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11 - Search in Machine Learning
- Deepak Khemani, IIT Madras, Chennai
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- Search Methods in Artificial Intelligence
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- 01 November 2025, pp 367-392
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Summary
The earliest programs were entirely hand coded. Both the algorithm and the knowledge that the algorithm embodied were created manually. Machines that learn were always on the wish list though. One of the earliest reported programs was the checkers playing program by Arthur Samuel that went on to beat its creator, evoking the spectre of Frankenstein's monster, a fear which still echoes today among some. Since then machine learning (ML) has steadily advanced due to three factors. First, the availability of vast amounts of data that the internet has made possible. Second, the tremendous increase in computing power available. And third, a continuous evolution of algorithms. But the core of ML is to process data using first principles and incrementally build models about the domain that the data comes from. In this chapter we look at this process.
The computer is ideally suited to learning. It can never forget. The key is to incorporate a ratchet mechanism à la natural selection – a mechanism to encapsulate the lessons learnt into a usable form, a model. Robustness demands that one must build in the ability to withstand occasional mistakes. Because the outlier must not become the norm.
Children, doctors, and machines – they all learn. A toddler touches a piece of burning firewood and is forced to withdraw her hand immediately. She learns to curb her curiosity and pay heed to adult supervision. As she grows up, she picks up motor skills like cycling and learns new languages. Doctors learn from their experience and become experts at their job – in fact, the words ‘expert’ and ‘experience’ are derived from the same root. The smartphone you hold in your hand learns to recognize your voice and handwriting and also tracks your preferences for recommending books, movies, and food outlets in ways that often leave you pleasantly surprised. This chapter is about how we can make machines learn. We also illustrate how such learning is intimately related to the broader class of search methods explored in the rest of this book.
Let us consider a simple example: the task of classifying an email as spam or non-spam. Given the ill-defined nature of the problem, it is hard for us to arrive at a comprehensive set of rules that can do this discrimination.
Frontmatter
- Deepak Khemani, IIT Madras, Chennai
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- Search Methods in Artificial Intelligence
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Dedication
- Laurence Gautier, Centre de Sciences Humaines
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- Between Nation and ‘Community'
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- 01 November 2025, pp vii-viii
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1 - A laboratory for composite India: Jamia Millia Islamia around the time of partition
- Laurence Gautier, Centre de Sciences Humaines
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- Between Nation and ‘Community'
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Summary
In November 1951, the Indian parliament decided, after long deliberations, to grant Aligarh Muslim University (AMU) the status of a central university. AMU thus became one of the first three central universities of independent India, directly benefiting from the central government's financial support.
Meanwhile, in Delhi's rural periphery, a small school, the Jamia Millia Islamia (JMI), continued to struggle for its survival. To those familiar with both institutions, this may appear to be a surprising paradox. Indeed, after partition, many regarded AMU as a ‘hotbed’ of ‘Muslim communalism’, especially after large numbers of students took part in the All-India Muslim League's campaign for Pakistan. Although university authorities quickly asserted their loyalty to the Indian state after independence, many outside the institution continued to see AMU as a symbol of Muslims’ so-called separatist tendencies.
By contrast, JMI appeared to be the ‘nationalist Muslim’ institution par excellence. Established in the wake of the Khilafat and Non-Cooperation movements, the ‘National Islamic University’ broke away from the loyalist attitude of MAO College. Its most prominent figures, Zakir Husain and Mohammad Mujeeb, shared strong personal and political connections with Indian National Congress leaders, particularly M. K. Gandhi. In the last decades of British rule, they remained firmly committed to the Congress’ one-nation policy, including at the time of partition. Why, then, did Jawaharlal Nehru's government neglect JMI after independence while it promoted AMU to the rank of a central university? What does this choice tell us about the government's attitude towards Muslim institutions and, more largely, towards India's Muslim citizens?
