Symbolic Artificial Intelligence

In synthetic intelligence, symbolic expert system (likewise called classical expert system or logic-based artificial intelligence) [1] [2] is the term for the collection of all approaches in expert system research study that are based upon top-level symbolic (human-readable) representations of problems, logic and search. [3] Symbolic AI utilized tools such as reasoning programming, production rules, semantic internet and frames, and it developed applications such as knowledge-based systems (in particular, skilled systems), symbolic mathematics, automated theorem provers, ontologies, the semantic web, and automated preparation and scheduling systems. The Symbolic AI paradigm led to critical ideas in search, symbolic shows languages, representatives, multi-agent systems, the semantic web, and the strengths and limitations of formal understanding and thinking systems.

Symbolic AI was the dominant paradigm of AI research study from the mid-1950s up until the mid-1990s. [4] Researchers in the 1960s and the 1970s were persuaded that symbolic techniques would ultimately prosper in producing a maker with artificial basic intelligence and considered this the supreme goal of their field. [citation required] An early boom, with early successes such as the Logic Theorist and Samuel’s Checkers Playing Program, resulted in unrealistic expectations and guarantees and was followed by the first AI Winter as funding dried up. [5] [6] A second boom (1969-1986) took place with the increase of professional systems, their promise of capturing corporate knowledge, and an enthusiastic corporate accept. [7] [8] That boom, and some early successes, e.g., with XCON at DEC, was followed once again by later on disappointment. [8] Problems with problems in knowledge acquisition, maintaining large knowledge bases, and brittleness in managing out-of-domain issues developed. Another, second, AI Winter (1988-2011) followed. [9] Subsequently, AI scientists focused on attending to underlying problems in managing uncertainty and in knowledge acquisition. [10] Uncertainty was attended to with formal techniques such as hidden Markov designs, Bayesian thinking, and statistical relational knowing. [11] [12] Symbolic device discovering resolved the knowledge acquisition issue with contributions consisting of Version Space, Valiant’s PAC learning, Quinlan’s ID3 decision-tree learning, case-based learning, and inductive logic programming to find out relations. [13]

Neural networks, a subsymbolic technique, had been pursued from early days and reemerged highly in 2012. Early examples are Rosenblatt’s perceptron learning work, the backpropagation work of Rumelhart, Hinton and Williams, [14] and operate in convolutional neural networks by LeCun et al. in 1989. [15] However, neural networks were not deemed successful up until about 2012: «Until Big Data became prevalent, the basic agreement in the Al neighborhood was that the so-called neural-network method was hopeless. Systems simply didn’t work that well, compared to other approaches. … A transformation came in 2012, when a number of people, including a team of scientists dealing with Hinton, exercised a way to use the power of GPUs to immensely increase the power of neural networks.» [16] Over the next several years, deep knowing had amazing success in handling vision, speech recognition, speech synthesis, image generation, and device translation. However, because 2020, as intrinsic troubles with predisposition, explanation, comprehensibility, and effectiveness ended up being more evident with deep learning approaches; an increasing number of AI scientists have required integrating the finest of both the symbolic and neural network techniques [17] [18] and resolving locations that both approaches have trouble with, such as sensible reasoning. [16]

A short history of symbolic AI to today day follows below. Time periods and titles are drawn from Henry Kautz’s 2020 AAAI Robert S. Engelmore Memorial Lecture [19] and the longer Wikipedia article on the History of AI, with dates and titles differing somewhat for increased clearness.

The first AI summer season: unreasonable exuberance, 1948-1966

Success at early efforts in AI happened in three primary locations: synthetic neural networks, understanding representation, and heuristic search, adding to high expectations. This area summarizes Kautz’s reprise of early AI history.

Approaches influenced by human or animal cognition or behavior

Cybernetic methods attempted to duplicate the feedback loops in between animals and their environments. A robotic turtle, with sensors, motors for driving and guiding, and 7 vacuum tubes for control, based on a preprogrammed neural internet, was built as early as 1948. This work can be viewed as an early precursor to later work in neural networks, support knowing, and located robotics. [20]

An essential early symbolic AI program was the Logic theorist, written by Allen Newell, Herbert Simon and Cliff Shaw in 1955-56, as it was able to show 38 elementary theorems from Whitehead and Russell’s Principia Mathematica. Newell, Simon, and Shaw later generalized this work to produce a domain-independent problem solver, GPS (General Problem Solver). GPS solved issues represented with official operators via state-space search using means-ends analysis. [21]

During the 1960s, symbolic approaches accomplished great success at replicating intelligent habits in structured environments such as game-playing, symbolic mathematics, and theorem-proving. AI research study was concentrated in four institutions in the 1960s: Carnegie Mellon University, Stanford, MIT and (later) University of Edinburgh. Each one developed its own style of research study. Earlier approaches based on cybernetics or synthetic neural networks were abandoned or pushed into the background.

Herbert Simon and Allen Newell studied human problem-solving abilities and attempted to formalize them, and their work laid the structures of the field of synthetic intelligence, as well as cognitive science, operations research and management science. Their research team utilized the results of psychological experiments to develop programs that simulated the strategies that people utilized to resolve problems. [22] [23] This tradition, centered at Carnegie Mellon University would eventually culminate in the development of the Soar architecture in the center 1980s. [24] [25]

Heuristic search

In addition to the highly specialized domain-specific sort of knowledge that we will see later utilized in specialist systems, early symbolic AI researchers discovered another more basic application of knowledge. These were called heuristics, general rules that assist a search in promising instructions: «How can non-enumerative search be practical when the underlying issue is greatly tough? The method promoted by Simon and Newell is to utilize heuristics: quick algorithms that might stop working on some inputs or output suboptimal options.» [26] Another essential advance was to discover a method to use these heuristics that guarantees a solution will be discovered, if there is one, not standing up to the occasional fallibility of heuristics: «The A * algorithm provided a basic frame for complete and ideal heuristically assisted search. A * is used as a subroutine within almost every AI algorithm today however is still no magic bullet; its guarantee of completeness is bought at the cost of worst-case exponential time. [26]

Early deal with knowledge representation and reasoning

Early work covered both applications of official thinking stressing first-order reasoning, together with attempts to manage common-sense reasoning in a less official manner.

