contributing to the development of piece-

move-oriented chunk libraries.

Figure 4: Rule representation for PBR chess system.

3.2 Reasoning and Generalization

The fact that analogous problems have analogous

solutions is a cornerstone of CBR Systems. When it

comes to a player's perspective, similar board

positions often lead to similar moves. This raises the

question of which features of a board position are

crucial for move selection and how they affect the

search process. (Lazzari, 1996) sought out similar

positions, including reversed similarity, by evaluating

both syntactic similarities (such as the exact location

of pieces) and semantic similarities related to plans

and similar strategic objectives. In (Sinclair, 1998),

the researcher attempted to characterize each position

in the case base by considering structural features like

pawn formations and material. This approach led to

similarity measurement based on the composite

distance between these representations. (Ganguly et

al., 2014) encoded the remaining pieces, their

reachable squares, and attack/defense configurations,

adopting an approximation search process that

considered the piece's mobility and connectivity.

With a simplistic textual representation of the

chessboard position, (Hesham et al., 2021) employed

base cases to illustrate potential moves for both the

player and their opponent. Subsequently, these moves

were input into a search algorithm (Plaat et al, 2014)

employing alpha-beta pruning (Sato & Ikeda, 2016)

to determine the optimal move.

Pattern-based systems, on the other hand, focus on

identifying dominant patterns within a query,

utilizing contextual adaptation mechanisms since the

rule's condition part is expressed in a pattern-like

form. In (Kass, 1990) and (Kerner, 1995), patterns

with binary properties are used to extract fundamental

explanation models from the board position, and the

most dominant ones are selected. In CHUNKER

Berliner & Campbell 1984), each model consists of

instantiable properties, and each instance has a set of

values for these properties. SUPREM (Berliner &

Board Position CBR

representation

Structural summarization

(Sinclair, 1998)

Pieces and attack/defense

relations

Exact positions

(Ganguly et al., 2014)

(Hesham et al., 2021)

Relative positions

(Brakto et al., 1978)

Augmented board

representation based on

players analysis

(Lazzari, 1996)

MBSE-AI Integration 2024 - Workshop on Model-based System Engineering and Artiﬁcial Intelligence

380

Ebeling, 1990) employs predefined pattern

recognition in the form of rules that define temporary

objectives for players and the necessary models to

recognize these goals during the search process.

Morph (Walker & Levinson, 2004), after being

trained in various games, learns to associate chess

piece formations with the possible winning moves.

As for (Cook, 2008), when a query is submitted, piece

groupings are extracted based on factors like attack,

defense, proximity, and more. These groupings are

then searched for in the position's legal move

libraries, constructed through the piece's move-

oriented chunk libraries.

3.3 Results and Insights

The efficiency of an artificial Reasoning system

fundamentally hinges on two critical components:

representation and similarity metrics. In this context,

the dynamic interaction prompts a central question:

How significant are the characteristics used for a

problem representation?

Within this context, the study conducted by

ICONCHESS, as presented in (Lazzari, 1996), places

significant emphasis on specific factors that play a

pivotal role in characterizing board positions. These

factors encompass the positions and types of pieces

and the intricate web of playing relations among

them. The research underscores the importance of

considering these elements when seeking to

comprehensively define and understand the unique

characteristics of board positions.

The research conducted by Sinclair (Sinclair,

1998) contributes valuable insights into this question.

Sinclair's work reveals that the choice of similarity

metrics plays a pivotal role in shaping the

performance and outcomes of CBR chess systems:

Quality vs. Quantity Trade-off: Sinclair's

observations demonstrate a fundamental trade-off.

When employing strict similarity metrics, the cases

retrieved exhibit a high level of quality. However, this

precision often comes at the cost of quantity, as the

number of results retrieved tends to be relatively low.

Summarization of Board Positions: Central to this

discussion is the representation of board positions.

The choice of which features to include, the number

of features, and their respective weighting in the

computational process can significantly affect the

system's performance.

Furthermore, (Qvarford, 2015) investigated the

performance of an AI agent that employed CBR with

an extensive similarity metric. The outcomes revealed

a subpar performance, with a low win rate across

different case bases. This underperformance can be

largely attributed to the utilization of a

comprehensive similarity metric, which may have led

to an overly strict matching criterion. The study's

findings underline the potential advantage of

employing, among other adjustments, a more abstract

knowledge base. This could enhance an AI agent's

overall performance, potentially leading to more

successful outcomes.