Mushirul Hasan has often emphasised the strong political and ideological affinities between JMI and the Congress. In his eyes, JMI epitomises the alliance between secular liberal Muslims and Congress leaders, particularly Gandhi and Nehru. By highlighting these connections, Hasan aims to prove that, far from endorsing the Muslim League's two-nation theory, a significant part of India's Muslim population continued to embrace the Congress’ secular nationalism, before and after partition. However, by focusing on the convergence of ideas between JMI members and Congress leaders, Hasan gives us little explanation for JMI's neglect after independence. Moreover, he tends to flatten out the differences between JMI and Congress leaders, as if these men all shared the same approach to secular nationalism, a point that we must question.
10 - Deduction as Search
- Deepak Khemani, IIT Madras, Chennai
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- Search Methods in Artificial Intelligence
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- 01 November 2025, pp 319-366
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Summary
An intelligent agent must be aware of the world it is operating in. This awareness comes mainly via perception. Human beings use the senses of sight, sound, and touch to update themselves. However, the entire world is not perceptible to any of us. Our senses have limitations. We cannot hear the dog whistle, or see the bacteria living on our skin or the mountain on the other side of the world. But through science and communication we know about the worlds beyond our sensory reach. Telescopes from Galileo to James Webb have delivered spectacular images of the universe, some taken in the infrared band in the spectrum. We augment whatever we know by making inferences. The conclusions we draw may be sound or they may be speculative yet useful. Evolution has preserved in us both kinds of inference making capability.
The world is dynamic and has other agencies making changes in the world too. If we observe something we may guess the cause or intention behind it. This kind of speculation is called abduction. The conclusion is possibly true, maybe even likely. If we see the local bully striding towards us, we may suspect ill intent on his part, and take evasive action. Better safe than sorry. If we develop a cough and fever, we may fear Covid and isolate ourselves from others. When we observe a few white swans, we may conclude that all swans are white. This is called induction. Neither abduction nor induction is always sound. Conclusions we draw may not always hold. But they are eminently useful.
In this chapter we study deduction, a form of inference that is sound. The conclusions that we draw using deduction are necessarily true. The machinery we use is the language of logic and the ability to derive proofs. We highlight the fact that behind deduction the fundamental activity is searching for a proof.
Logic and mathematics are often considered to be synonymous. Both are concerned with truth of statements. In this chapter we confine ourselves to the family of classical logics, also known as mathematical logics, in which every sentence has exactly two possible truth values – true and false. Nothing in between. No fuzzy concepts like tall and dark. Is a person whose height is 176 centimetres tall? What about 175 then? And 174? When does she become not tall? Or modalities like maybe.
Appendix: Algorithm and Pseudocode Conventions
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- By S. Baskaran
- Deepak Khemani, IIT Madras, Chennai
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- Search Methods in Artificial Intelligence
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- 01 November 2025, pp 441-448
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Summary
The algorithms presented in this book assume eager evaluation. The values of primitive types (integers, reals, strings) are passed by value, and tuples, lists, arrays, sets, stacks, queues, etc., are passed by reference, similar to how Java treats primitive values and objects.
The data structures (container types) like sets, arrays, stacks and queues, and the operations on those structures carry their usual meaning, and their usages in the algorithms are self explanatory.
Tuple
A tuple is an ordered collection of fixed number of elements, where each element may be of a different type. A tuple is represented as a comma separated sequence of elements, surrounded by parenthesis.
tuple → ( ELEMENT 1 , ELEMENT 2 , … , ELEMENT k)
A tuple of two elements is called a pair, for example, (S, null), ((A, S), 1), (S, [A, B]) are pairs. And a tuple of three elements is called a triple, for example, (S, null, 0), (A, S, 1), (S, A, B) are triples. A tuple of k elements is called a k-tuple, for example, (S, MAX, −∞, ∞), (A, MIN, LIVE, ∞, 42).
Note: parenthesis is also used to indicate precedence, like in (3+1) * 4 or in (1 : (4 : [ ])), its usage will be clear from the context.