Modeling official reasoning with reasoning: the «neats»

Unlike Simon and Newell, John McCarthy felt that makers did not require to mimic the specific mechanisms of human idea, but might instead attempt to find the essence of abstract thinking and analytical with reasoning, [27] despite whether people used the very same algorithms. [a] His lab at Stanford (SAIL) concentrated on utilizing official reasoning to fix a variety of issues, consisting of knowledge representation, planning and knowing. [31] Logic was likewise the focus of the work at the University of Edinburgh and in other places in Europe which caused the development of the programming language Prolog and the science of logic programs. [32] [33]

Modeling implicit common-sense understanding with frames and scripts: the «scruffies»

Researchers at MIT (such as Marvin Minsky and Seymour Papert) [34] [35] [6] discovered that fixing hard problems in vision and natural language processing required ad hoc solutions-they argued that no simple and general principle (like reasoning) would capture all the aspects of smart habits. Roger Schank described their «anti-logic» approaches as «shabby» (instead of the «neat» paradigms at CMU and Stanford). [36] [37] Commonsense knowledge bases (such as Doug Lenat’s Cyc) are an example of «shabby» AI, because they must be built by hand, one complicated principle at a time. [38] [39] [40]

The very first AI winter season: crushed dreams, 1967-1977

The first AI winter season was a shock:

During the first AI summertime, lots of people believed that device intelligence might be accomplished in simply a couple of years. The Defense Advance Research Projects Agency (DARPA) released programs to support AI research to use AI to resolve issues of national security; in particular, to automate the translation of Russian to English for intelligence operations and to develop autonomous tanks for the battlefield. Researchers had actually started to realize that accomplishing AI was going to be much harder than was expected a years previously, but a combination of hubris and disingenuousness led numerous university and think-tank researchers to accept financing with guarantees of deliverables that they ought to have known they could not satisfy. By the mid-1960s neither helpful natural language translation systems nor autonomous tanks had actually been produced, and a dramatic reaction embeded in. New DARPA management canceled existing AI funding programs.

Beyond the United States, the most fertile ground for AI research was the UK. The AI winter season in the United Kingdom was spurred on not a lot by dissatisfied military leaders as by competing academics who viewed AI scientists as charlatans and a drain on research study funding. A teacher of applied mathematics, Sir James Lighthill, was commissioned by Parliament to examine the state of AI research in the nation. The report mentioned that all of the issues being dealt with in AI would be much better handled by researchers from other disciplines-such as used mathematics. The report also declared that AI successes on toy problems might never ever scale to real-world applications due to combinatorial explosion. [41]

The 2nd AI summer: knowledge is power, 1978-1987

Knowledge-based systems

As constraints with weak, domain-independent techniques ended up being more and more obvious, [42] scientists from all three traditions started to construct knowledge into AI applications. [43] [7] The knowledge transformation was driven by the realization that understanding underlies high-performance, domain-specific AI applications.

Edward Feigenbaum stated:

– «In the knowledge lies the power.» [44]
to explain that high efficiency in a particular domain requires both basic and extremely domain-specific understanding. Ed Feigenbaum and Doug Lenat called this The Knowledge Principle:

( 1) The Knowledge Principle: if a program is to perform an intricate task well, it must know a lot about the world in which it operates.
( 2) A possible extension of that principle, called the Breadth Hypothesis: there are 2 additional abilities necessary for intelligent behavior in unforeseen scenarios: drawing on progressively general understanding, and analogizing to specific however distant knowledge. [45]

Success with professional systems

This «knowledge revolution» resulted in the advancement and deployment of professional systems (introduced by Edward Feigenbaum), the very first commercially successful form of AI software. [46] [47] [48]

Key expert systems were:

DENDRAL, which discovered the structure of natural particles from their chemical formula and mass spectrometer readings.
MYCIN, which detected bacteremia – and recommended further lab tests, when essential – by interpreting lab results, client history, and medical professional observations. «With about 450 guidelines, MYCIN had the ability to carry out along with some professionals, and considerably better than junior physicians.» [49] INTERNIST and CADUCEUS which dealt with internal medication medical diagnosis. Internist attempted to catch the expertise of the chairman of internal medication at the University of Pittsburgh School of Medicine while CADUCEUS could ultimately diagnose approximately 1000 various diseases.
– GUIDON, which demonstrated how an understanding base constructed for specialist problem fixing could be repurposed for mentor. [50] XCON, to set up VAX computers, a then laborious process that could take up to 90 days. XCON decreased the time to about 90 minutes. [9]
DENDRAL is considered the first expert system that depend on knowledge-intensive analytical. It is described below, by Ed Feigenbaum, from a Communications of the ACM interview, Interview with Ed Feigenbaum:

One of individuals at Stanford thinking about computer-based designs of mind was Joshua Lederberg, the 1958 Nobel Prize winner in genes. When I informed him I desired an induction «sandbox», he said, «I have simply the one for you.» His lab was doing mass spectrometry of amino acids. The question was: how do you go from looking at the spectrum of an amino acid to the chemical structure of the amino acid? That’s how we began the DENDRAL Project: I was excellent at heuristic search approaches, and he had an algorithm that was good at generating the chemical problem area.

We did not have a grandiose vision. We worked bottom up. Our chemist was Carl Djerassi, inventor of the chemical behind the birth control pill, and likewise among the world’s most appreciated mass spectrometrists. Carl and his postdocs were world-class specialists in mass spectrometry. We began to include to their knowledge, creating knowledge of engineering as we went along. These experiments amounted to titrating DENDRAL increasingly more understanding. The more you did that, the smarter the program became. We had great outcomes.

The generalization was: in the knowledge lies the power. That was the huge idea. In my career that is the huge, «Ah ha!,» and it wasn’t the method AI was being done formerly. Sounds basic, but it’s probably AI’s most effective generalization. [51]

The other professional systems mentioned above came after DENDRAL. MYCIN exemplifies the classic professional system architecture of a knowledge-base of rules paired to a symbolic thinking system, consisting of making use of certainty aspects to manage unpredictability. GUIDON demonstrates how an explicit knowledge base can be repurposed for a second application, tutoring, and is an example of an intelligent tutoring system, a specific type of knowledge-based application. Clancey revealed that it was not adequate just to use MYCIN’s guidelines for direction, however that he likewise required to add rules for dialogue management and trainee modeling. [50] XCON is considerable due to the fact that of the countless dollars it conserved DEC, which triggered the expert system boom where most all significant corporations in the US had professional systems groups, to catch corporate expertise, protect it, and automate it:

By 1988, DEC’s AI group had 40 expert systems deployed, with more on the way. DuPont had 100 in use and 500 in advancement. Nearly every major U.S. corporation had its own Al group and was either using or investigating professional systems. [49]

Chess expert knowledge was encoded in Deep Blue. In 1996, this enabled IBM’s Deep Blue, with the aid of symbolic AI, to win in a video game of chess versus the world champion at that time, Garry Kasparov. [52]

Architecture of knowledge-based and professional systems

A crucial element of the system architecture for all expert systems is the knowledge base, which stores truths and guidelines for problem-solving. [53] The simplest technique for a skilled system understanding base is merely a collection or network of production rules. Production guidelines link symbols in a relationship comparable to an If-Then statement. The professional system processes the rules to make deductions and to identify what extra details it needs, i.e. what concerns to ask, using human-readable signs. For instance, OPS5, CLIPS and their followers Jess and Drools operate in this fashion.