However, it's worth noting that the studies

discussed in this article exhibit substantial variations

in terms of their training data, objectives, and the

specific computing platforms on which they were

implemented. This diversity makes it challenging to

classify these papers solely based on the level of

playing they address. A concise summary of the key

aspects explored in these various research endeavors

is presented in Table 1 for reference and clarity.

The majority of pattern-based systems discussed

in this context were conceived and implemented with

the primary objective of mitigating the branching

factor challenges inherent in alpha-beta search

algorithms (Sato & Ikeda, 2016). This challenging

task of narrowing down the search space is crucial for

achieving computational efficiency in AI systems.

Some noteworthy examples include (BRATKO et al.,

1978), CHUNKER Berliner & Campbell 1984),

SUPREM (Berliner & Ebeling, 1990), (Ganguly et

al., 2014) and (Hesham et al., 2021) which

demonstrated high playing performances.

For instance, Clamp (Cook, 2008) introduced an

approach that resulted in a substantial 50% reduction

in the number of nodes examined during the search

process. Although this achievement was

commendable, Clamp had a relatively modest 17%

success rate in selecting the optimal move, illustrating

the intricate balance between computational

efficiency and decision quality. In essence, it

highlights the trade-off that many pattern-based

systems encounter.

The case of Morph (Walker & Levinson, 2004) in

the context of PBR systems provides valuable

insights into the challenges and adaptability of an

abductive approach. its noteworthy achievement was

its ability to enhance pattern extraction efficiency

over multiple games. However, Morph also faced

persistent challenges when it came to understanding

how to successfully conclude games and secure

victory. This particular limitation highlights a key

aspect of abductive PBR: the need for a

comprehensive and well-structured knowledge base.

It's not enough to identify patterns; the system must

also know how to effectively apply these patterns to

achieve a winning outcome.

The adaptability of an abductive PBR approach

On the Artiﬁcial Reasoning with Chess: A CBR vs PBR View

381

depends on several factors, including the quality and

diversity of the training data, the sophistication of the

pattern extraction algorithms, and the system's ability

to derive actionable strategies from identified

patterns. Over time, with access to more

comprehensive and diverse data, an abductive PBR

system may become increasingly adept at adapting to

different gameplay scenarios and improving its

overall performance.

The case of CHUNKER (Berliner & Campbell

1984) and SUPREM (Berliner & Ebeling, 1990)

represents a perfect example of inductive (PBR).

These systems, in contrast to purely abductive

approaches, overcame the inherent challenges and

exhibited the capability to play complete games at a

master's level. Their achievement was underpinned

by predefined pattern recognition, which essentially

means that they were initially designed based on a

foundation of hypothetical expert knowledge. The

success of CHUNKER and SUPREM suggests the

potential of a PBR approach in addressing complex

gameplay problems and problem-solving in general.

In the case of these systems, predefined patterns serve

as a form of knowledge that guides their gameplay

strategy. The study outlined in (Ganguly et al., 2014),

hints at the tantalizing possibility of constructing a

fully knowledge-based algorithm. This is contingent

on the feasibility of implementing an automatic

knowledge extraction process.

3.4 Theoretical Model Evaluation

The research in this area draws significantly from the

work of Chase and Simon (Chase & Simon, 1973)

and Gong et al. (Gong et al., 2015), who conducted

studies focusing on the perceptual abilities of chess

players. Their investigations aimed to gain insights

into how players mentally perceive chess board

positions. The key finding from their studies is that a

Table 1: Knowledge-based chess systems.

Knowledge

representation

Reasoning and

generalization

Goal Game stage Results

Relative piece position +

attack defense relation

(BRATKO et al., 1978)

Implementation of

expert hypothesis on

endgame

Elicitation of pattern-

based representation

for endgames

End game Evidence that a more

knowledge-based approach

is require

Fuzzy logic using fixed

patterns: material king

protection, pawn

structure

(

Lazzari, 1996

)

customizable weighted

function for

classification

Human theory-based

classification for

board position

evaluation

Middle

game

Proof that joining CBR and

fuzzy logic is valuable for

the teaching of high-level

chess strate

ies

Structural features

representation with PCA

(Sinclair, 1998)