List
A list is an ordered collection of an arbitrary number of elements of the same type. A list is read from left to right and new elements are added at the left end. Lists are constructed recursively like in Haskell.
list → ELEMENT : list
list → [ ]
The ‘:’ operator is a list constructor; it takes an element (HEAD) and a list (TAIL) and constructs a new list (HEAD : TAIL) similar to cons(HEAD, TAIL) in LISP. Using head:tail notation, a list such as [3, 1, 4] is recursively constructed from (3 : (1 : (4 : [ ]))), similar to cons(3, cons(1, cons(4, nil))) in LISP. The empty list [ ] has no head or tail.
List of figures
- Laurence Gautier, Centre de Sciences Humaines
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- Between Nation and ‘Community'
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Glossary
- Laurence Gautier, Centre de Sciences Humaines
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12 - Constraint Satisfaction
- Deepak Khemani, IIT Madras, Chennai
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- Search Methods in Artificial Intelligence
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- 01 November 2025, pp 393-440
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Summary
What is common between solving a sudoku or a crossword puzzle and placing eight queens on a chessboard so that none attacks another? They are all problems where each number or word or queen placed on the board is not independent of the others. Each constrains some others. Like a piece in a jigsaw puzzle that must conform to its neighbours. Interestingly, all these puzzles can be posed in a uniform formalism, constraints. The constraints must be respected by the solution – the constraints must be satisfied. And a unified representation admits general purpose solvers. This has given rise to an entire community engaged in constraint processing. Constraint processing goes beyond constraint satisfaction, with variations concerned with optimization. And it is applicable on a vast plethora of problems, some of which have been tackled by specialized algorithms like linear programming and integer programming.
In this chapter we confine ourselves to finite domain constraint satisfaction problems (CSPs) and study different approaches to solving them. We highlight the fact that CSP solvers can combine search and logical inferences in a flexible manner.
A constraint network R or a CSP is a triple,
R = <X, D, C>
where X is a set of variable names, D is a set of domains, one for each variable, and C is a set of constraints on some subsets of variables (Dechter, 2003). We will use the names X = ﹛x1, x2, …, xn﹜ where convenient with the corresponding domains D = ﹛D1, D2, …, Dn﹜. The domains can be different for each variable and each domain has values that the variable can take, Di = ﹛ai1, ai2, …, aik﹜. Let C = ﹛C1, C2, …, Cm﹜ be the constraints. Each constraint Ci has a scope Si R X and a relation Ri that is a subset of the cross product of the domains of the variables in Si. Based on the size of Si, we will refer to the constraints as unary, binary, ternary, and so on. A CSP is often depicted by a constraint graph and a matching diagram, as described in the examples to follow.
We will confine ourselves to finite domain CSPs, in which the domain of each variable is discrete and finite. We will also specify the relations in extensional form well suited for our algorithms.
9 - Automated Planning
- Deepak Khemani, IIT Madras, Chennai
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- Search Methods in Artificial Intelligence
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Summary
So far in this book we have not thought of plans as explicit representations. True, we have referred to the path from the start node in the state space to the goal node as a plan, but that has been represented as a sequence of states. When we looked at goal trees we could also think of the solution subtree as a plan. Likewise, the strategy found by the SSS* algorithm is also a plan. But even here the intent of the problem solving agent is captured in terms of what state or board position will the player move to.
In this chapter we see problem solving from the perspective of actions. We represent plans explicitly, and the agent goes about the task of synthesizing a plan. At the simplest level, a plan is a sequence of named actions designed to achieve a goal. We begin with planning in the state space and move on to searching in the plan space. We also look at a two stage approach to planning with the algorithms Graphplan and Satplan.
We end with a brief look at some directions in planning in richer domains.
An intelligent agent acts in the world to achieve its goals. Given the state of the world it is in, and given the goals it has, it has to choose an appropriate set of actions. The process of selecting those actions is called planning. Planning is the reasoning side of acting (Ghallab, Nau, and Traverso, 2004). Planning and acting do not happen in isolation. A third process is an integral part of intelligent agency – perceiving. An agent senses the world it is operating in, deliberates upon its goals to produce a plan, and executes the actions in the plan. This is often referred to as the sense–deliberate–act cycle. The entire process may need to be monitored by the agent. Since the world may be changing owing to other agencies, it may even have to modify its plans on the fly.