Expert systems can operate in either a forward chaining – from proof to conclusions – or backwards chaining – from objectives to needed data and requirements – manner. More sophisticated knowledge-based systems, such as Soar can also carry out meta-level reasoning, that is thinking about their own thinking in regards to deciding how to fix problems and keeping an eye on the success of problem-solving strategies.

Blackboard systems are a second sort of knowledge-based or professional system architecture. They model a community of professionals incrementally contributing, where they can, to solve an issue. The issue is represented in several levels of abstraction or alternate views. The specialists (understanding sources) offer their services whenever they recognize they can contribute. Potential analytical actions are represented on a program that is upgraded as the issue circumstance changes. A controller decides how beneficial each contribution is, and who need to make the next analytical action. One example, the BB1 blackboard architecture [54] was initially influenced by research studies of how people plan to perform several jobs in a trip. [55] A development of BB1 was to use the exact same chalkboard model to fixing its control issue, i.e., its controller performed meta-level thinking with understanding sources that kept an eye on how well a strategy or the problem-solving was proceeding and might switch from one method to another as conditions – such as objectives or times – altered. BB1 has been used in several domains: building and construction site planning, intelligent tutoring systems, and real-time client tracking.

The second AI winter, 1988-1993

At the height of the AI boom, companies such as Symbolics, LMI, and Texas Instruments were selling LISP makers specifically targeted to speed up the development of AI applications and research. In addition, several expert system companies, such as Teknowledge and Inference Corporation, were offering professional system shells, training, and consulting to corporations.

Unfortunately, the AI boom did not last and Kautz best describes the second AI winter season that followed:

Many reasons can be provided for the arrival of the 2nd AI winter season. The hardware companies failed when far more economical basic Unix workstations from Sun together with excellent compilers for LISP and Prolog came onto the market. Many industrial deployments of specialist systems were stopped when they showed too expensive to maintain. Medical professional systems never caught on for numerous factors: the problem in keeping them as much as date; the obstacle for medical professionals to find out how to utilize an overwelming variety of different specialist systems for various medical conditions; and possibly most crucially, the reluctance of physicians to rely on a computer-made diagnosis over their gut instinct, even for specific domains where the expert systems might outperform an average physician. Equity capital cash deserted AI virtually over night. The world AI conference IJCAI hosted a huge and luxurious trade show and thousands of nonacademic attendees in 1987 in Vancouver; the main AI conference the list below year, AAAI 1988 in St. Paul, was a small and strictly academic affair. [9]

Adding in more extensive foundations, 1993-2011

Uncertain thinking

Both analytical techniques and extensions to reasoning were tried.

One analytical technique, concealed Markov models, had already been promoted in the 1980s for speech acknowledgment work. [11] Subsequently, in 1988, Judea Pearl popularized making use of Bayesian Networks as a noise but effective way of handling uncertain thinking with his publication of the book Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. [56] and Bayesian techniques were used effectively in specialist systems. [57] Even later on, in the 1990s, statistical relational knowing, a technique that combines likelihood with sensible solutions, permitted possibility to be combined with first-order reasoning, e.g., with either Markov Logic Networks or Probabilistic Soft Logic.

Other, non-probabilistic extensions to first-order logic to assistance were also attempted. For example, non-monotonic reasoning could be utilized with reality maintenance systems. A truth maintenance system tracked assumptions and validations for all reasonings. It enabled inferences to be withdrawn when assumptions were discovered to be incorrect or a contradiction was obtained. Explanations might be offered for an inference by discussing which rules were used to produce it and then continuing through underlying inferences and rules all the way back to root assumptions. [58] Lofti Zadeh had actually introduced a different sort of extension to handle the representation of uncertainty. For example, in deciding how «heavy» or «tall» a male is, there is frequently no clear «yes» or «no» answer, and a predicate for heavy or tall would instead return values in between 0 and 1. Those values represented to what degree the predicates were true. His fuzzy logic further offered a way for propagating combinations of these values through logical solutions. [59]

Machine knowing

Symbolic machine discovering approaches were investigated to address the understanding acquisition bottleneck. Among the earliest is Meta-DENDRAL. Meta-DENDRAL utilized a generate-and-test method to generate possible rule hypotheses to test against spectra. Domain and task understanding decreased the variety of prospects evaluated to a manageable size. Feigenbaum described Meta-DENDRAL as

… the conclusion of my dream of the early to mid-1960s involving theory development. The conception was that you had an issue solver like DENDRAL that took some inputs and produced an output. In doing so, it utilized layers of understanding to steer and prune the search. That understanding got in there because we interviewed individuals. But how did individuals get the knowledge? By looking at thousands of spectra. So we wanted a program that would look at countless spectra and infer the knowledge of mass spectrometry that DENDRAL might utilize to fix specific hypothesis development issues. We did it. We were even able to publish brand-new knowledge of mass spectrometry in the Journal of the American Chemical Society, giving credit just in a footnote that a program, Meta-DENDRAL, actually did it. We had the ability to do something that had actually been a dream: to have a computer program created a brand-new and publishable piece of science. [51]

In contrast to the knowledge-intensive technique of Meta-DENDRAL, Ross Quinlan invented a domain-independent technique to statistical classification, choice tree learning, beginning first with ID3 [60] and then later extending its abilities to C4.5. [61] The choice trees created are glass box, interpretable classifiers, with human-interpretable category guidelines.