K nearest neighbors

based similarity for

move selection

Quality of Results

Assessment

Full game The need to balance

between quality and the

number of results

Exact piece positions +

attack/defense relation

(Ganguly et al., 2014)

Piece’s mobility and

connectivity

approximation for

move selection

Search time sizing Full game Low runtime overhead

Exact piece position

(Hesham et al., 2021)

potential moves for

both players and their

opponent

Downsizing the search

space

Full game Enhanced playing

performances (using

minimax algorithm and

ha-

eta

runin

Explanation Patterns

(Kass, 1990, Kerner,

1995

)

Pattern instantiation chess expert system

for game evaluation

Full game Comprehensive board

position evaluation

Construction of fixed-

sized chunks based on

attack, defense, and color

(Cook, 2008)

The exact

correspondence of

board positions chunks

Investigating decisive

chunk size and

composition

Middle

game

4 to 5 pieces attack

defense chunk tend to be

more decisive in move

making

Abstract predefined

pattern Berliner &

Campbell 1984)

Guided pattern

generation

Board position

evaluation

Pawn

endgame

Evaluation of entire board

configurations based on

predefined abstract pattern

libraries

Predefined pattern

(Berliner & Ebeling,

1984)

Interim goals and their

defining pattern for

recognition

Pattern-based advice

for guiding Alpha-beta

Full game Playing a full game at a

master’s level

MBSE-AI Integration 2024 - Workshop on Model-based System Engineering and Artiﬁcial Intelligence

382

player's level of expertise is closely linked to their

chunking abilities. This chunking process involves

players breaking down a complex board position into

manageable and meaningful "chunks."

These "chunks" are essentially cognitive units that

encapsulate specific patterns and structures within the

chessboard. Players establish these chunks based on

various criteria, including pawn structures, color,

attack and defense relationship, and local proximity.

The chunking process allows players to efficiently

process and remember complex board positions. They

recognize recurring patterns and structures, which

simplifies decision-making during a game.

León-Villagrá and Jäkel (Leon-Villagra & Jakel,

2013) have made contributions to this body of

knowledge. Their research indicates that chess

players do not rely on visual memory alone to think

and remember game situations and features. Instead,

players tend to think more abstractly, focusing on the

underlying structures, patterns, and relationships

between pieces. This abstract approach to thinking

enables them to generalize their knowledge and apply

it to a broader range of situations, ultimately

contributing to their expertise.

The different implementations of these cognitive

processes serve to answer RQ1, they underline the

adaptability of CBR systems, promote the

applicability of PBRs, and shed light on the

relationship between case bases and pattern base

extraction. Case bases serve as valuable sources of

information that can potentially lead to knowledge

base extraction. They provide the raw material from

which generalizations and patterns are derived,

ultimately contributing to the development of a

knowledge base that enables the system to reason,

strategize, and make decisions based on past

experiences and expertise.

Here's how this connection works:

Case Bases as a Source of Cases: Case bases store

collections of specific cases, each comprising a

problem and its corresponding solution or outcome.

These cases represent instances of real-world

situations, often related to a particular domain, such

as chess.

Generalization of Cases: In PBR, the process of

generalization involves identifying patterns or

commonalities among a set of cases. These patterns

could be certain strategies, tactics, or recurring

themes that emerge from analyzing multiple cases.

The goal is to extract generalized rules or patterns

from these individual cases.

Knowledge Base Extraction: The generalized

patterns or rules extracted from the case base can be

viewed as a form of knowledge base. These rules

represent the distilled wisdom and expertise

contained within the individual cases. They offer

guidance and strategies for addressing similar

problems or situations in the future. In essence, the

knowledge base is created by summarizing and

codifying the general principles that underlie the

cases.

Application to New Problems: Once a knowledge

base is constructed from the case base, it can be used

to tackle new, previously unseen problems. When a

new problem arises, the system can consult the

knowledge base to identify relevant rules or patterns

that apply to the current problem. This allows for

informed decision-making and problem-solving.

Most advanced neural-network-based chess

programs (He et al, 2018), (Sabatelli et al, 2018),

share the overarching concept of learning from data

and applying this learning to new problems, to

evaluate positions and calculate strategies. Yet it has

been proven that neural networks, particularly those

involved in deep learning, tend to forget previously

learned information upon learning new information

(Babakniya et al, 2023). This phenomenon, known as

catastrophic forgetting, is a significant barrier to

effective generalization over time.