There has been considerable work on autonomous agents that plan their activity. This became necessary in space applications where communication with Earth takes too long, necessitating autonomy. This was the case with the Mars rovers experiments by NASA, and even ten years after landing on Mars the rover Curiosity is still active.
Acknowledgements
- Laurence Gautier, Centre de Sciences Humaines
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3 - Re-legitimising minority rights: The campaign for Aligarh Muslim University’s minority status
- Laurence Gautier, Centre de Sciences Humaines
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- Between Nation and ‘Community'
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I have promised the House that I will take every step to eradicate the communal and reactionary element in the Aligarh University.
—M. C. Chagla, education minister, to Gulzari Lal Nanda, home ministerThe problem of the Muslim University is not the problem of any particular group or organisation of the Muslims. It has become the problem of the entire Muslim community of India.
—Maulana Abul Lais, Jamaat-e-IslamiLate April 1965: A students’ protest escalates into a violent attack against Ali Yavar Jung, AMU's vice-chancellor. The very next day, the education minister, M. C. Chagla, announces the closure of the institution and the suspension of the University Act. He then swiftly passes an ordinance to extend government's control over AMU and to ‘eradicate’—he promises—‘the communal and reactionary element’ in the university.
Narrated in this way, the incident might appear to be the culmination of internal rivalries that unfolded after partition over the re-orientation of the university. Yet the controversies erupting at AMU did not remain confined to the university for very long. The adoption of the government's ordinance soon sparked an unprecedented wave of mobilisation, within and beyond the campus, which rapidly transformed into a large-scale campaign for the recognition of AMU's minority status. As the president of the Jamaat-e-Islami argued, the problem of the university quickly became, in the eyes of many university members and Muslim leaders, ‘the problem of the entire Muslim community of India’.
Mushirul Hasan regards the 1965 protests at AMU as a symptom of the sectarian passions that characterised the post-Nehruvian period. Like him, other scholars interpret the post-Nehruvian period as one of crisis—a crisis of the state's legitimacy and democracy, epitomised by the emergency, and a crisis of Indian secularism, symbolised by the rise of communal violence and the coming to power of the Hindu right in the 1990s. Sunil Khilnani, for instance, contrasts Nehru's supposed achievements—the establishment of a strong state and a stable social order—with the rise of political competition and the emergence of group-based demands in the latter period. He argues that this political competition encouraged politicians to resort, increasingly, to identity politics in order to mobilise their electorates. For him, this process of identity creation was dangerous as it often led to conflict, not just competition, thereby corrupting democratic principles.
List of abbreviations
- Laurence Gautier, Centre de Sciences Humaines
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3 - Blind Search
- Deepak Khemani, IIT Madras, Chennai
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- Search Methods in Artificial Intelligence
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Summary
In this chapter we introduce the basic machinery needed for search. We devise algorithms for navigating the implicit search space and look at their properties. One distinctive feature of the algorithms in this chapter is that they are all blind or uninformed. This means that the way the algorithms search the space is always the same irrespective of the problem instance being solved.
We look at a few variations and analyse them on the four parameters we defined in the last chapter: completeness, quality of solution, time complexity, and space complexity. We observe that complexity becomes a stumbling block, as our principal foe CombEx inevitably rears its head. We end by making a case for different approaches to fight CombEx in the chapters that follow.
In the last chapter we looked at the notion of search spaces. Search spaces, as shown in Figure 2.2, are trees corresponding to the different traversals possible in the state space or the solution space. In this chapter we begin by constructing the machinery, viz. algorithms, for navigating this space. We begin our study with the corresponding tiny state space shown in Figure 3.1.
The tiny search problem has seven nodes, including the start node S, the goal node G, and five other nodes named A, B, C, D, and E. Without any loss of generality, let us assume that the nodes are states in a state space. The algorithms apply to the solution space as well. The left side of the figure describes the MoveGen function with the notation Node → (list of neighbours). On the right side is the corresponding graph which, remember, is implicit and not given upfront. The algorithm itself works with the MoveGen function and also the GoalTest function. The latter, for this example, simply knows that state G is the goal node. For configuration problems like the N-queens, it will need to inspect the node given as the argument.