Advances were made in comprehending machine learning theory, too. Tom Mitchell introduced version area learning which explains learning as an explore a space of hypotheses, with upper, more general, and lower, more particular, boundaries encompassing all practical hypotheses constant with the examples seen up until now. [62] More formally, Valiant introduced Probably Approximately Correct Learning (PAC Learning), a structure for the mathematical analysis of maker learning. [63]

Symbolic maker learning included more than finding out by example. E.g., John Anderson provided a cognitive model of human knowing where skill practice leads to a collection of rules from a declarative format to a procedural format with his ACT-R cognitive architecture. For example, a trainee may discover to use «Supplementary angles are 2 angles whose procedures sum 180 degrees» as several different procedural rules. E.g., one rule might say that if X and Y are additional and you know X, then Y will be 180 – X. He called his technique «understanding compilation». ACT-R has been utilized successfully to design elements of human cognition, such as discovering and retention. ACT-R is likewise used in intelligent tutoring systems, called cognitive tutors, to successfully teach geometry, computer shows, and algebra to school children. [64]

Inductive logic shows was another method to finding out that enabled reasoning programs to be manufactured from input-output examples. E.g., Ehud Shapiro’s MIS (Model Inference System) might synthesize Prolog programs from examples. [65] John R. Koza used genetic algorithms to program synthesis to create hereditary programs, which he utilized to synthesize LISP programs. Finally, Zohar Manna and Richard Waldinger supplied a more basic technique to program synthesis that manufactures a functional program in the course of showing its specifications to be right. [66]

As an alternative to logic, Roger Schank introduced case-based thinking (CBR). The CBR approach detailed in his book, Dynamic Memory, [67] focuses initially on keeping in mind key analytical cases for future usage and generalizing them where suitable. When faced with a new issue, CBR recovers the most comparable previous case and adjusts it to the specifics of the present problem. [68] Another option to logic, hereditary algorithms and genetic programming are based upon an evolutionary model of learning, where sets of rules are encoded into populations, the rules govern the habits of individuals, and choice of the fittest prunes out sets of inappropriate rules over numerous generations. [69]

Symbolic machine learning was applied to discovering principles, rules, heuristics, and problem-solving. Approaches, aside from those above, include:

1. Learning from guideline or advice-i.e., taking human guideline, impersonated suggestions, and identifying how to operationalize it in specific situations. For example, in a video game of Hearts, discovering exactly how to play a hand to «prevent taking points.» [70] 2. Learning from exemplars-improving efficiency by accepting subject-matter expert (SME) feedback during training. When problem-solving fails, querying the expert to either discover a new prototype for problem-solving or to find out a brand-new explanation as to precisely why one exemplar is more appropriate than another. For instance, the program Protos found out to diagnose tinnitus cases by connecting with an audiologist. [71] 3. Learning by analogy-constructing problem options based on similar issues seen in the past, and then modifying their services to fit a new scenario or domain. [72] [73] 4. Apprentice learning systems-learning unique solutions to problems by observing human problem-solving. Domain understanding explains why novel solutions are right and how the service can be generalized. LEAP discovered how to develop VLSI circuits by observing human designers. [74] 5. Learning by discovery-i.e., creating jobs to carry out experiments and after that discovering from the results. Doug Lenat’s Eurisko, for example, found out heuristics to beat human players at the Traveller role-playing video game for 2 years in a row. [75] 6. Learning macro-operators-i.e., looking for helpful macro-operators to be discovered from sequences of basic problem-solving actions. Good macro-operators simplify problem-solving by permitting issues to be solved at a more abstract level. [76]
Deep knowing and neuro-symbolic AI 2011-now

With the rise of deep knowing, the symbolic AI method has been compared to deep learning as complementary «… with parallels having actually been drawn lot of times by AI researchers between Kahneman’s research study on human reasoning and decision making – reflected in his book Thinking, Fast and Slow – and the so-called «AI systems 1 and 2″, which would in principle be designed by deep learning and symbolic reasoning, respectively.» In this view, symbolic thinking is more apt for deliberative reasoning, planning, and description while deep learning is more apt for quick pattern recognition in perceptual applications with noisy information. [17] [18]

Neuro-symbolic AI: integrating neural and symbolic methods

Neuro-symbolic AI efforts to incorporate neural and symbolic architectures in a manner that addresses strengths and weaknesses of each, in a complementary style, in order to support robust AI capable of thinking, learning, and cognitive modeling. As argued by Valiant [77] and many others, [78] the effective construction of rich computational cognitive models requires the mix of sound symbolic thinking and effective (machine) knowing models. Gary Marcus, similarly, argues that: «We can not construct rich cognitive designs in a sufficient, automated method without the triumvirate of hybrid architecture, abundant anticipation, and advanced techniques for thinking.», [79] and in specific: «To construct a robust, knowledge-driven technique to AI we should have the machinery of symbol-manipulation in our toolkit. Excessive of helpful knowledge is abstract to make do without tools that represent and control abstraction, and to date, the only equipment that we understand of that can control such abstract knowledge reliably is the device of symbol manipulation. » [80]

Henry Kautz, [19] Francesca Rossi, [81] and Bart Selman [82] have also argued for a synthesis. Their arguments are based upon a requirement to address the two type of thinking talked about in Daniel Kahneman’s book, Thinking, Fast and Slow. Kahneman explains human thinking as having two parts, System 1 and System 2. System 1 is fast, automatic, instinctive and unconscious. System 2 is slower, detailed, and explicit. System 1 is the kind used for pattern recognition while System 2 is far much better matched for preparation, reduction, and deliberative thinking. In this view, deep knowing finest models the first kind of believing while symbolic thinking finest designs the second kind and both are needed.

Garcez and Lamb explain research study in this area as being continuous for at least the previous twenty years, [83] dating from their 2002 book on neurosymbolic learning systems. [84] A series of workshops on neuro-symbolic reasoning has been held every year considering that 2005, see http://www.neural-symbolic.org/ for information.