Psychological studies, particularly those

conducted by Dingeman and DeGroot (Dingeman &

DeGroot, 1965), have provided intriguing insights

into the cognitive processes of players, highlighting

the differences between experts and beginners. Key

findings from these studies include:

Real-Time Decision-Making: Regardless of their

expertise, players are observed to make their move

decisions in the here and now, responding directly to

the board position before them. This implies that even

experts do not rely solely on pre-planned sequences

of moves, dispelling the myth that chess experts have

every move planned far in advance.

Contextual Analysis: To make these real-time

move decisions, players engage in contextual

analysis. They carefully evaluate the local situations

on the board, identifying those that hold promise for

their plans and moves. This emphasis on contextual

analysis highlights the significance of a global

contextual scan, which encompasses a broad

assessment of the game situation.

Capacity for Memorization: Remarkably, Simon

and Gilmartin (Simon & Gilmartin, 1973) have found

that expert-level players possess an impressive

capacity for memorization. They can commit a vast

number of different game scenarios to memory,

ranging from 10,000 to a staggering 100,000 unique

situations. This ability to remember and recognize

On the Artiﬁcial Reasoning with Chess: A CBR vs PBR View

383

specific board positions further contributes to their

expertise.

This can answer the question of why Morph

(Walker & Levinson, 2004) couldn't successfully

conclude games and the need for a comprehensive

and well-structured knowledge base, thus solving

RQ2. Retaining the cases that were used to generate

rule bases can indeed be considered a constraint

imposed to address the issue of rule validity. This

approach serves several valuable purposes:

Rule Validation: Keeping the source cases allows

for continuous validation and verification of the

generated rules. By maintaining the original cases,

reasoning systems can periodically check whether the

rules are consistent with the actual experiences and

expertise contained in the cases. This helps ensure

that the rules remain valid and up to date.

Dynamic Adaptation: Cases are real-world

instances and, as such, they capture a dynamic and

evolving body of knowledge. New cases are added

over time as more experiences are gained. By

retaining these cases, reasoning systems can adapt

and refine the rules as new information becomes

available, enhancing the system's adaptability and

accuracy.

Handling Exceptions: In complex domains like

chess, there may be scenarios or exceptions that rules

alone cannot adequately address. The original cases

serve as a safety net to handle such exceptions. If a

new problem or situation does not fit well with the

existing rules, the system can fall back on the cases

for guidance.

Explanation and Transparency: Maintaining the

source cases offers transparency in rule generation. It

allows system users to trace back to the original cases,

making it easier to understand how and why specific

rules were generated. This transparency can be

crucial in critical applications or when users need to

trust the system's decisions.

However, it's important to consider the trade-off

between the advantages of retaining cases and the

associated computational complexity. Managing a

large number of cases can be resource-intensive.

Therefore, Reasoning systems should strike a balance

between retaining enough cases for validation and

adaptability while ensuring efficient system

performance, thus leading to a new generalization

approach, thus treating the suggesting an answer for

RQ3.

4 CONCLUSIONS AND

PERSPECTIVES

In the realm of chess AI, the exploration of CBR and

PBR uncovers the nuanced dynamics of knowledge

representation and application. CBR mirrors human

problem-solving behavior, but its applicability is

challenged in the context of chess gameplay. PBR

systems demonstrate the delicate balance between

efficiency and decision quality, with trade-offs based

on the choice of similarity metrics.

Psychological studies shed light on the real-time

decision-making capabilities of chess players,

offering insights into the cognitive processes that

underpin expertise. The research underscores the

importance of problem-specific characteristics and

adaptability in PBR systems.

CBR systems are renowned for their scalability

and are generally more approachable in design

compared to rule-based systems. However, in

practice, rule-based systems are often preferred over

cases due to their greater applicability. Consequently,

the challenge lies in automating the creation of rule

bases, which can be viewed as a generalization of

case bases.

Retaining cases used for rule generation emerges

as a valuable constraint to ensure rule validation,

dynamic adaptation, handling exceptions, and system

transparency. Striking a balance between

computational efficiency and the advantages of

retaining cases remains a key consideration.

This comprehensive exploration of CBR and PBR

in chess AI provides a deeper understanding of the

challenges and accomplishments in building

intelligent systems (Berramla et al, 2020) that

navigate the complexities of chess gameplay and

problem-solving in general. It opens doors to further

research and development in artificial reasoning.

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