The search space that an algorithm explores is implicit. It is generated on the fly by the MoveGen function, as described in Algorithm 2.1. The candidates generated are added to what is traditionally called OPEN, from where they are picked one by one for inspection. In this chapter we represent OPEN as a list data structure.
Contents
- Laurence Gautier, Centre de Sciences Humaines
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8 - Chess and Other Games
- Deepak Khemani, IIT Madras, Chennai
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Summary
Acting rationally in a multi-agent scenario has long been studied under the umbrella of games. Game theory is a study of decision making in the face of other players, usually adversaries of the given player or agent. Economists study games to understand the behaviour of governments and corporates when everyone has the goal of maximizing their own payoffs. A stark example is the choice of NATO countries refusing to act directly against the Russian invasion of Ukraine given the threat of nuclear escalation.
In this chapter we turn our attention to the simplified situation in which the agent has one adversary. Board games like chess exemplify this scenario and have received considerable attention in the world of computing. In such games each player makes a move on her turn, and the information is complete since both players can see the board, and where the outcome is a win for one and a loss for the other. We look at the most popular algorithms for playing board games.
Chess has long fascinated humankind as a game of strategy and skill. It was probably invented in India in the sixth century in the Gupta empire when it was known as chaturanga. A comprehensive account of its history was penned in 1913 by H.J.R. Murray (2015). The name refers to the four divisions an army may have. The infantry includes the pawns, the knights make up the cavalry, the rooks correspond to the chariotry, and the bishops the elephantry (though the Hindi word for the piece calls it a camel). In Persia the name was shortened to chatrang. This in turn transformed to shatranj as exemplified in the 1924 story by Munshi Premchand (2020) and the film of the same name by Satyajit Ray, Shatranj Ke Khiladi (The Chess Players). It became customary to warn the king by uttering shāh (the Persian word for king) which became check, and the word mate came from māt which means defeated. Checkmate is derived from shāh māt which says that the king has been vanquished.
Table 8.1 lists the names of the chess pieces in Sanskrit, Persian, Arabic, and English (Murray, 2015). In Hindi users often say oont (camel) for bishop and haathi (elephant) for rook.
From India the game spread to Persia, and then to Russia, Europe, and East Asia around the ninth century.
5 - Uplifting backward Muslims: The new consensus?
- Laurence Gautier, Centre de Sciences Humaines
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- Between Nation and ‘Community'
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The University shall have the powers … to promote especially the educational and cultural advancement of the Muslims of India.
—AMU (Amendment) Act (1981)The way the traditional Muslim leaders reacted to the Babri Masjid issue made me think that there was an urgent need for the Dalit Muslims to come up with their own leaders, championing bread-and-butter concerns rather than emotional and symbolic issues…. Our first concern should be jobs and education for our people … the traditional Muslim leadership has been championing merely symbolic issues, be it the cause of Urdu, the minority character of the Aligarh Muslim University, Muslim Personal Law or the Babri Masjid.
—Ejaz Ali, leader of the All-India Backward Muslim MorchaThe demolition of the Babri Masjid in December 1992 constituted for many Indian Muslims, as well as for a great many other Indian citizens, a shocking landmark moment in the history of the republic. For Mushirul Hasan, Muslims’ response to this ‘cataclysmic event’ was one of ‘anger, indignation and disbelief ‘. The demolition laid bare the state's failure to uphold the rule of law and to protect its minority population from the attacks—physical and symbolic—of self-legitimising Hindutva forces. For many, this was a devastating blow not only against Muslims but against the very idea of India as a secular democracy.
This was also a moment of reckoning for Muslim leaders. A number of individuals and organisations called for a radical transformation of Muslim politics. In their minds, established Muslim leaders were partly to blame for this ‘cataclysm’. By focusing on divisive ‘emotive and symbolic issues’, they had contributed to the sharp rise of communal tensions and failed to protect Muslims. The demolition of the Babri Masjid thus prompted the emergence of new backward Muslim (pasmanda) organisations, such as Ejaz Ali's All-India Backward Muslim Morcha, which rejected these ‘traditional Muslim leaders’ and their claim to speak for all Muslims. The ‘emotive and symbolic issues’ that they stood for (including AMU's status) mattered to Muslim elites alone, they suggested. These organisations instead called pasmanda Muslims to ‘come up with their own leaders’ to champion ‘bread-and-butter issues’.