In their 2015 paper, Neural-Symbolic Learning and Reasoning: Contributions and Challenges, Garcez et al. argue that:

The combination of the symbolic and connectionist paradigms of AI has been pursued by a fairly little research community over the last 2 decades and has yielded several considerable outcomes. Over the last decade, neural symbolic systems have been revealed efficient in getting rid of the so-called propositional fixation of neural networks, as McCarthy (1988) put it in reaction to Smolensky (1988 ); see also (Hinton, 1990). Neural networks were shown capable of representing modal and temporal logics (d’Avila Garcez and Lamb, 2006) and pieces of first-order logic (Bader, Hitzler, Hölldobler, 2008; d’Avila Garcez, Lamb, Gabbay, 2009). Further, neural-symbolic systems have been used to a variety of issues in the areas of bioinformatics, control engineering, software confirmation and adjustment, visual intelligence, ontology knowing, and computer video games. [78]

Approaches for combination are varied. Henry Kautz’s taxonomy of neuro-symbolic architectures, together with some examples, follows:

– Symbolic Neural symbolic-is the present technique of many neural designs in natural language processing, where words or subword tokens are both the supreme input and output of large language designs. Examples include BERT, RoBERTa, and GPT-3.
– Symbolic [Neural] -is exhibited by AlphaGo, where symbolic methods are used to call neural methods. In this case the symbolic method is Monte Carlo tree search and the neural strategies learn how to assess game positions.
– Neural|Symbolic-uses a neural architecture to interpret perceptual information as signs and relationships that are then reasoned about symbolically.
– Neural: Symbolic → Neural-relies on symbolic reasoning to generate or identify training information that is subsequently found out by a deep learning design, e.g., to train a neural design for symbolic computation by utilizing a Macsyma-like symbolic mathematics system to create or identify examples.
– Neural _ Symbolic -utilizes a neural internet that is created from symbolic rules. An example is the Neural Theorem Prover, [85] which constructs a neural network from an AND-OR evidence tree created from understanding base rules and terms. Logic Tensor Networks [86] also fall into this classification.
– Neural [Symbolic] -permits a neural design to straight call a symbolic reasoning engine, e.g., to carry out an action or evaluate a state.

Many key research concerns stay, such as:

– What is the very best way to integrate neural and symbolic architectures? [87]- How should symbolic structures be represented within neural networks and drawn out from them?
– How should sensible knowledge be discovered and reasoned about?
– How can abstract understanding that is tough to encode realistically be managed?

Techniques and contributions

This section offers a summary of techniques and contributions in an overall context causing many other, more comprehensive posts in Wikipedia. Sections on Artificial Intelligence and Uncertain Reasoning are covered previously in the history section.

AI shows languages

The essential AI shows language in the US throughout the last symbolic AI boom period was LISP. LISP is the 2nd oldest programs language after FORTRAN and was created in 1958 by John McCarthy. LISP supplied the first read-eval-print loop to support fast program development. Compiled functions could be freely blended with translated functions. Program tracing, stepping, and breakpoints were also supplied, along with the ability to alter values or functions and continue from breakpoints or mistakes. It had the first self-hosting compiler, suggesting that the compiler itself was originally composed in LISP and then ran interpretively to put together the compiler code.

Other crucial developments pioneered by LISP that have infected other programs languages include:

Garbage collection
Dynamic typing
Higher-order functions
Recursion
Conditionals

Programs were themselves data structures that other programs could run on, allowing the simple definition of higher-level languages.

In contrast to the US, in Europe the essential AI programs language throughout that very same duration was Prolog. Prolog offered an integrated store of truths and clauses that might be queried by a read-eval-print loop. The shop might serve as a knowledge base and the provisions might serve as rules or a restricted type of logic. As a subset of first-order reasoning Prolog was based upon Horn clauses with a closed-world assumption-any realities not understood were considered false-and an unique name presumption for primitive terms-e.g., the identifier barack_obama was considered to describe exactly one things. Backtracking and unification are integrated to Prolog.

Alain Colmerauer and Philippe Roussel are credited as the developers of Prolog. Prolog is a type of logic programming, which was created by Robert Kowalski. Its history was likewise affected by Carl Hewitt’s PLANNER, an assertional database with pattern-directed invocation of methods. For more information see the section on the origins of Prolog in the PLANNER post.

Prolog is also a type of declarative shows. The logic provisions that explain programs are straight interpreted to run the programs specified. No specific series of actions is required, as holds true with crucial shows languages.

Japan promoted Prolog for its Fifth Generation Project, intending to construct special hardware for high performance. Similarly, LISP machines were constructed to run LISP, but as the 2nd AI boom turned to bust these business could not compete with new workstations that might now run LISP or Prolog natively at similar speeds. See the history section for more information.

Smalltalk was another influential AI programs language. For example, it presented metaclasses and, together with Flavors and CommonLoops, affected the Common Lisp Object System, or (CLOS), that is now part of Common Lisp, the current standard Lisp dialect. CLOS is a Lisp-based object-oriented system that allows several inheritance, in addition to incremental extensions to both classes and metaclasses, thus providing a run-time meta-object protocol. [88]

For other AI programs languages see this list of shows languages for synthetic intelligence. Currently, Python, a multi-paradigm shows language, is the most popular shows language, partially due to its comprehensive plan library that supports data science, natural language processing, and deep knowing. Python consists of a read-eval-print loop, practical components such as higher-order functions, and object-oriented programs that consists of metaclasses.

Search

Search arises in lots of type of problem fixing, including planning, restriction satisfaction, and playing games such as checkers, chess, and go. The very best understood AI-search tree search algorithms are breadth-first search, depth-first search, A *, and Monte Carlo Search. Key search algorithms for Boolean satisfiability are WalkSAT, conflict-driven stipulation knowing, and the DPLL algorithm. For adversarial search when playing games, alpha-beta pruning, branch and bound, and minimax were early contributions.

Knowledge representation and thinking

Multiple various methods to represent knowledge and then factor with those representations have actually been examined. Below is a fast summary of techniques to knowledge representation and automated thinking.

Knowledge representation

Semantic networks, conceptual graphs, frames, and reasoning are all methods to modeling knowledge such as domain knowledge, analytical knowledge, and the semantic significance of language. Ontologies design essential principles and their relationships in a domain. Example ontologies are YAGO, WordNet, and DOLCE. DOLCE is an example of an upper ontology that can be utilized for any domain while WordNet is a lexical resource that can also be considered as an ontology. YAGO incorporates WordNet as part of its ontology, to line up facts drawn out from Wikipedia with WordNet synsets. The Disease Ontology is an example of a medical ontology currently being utilized.

Description reasoning is a reasoning for automated category of ontologies and for detecting inconsistent category data. OWL is a language used to represent ontologies with description logic. Protégé is an ontology editor that can check out in OWL ontologies and then examine consistency with deductive classifiers such as such as HermiT. [89]

First-order logic is more basic than description reasoning. The automated theorem provers gone over below can show theorems in first-order logic. Horn stipulation reasoning is more restricted than first-order logic and is utilized in reasoning programs languages such as Prolog. Extensions to first-order reasoning consist of temporal logic, to manage time; epistemic reasoning, to reason about agent knowledge; modal logic, to deal with possibility and need; and probabilistic logics to deal with logic and probability together.

Automatic theorem showing

Examples of automated theorem provers for first-order reasoning are:

Prover9.
ACL2.
Vampire.

Prover9 can be used in combination with the Mace4 model checker. ACL2 is a theorem prover that can manage proofs by induction and is a descendant of the Boyer-Moore Theorem Prover, also called Nqthm.

Reasoning in knowledge-based systems

Knowledge-based systems have a specific knowledge base, typically of rules, to improve reusability throughout domains by separating procedural code and domain knowledge. A different inference engine procedures guidelines and includes, deletes, or customizes a knowledge shop.

Forward chaining inference engines are the most typical, and are seen in CLIPS and OPS5. Backward chaining happens in Prolog, where a more minimal rational representation is utilized, Horn Clauses. Pattern-matching, particularly marriage, is used in Prolog.

A more versatile sort of analytical occurs when thinking about what to do next takes place, rather than just choosing one of the readily available actions. This sort of meta-level thinking is used in Soar and in the BB1 blackboard architecture.

Cognitive architectures such as ACT-R might have additional capabilities, such as the capability to put together frequently used understanding into higher-level portions.

Commonsense thinking

Marvin Minsky first proposed frames as a way of analyzing typical visual situations, such as an office, and Roger Schank extended this concept to scripts for common routines, such as eating in restaurants. Cyc has actually attempted to capture useful common-sense knowledge and has «micro-theories» to handle specific kinds of domain-specific thinking.

Qualitative simulation, such as Benjamin Kuipers’s QSIM, [90] estimates human reasoning about naive physics, such as what happens when we warm a liquid in a pot on the stove. We anticipate it to heat and potentially boil over, although we may not understand its temperature, its boiling point, or other information, such as air pressure.

Similarly, Allen’s temporal period algebra is a simplification of reasoning about time and Region Connection Calculus is a simplification of reasoning about spatial relationships. Both can be fixed with restraint solvers.

Constraints and constraint-based thinking

Constraint solvers carry out a more restricted sort of inference than first-order logic. They can streamline sets of spatiotemporal constraints, such as those for RCC or Temporal Algebra, in addition to resolving other type of puzzle problems, such as Wordle, Sudoku, cryptarithmetic problems, and so on. Constraint logic programs can be used to resolve scheduling issues, for example with restraint managing rules (CHR).

Automated preparation

The General Problem Solver (GPS) cast preparation as problem-solving utilized means-ends analysis to produce plans. STRIPS took a various approach, seeing planning as theorem proving. Graphplan takes a least-commitment technique to preparation, instead of sequentially choosing actions from an initial state, working forwards, or a goal state if working in reverse. Satplan is a technique to planning where a preparation issue is minimized to a Boolean satisfiability problem.

Natural language processing

Natural language processing concentrates on treating language as data to carry out jobs such as identifying topics without necessarily comprehending the intended significance. Natural language understanding, in contrast, constructs a significance representation and utilizes that for further processing, such as answering concerns.

Parsing, tokenizing, spelling correction, part-of-speech tagging, noun and verb phrase chunking are all aspects of natural language processing long handled by symbolic AI, but since improved by deep knowing techniques. In symbolic AI, discourse representation theory and first-order reasoning have been used to represent sentence significances. Latent semantic analysis (LSA) and specific semantic analysis likewise provided vector representations of files. In the latter case, vector elements are interpretable as ideas called by Wikipedia short articles.

New deep knowing techniques based on Transformer models have now eclipsed these earlier symbolic AI techniques and achieved advanced performance in natural language processing. However, Transformer models are opaque and do not yet produce human-interpretable semantic representations for sentences and documents. Instead, they produce task-specific vectors where the significance of the vector elements is opaque.

Agents and multi-agent systems

Agents are autonomous systems embedded in an environment they view and act upon in some sense. Russell and Norvig’s basic book on synthetic intelligence is arranged to reflect representative architectures of increasing elegance. [91] The sophistication of agents varies from easy reactive representatives, to those with a design of the world and automated preparation abilities, potentially a BDI agent, i.e., one with beliefs, desires, and intentions – or additionally a reinforcement finding out design learned over time to pick actions – as much as a mix of alternative architectures, such as a neuro-symbolic architecture [87] that consists of deep knowing for perception. [92]

In contrast, a multi-agent system consists of numerous representatives that interact amongst themselves with some inter-agent interaction language such as Knowledge Query and Manipulation Language (KQML). The agents require not all have the exact same internal architecture. Advantages of multi-agent systems consist of the capability to divide work amongst the agents and to increase fault tolerance when agents are lost. Research problems include how representatives reach agreement, distributed problem solving, multi-agent knowing, multi-agent preparation, and dispersed restraint optimization.

Controversies developed from at an early stage in symbolic AI, both within the field-e.g., in between logicists (the pro-logic «neats») and non-logicists (the anti-logic «scruffies»)- and between those who welcomed AI but rejected symbolic approaches-primarily connectionists-and those outside the field. Critiques from exterior of the field were mainly from philosophers, on intellectual grounds, but also from financing firms, specifically throughout the two AI winter seasons.

The Frame Problem: understanding representation obstacles for first-order reasoning

Limitations were found in using basic first-order logic to factor about vibrant domains. Problems were discovered both with concerns to specifying the preconditions for an action to be successful and in offering axioms for what did not alter after an action was carried out.

McCarthy and Hayes introduced the Frame Problem in 1969 in the paper, «Some Philosophical Problems from the Standpoint of Artificial Intelligence.» [93] A simple example occurs in «showing that one person might enter into conversation with another», as an axiom asserting «if an individual has a telephone he still has it after looking up a number in the telephone book» would be needed for the reduction to succeed. Similar axioms would be required for other domain actions to define what did not change.

A comparable problem, called the Qualification Problem, happens in trying to enumerate the preconditions for an action to succeed. A boundless variety of pathological conditions can be imagined, e.g., a banana in a tailpipe might prevent an automobile from operating properly.

McCarthy’s technique to repair the frame problem was circumscription, a type of non-monotonic reasoning where reductions might be made from actions that require only specify what would alter while not needing to explicitly define whatever that would not change. Other non-monotonic reasonings offered reality maintenance systems that revised beliefs leading to contradictions.

Other methods of handling more open-ended domains included probabilistic thinking systems and artificial intelligence to discover brand-new ideas and rules. McCarthy’s Advice Taker can be viewed as an inspiration here, as it could incorporate brand-new knowledge supplied by a human in the kind of assertions or guidelines. For instance, experimental symbolic maker learning systems explored the capability to take top-level natural language recommendations and to analyze it into domain-specific actionable guidelines.