7 - Problem Decomposition
- Deepak Khemani, IIT Madras, Chennai
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- Search Methods in Artificial Intelligence
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Summary
So far our approach to solving problems has been characterized by state space search. We are in a given state, and we have a desired or goal state. We have a set of moves available to us which allow us to navigate from one state to another. We search through the possible moves, and we employ a heuristic function to explore the space in an informed manner. In this chapter we study two different approaches to problem solving.
One, with emphasis on knowledge that we can acquire from domain experts. We look at mechanisms to harness and exploit such knowledge. In the last century in the 1980s, an approach to express knowledge in the form of if–then rules gained momentum, and many systems were developed under the umbrella of expert systems. Although only a few lived up to expert level expectations, the technology matured into an approach to allow human users to impart their knowledge into systems. The key to this approach was the Rete algorithm that allowed an inference engine to efficiently match rules with data.
The other looks at problem solving from a teleological perspective. That is, we look at a goal based approach which investigates what needs to be done to achieve a goal. In that sense, it is reasoning backwards from the goal. We look at how problems can be formulated as goal trees, and an algorithm AO* to solve them.
The search algorithms we have studied so far take a holistic view of a state representing the given situation. In practice, states are represented in some language in which the different constituents are described. The state description is essentially a set of statements. As the importance of knowledge for problem solving became evident, using rules to spot patterns in the description and proposing actions emerged as a problem solving strategy.
Pattern Directed Inference Systems
An approach to problem solving that was developed in the mid-1970s was called pattern directed inference systems (Waterman and Hayes-Roth, 1978). The basic idea is that patterns in a given state are associated with actions.
Conclusion
- Laurence Gautier, Centre de Sciences Humaines
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This book has highlighted the role of AMU and JMI as political sites that served as symbols for the Muslim community as well as crucibles for competing conceptions of Muslim citizenship and identity in post-independence India. While historical works on post-independence India have largely focused on the long aftermath of partition, this book has shifted attention to the different ways in which these institutions channelled part of the Indian Muslims’ responses to partition as well as to the emergence of the Indian nation state.
The book argued, first, that AMU and JMI constituted platforms to imagine the nation as much as the Muslim qaum. As state-sponsored and Muslim-majority institutions, they found themselves at a symbolic juncture between central state authorities and the Muslim population. After partition, many at JMI and AMU made it their mission to develop an inclusive conception of the nation, of which Muslims would be a full part. In the aftermath of partition, they presented Hindu–Muslim reconciliation as the cornerstone of the nation's construction. At a time when many ordinary and state actors repeatedly questioned Muslims’ Indianness, they articulated composite representations of India's past and culture. In so doing, they asserted Muslims’ right to belong to the Indian nation, thereby rejecting exclusionary interpretations of ‘Indianness’ defined in majoritarian terms.
Their efforts to promote national integration did not result merely from top-down state-driven policies. This book has argued that JMI and AMU members actively contributed, through their educational policies and their interactions with state actors, to shaping ideas of the nation, of secularism and of projects of ‘emotional integration’. In so doing, this work calls for a revision of our understanding of the so-called Nehruvian secularism. Instead of focusing on Nehru alone, it hints at the wide range of actors and institutions, including Muslim ones, involved in the making of the ‘Nehruvian’ discourse on national integration. Just as historians have pointed out the limits of Nehru's capacity to influence Congress party members and state authorities, I suggest that further research is required to locate Nehru within a wider network of institutional and non-institutional actors in order to understand how these different actors contributed to defining what came to be known as the ‘Nehruvian’ discourse on national integration.
Index
- Deepak Khemani, IIT Madras, Chennai
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- Search Methods in Artificial Intelligence
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- 01 November 2025, pp 461-473
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