Similar to the issues in dealing with dynamic domains, sensible thinking is also tough to capture in official thinking. Examples of common-sense reasoning include implicit reasoning about how individuals believe or general understanding of everyday occasions, objects, and living animals. This kind of understanding is considered approved and not viewed as noteworthy. Common-sense reasoning is an open location of research and challenging both for symbolic systems (e.g., Cyc has actually tried to capture essential parts of this knowledge over more than a decade) and neural systems (e.g., self-driving automobiles that do not understand not to drive into cones or not to hit pedestrians walking a bike).

McCarthy saw his Advice Taker as having common-sense, but his meaning of sensible was different than the one above. [94] He specified a program as having sound judgment «if it immediately deduces for itself an class of instant effects of anything it is informed and what it currently understands. «

Connectionist AI: philosophical difficulties and sociological conflicts

Connectionist approaches consist of earlier deal with neural networks, [95] such as perceptrons; work in the mid to late 80s, such as Danny Hillis’s Connection Machine and Yann LeCun’s advances in convolutional neural networks; to today’s advanced approaches, such as Transformers, GANs, and other work in deep learning.

Three philosophical positions [96] have actually been described among connectionists:

1. Implementationism-where connectionist architectures execute the abilities for symbolic processing,
2. Radical connectionism-where symbolic processing is declined absolutely, and connectionist architectures underlie intelligence and are fully sufficient to describe it,
3. Moderate connectionism-where symbolic processing and connectionist architectures are considered as complementary and both are required for intelligence

Olazaran, in his sociological history of the controversies within the neural network community, described the moderate connectionism consider as essentially compatible with existing research study in neuro-symbolic hybrids:

The third and last position I wish to examine here is what I call the moderate connectionist view, a more eclectic view of the present debate between connectionism and symbolic AI. One of the researchers who has actually elaborated this position most clearly is Andy Clark, a philosopher from the School of Cognitive and Computing Sciences of the University of Sussex (Brighton, England). Clark defended hybrid (partly symbolic, partly connectionist) systems. He declared that (a minimum of) two type of theories are needed in order to study and model cognition. On the one hand, for some information-processing jobs (such as pattern acknowledgment) connectionism has advantages over symbolic models. But on the other hand, for other cognitive procedures (such as serial, deductive thinking, and generative sign manipulation processes) the symbolic paradigm provides appropriate designs, and not just «approximations» (contrary to what radical connectionists would claim). [97]

Gary Marcus has actually claimed that the animus in the deep learning neighborhood versus symbolic methods now might be more sociological than philosophical:

To believe that we can simply desert symbol-manipulation is to suspend disbelief.

And yet, for the most part, that’s how most existing AI profits. Hinton and numerous others have striven to get rid of signs entirely. The deep learning hope-seemingly grounded not so much in science, but in a sort of historic grudge-is that intelligent habits will emerge purely from the confluence of huge data and deep knowing. Where classical computer systems and software resolve jobs by defining sets of symbol-manipulating guidelines devoted to particular tasks, such as editing a line in a word processor or carrying out a calculation in a spreadsheet, neural networks usually try to solve jobs by statistical approximation and gaining from examples.

According to Marcus, Geoffrey Hinton and his colleagues have actually been vehemently «anti-symbolic»:

When deep knowing reemerged in 2012, it was with a kind of take-no-prisoners mindset that has actually defined the majority of the last decade. By 2015, his hostility toward all things symbols had actually fully taken shape. He gave a talk at an AI workshop at Stanford comparing signs to aether, among science’s greatest errors.

…

Ever since, his anti-symbolic project has just increased in strength. In 2016, Yann LeCun, Bengio, and Hinton composed a manifesto for deep knowing in one of science’s essential journals, Nature. It closed with a direct attack on symbol adjustment, calling not for reconciliation however for straight-out replacement. Later, Hinton told a gathering of European Union leaders that investing any more money in symbol-manipulating methods was «a huge error,» comparing it to purchasing internal combustion engines in the era of electric automobiles. [98]

Part of these disagreements might be due to uncertain terminology:

Turing award winner Judea Pearl provides a review of device learning which, regrettably, conflates the terms maker learning and deep learning. Similarly, when Geoffrey Hinton refers to symbolic AI, the undertone of the term tends to be that of expert systems dispossessed of any ability to discover. Using the terms requires information. Machine learning is not restricted to association guideline mining, c.f. the body of work on symbolic ML and relational knowing (the differences to deep learning being the choice of representation, localist sensible instead of dispersed, and the non-use of gradient-based learning algorithms). Equally, symbolic AI is not simply about production guidelines written by hand. An appropriate meaning of AI concerns understanding representation and reasoning, autonomous multi-agent systems, planning and argumentation, along with knowing. [99]

Situated robotics: the world as a design

Another review of symbolic AI is the embodied cognition technique:

The embodied cognition method declares that it makes no sense to consider the brain individually: cognition happens within a body, which is embedded in an environment. We need to study the system as a whole; the brain’s functioning exploits regularities in its environment, consisting of the rest of its body. Under the embodied cognition method, robotics, vision, and other sensors become central, not peripheral. [100]

Rodney Brooks invented behavior-based robotics, one technique to embodied cognition. Nouvelle AI, another name for this method, is considered as an alternative to both symbolic AI and connectionist AI. His method turned down representations, either symbolic or distributed, as not just unneeded, but as damaging. Instead, he produced the subsumption architecture, a layered architecture for embodied representatives. Each layer achieves a different function and should work in the real life. For example, the first robotic he describes in Intelligence Without Representation, has three layers. The bottom layer analyzes finder sensing units to avoid items. The middle layer causes the robot to wander around when there are no barriers. The leading layer causes the robotic to go to more far-off locations for more expedition. Each layer can temporarily hinder or reduce a lower-level layer. He slammed AI scientists for specifying AI problems for their systems, when: «There is no tidy division in between perception (abstraction) and reasoning in the real life.» [101] He called his robots «Creatures» and each layer was «made up of a fixed-topology network of simple finite state makers.» [102] In the Nouvelle AI method, «First, it is vitally essential to test the Creatures we integrate in the real life; i.e., in the very same world that we human beings occupy. It is devastating to fall into the temptation of checking them in a simplified world first, even with the finest objectives of later moving activity to an unsimplified world.» [103] His focus on real-world screening remained in contrast to «Early work in AI focused on games, geometrical problems, symbolic algebra, theorem proving, and other official systems» [104] and making use of the blocks world in symbolic AI systems such as SHRDLU.

Current views

Each approach-symbolic, connectionist, and behavior-based-has advantages, but has been slammed by the other techniques. Symbolic AI has actually been criticized as disembodied, liable to the qualification problem, and bad in managing the affective issues where deep finding out excels. In turn, connectionist AI has actually been criticized as inadequately suited for deliberative detailed issue resolving, incorporating understanding, and dealing with planning. Finally, Nouvelle AI stands out in reactive and real-world robotics domains but has actually been criticized for problems in including learning and understanding.

Hybrid AIs integrating several of these approaches are currently seen as the course forward. [19] [81] [82] Russell and Norvig conclude that:

Overall, Dreyfus saw locations where AI did not have total responses and stated that Al is for that reason impossible; we now see many of these exact same areas undergoing continued research study and development leading to increased ability, not impossibility. [100]

Artificial intelligence.
Automated planning and scheduling
Automated theorem proving
Belief revision
Case-based thinking
Cognitive architecture
Cognitive science
Connectionism
Constraint programming
Deep knowing
First-order logic
GOFAI
History of expert system
Inductive logic programs
Knowledge-based systems
Knowledge representation and reasoning
Logic shows
Artificial intelligence
Model checking
Model-based reasoning
Multi-agent system
Natural language processing
Neuro-symbolic AI
Ontology
Philosophy of expert system
Physical sign systems hypothesis
Semantic Web
Sequential pattern mining
Statistical relational learning
Symbolic mathematics
YAGO ontology
WordNet

Notes

^ McCarthy once stated: «This is AI, so we do not care if it’s emotionally genuine». [4] McCarthy repeated his position in 2006 at the AI@50 conference where he said «Expert system is not, by meaning, simulation of human intelligence». [28] Pamela McCorduck composes that there are «2 significant branches of artificial intelligence: one aimed at producing smart behavior regardless of how it was achieved, and the other intended at modeling smart procedures found in nature, particularly human ones.», [29] Stuart Russell and Peter Norvig composed «Aeronautical engineering texts do not specify the goal of their field as making ‘makers that fly so exactly like pigeons that they can deceive even other pigeons.'» [30] Citations

^ Garnelo, Marta; Shanahan, Murray (October 2019). «Reconciling deep knowing with symbolic synthetic intelligence: representing items and relations». Current Opinion in Behavioral Sciences. 29: 17-23. doi:10.1016/ j.cobeha.2018.12.010. hdl:10044/ 1/67796.
^ Thomason, Richmond (February 27, 2024). «Logic-Based Artificial Intelligence». In Zalta, Edward N. (ed.). Stanford Encyclopedia of Philosophy.
^ Garnelo, Marta; Shanahan, Murray (2019-10-01). «Reconciling deep knowing with symbolic artificial intelligence: representing objects and relations». Current Opinion in Behavioral Sciences. 29: 17-23. doi:10.1016/ j.cobeha.2018.12.010. hdl:10044/ 1/67796. S2CID 72336067.
^ a b Kolata 1982.
^ Kautz 2022, pp. 107-109.
^ a b Russell & Norvig 2021, p. 19.
^ a b Russell & Norvig 2021, pp. 22-23.
^ a b Kautz 2022, pp. 109-110.
^ a b c Kautz 2022, p. 110.
^ Kautz 2022, pp. 110-111.
^ a b Russell & Norvig 2021, p. 25.
^ Kautz 2022, p. 111.
^ Kautz 2020, pp. 110-111.
^ Rumelhart, David E.; Hinton, Geoffrey E.; Williams, Ronald J. (1986 ). «Learning representations by back-propagating errors». Nature. 323 (6088 ): 533-536. Bibcode:1986 Natur.323..533 R. doi:10.1038/ 323533a0. ISSN 1476-4687. S2CID 205001834.
^ LeCun, Y.; Boser, B.; Denker, I.; Henderson, D.; Howard, R.; Hubbard, W.; Tackel, L. (1989 ). «Backpropagation Applied to Handwritten Zip Code Recognition». Neural Computation. 1 (4 ): 541-551. doi:10.1162/ neco.1989.1.4.541. S2CID 41312633.
^ a b Marcus & Davis 2019.
^ a b Rossi, Francesca. «Thinking Fast and Slow in AI». AAAI. Retrieved 5 July 2022.
^ a b Selman, Bart. «AAAI Presidential Address: The State of AI». AAAI. Retrieved 5 July 2022.
^ a b c Kautz 2020.
^ Kautz 2022, p. 106.
^ Newell & Simon 1972.
^ & McCorduck 2004, pp. 139-179, 245-250, 322-323 (EPAM).
^ Crevier 1993, pp. 145-149.
^ McCorduck 2004, pp. 450-451.
^ Crevier 1993, pp. 258-263.
^ a b Kautz 2022, p. 108.
^ Russell & Norvig 2021, p. 9 (logicist AI), p. 19 (McCarthy’s work).
^ Maker 2006.
^ McCorduck 2004, pp. 100-101.
^ Russell & Norvig 2021, p. 2.
^ McCorduck 2004, pp. 251-259.
^ Crevier 1993, pp. 193-196.
^ Howe 1994.
^ McCorduck 2004, pp. 259-305.
^ Crevier 1993, pp. 83-102, 163-176.
^ McCorduck 2004, pp. 421-424, 486-489.
^ Crevier 1993, p. 168.
^ McCorduck 2004, p. 489.
^ Crevier 1993, pp. 239-243.
^ Russell & Norvig 2021, p. 316, 340.
^ Kautz 2022, p. 109.
^ Russell & Norvig 2021, p. 22.
^ McCorduck 2004, pp. 266-276, 298-300, 314, 421.
^ Shustek, Len (June 2010). «An interview with Ed Feigenbaum». Communications of the ACM. 53 (6 ): 41-45. doi:10.1145/ 1743546.1743564. ISSN 0001-0782. S2CID 10239007. Retrieved 2022-07-14.
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^ Russell & Norvig 2021, pp. 22-24.
^ McCorduck 2004, pp. 327-335, 434-435.
^ Crevier 1993, pp. 145-62, 197-203.
^ a b Russell & Norvig 2021, p. 23.
^ a b Clancey 1987.
^ a b Shustek, Len (2010 ). «An interview with Ed Feigenbaum». Communications of the ACM. 53 (6 ): 41-45. doi:10.1145/ 1743546.1743564. ISSN 0001-0782. S2CID 10239007. Retrieved 2022-08-05.
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