Symbolic Artificial Intelligence

In artificial intelligence, symbolic expert system (likewise known as classical expert system or logic-based artificial intelligence) [1] [2] is the term for the collection of all approaches in artificial intelligence research that are based upon top-level symbolic (human-readable) representations of issues, logic and search. [3] Symbolic AI utilized tools such as logic programming, production rules, semantic webs and frames, and it established applications such as knowledge-based systems (in particular, expert systems), symbolic mathematics, automated theorem provers, ontologies, the semantic web, and automated preparation and scheduling systems. The Symbolic AI paradigm resulted in seminal concepts in search, symbolic programming 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 from the mid-1950s until the mid-1990s. [4] Researchers in the 1960s and the 1970s were encouraged that symbolic approaches would eventually be successful in producing a device with synthetic general intelligence and considered this the ultimate objective of their field. [citation required] An early boom, with early successes such as the Logic Theorist and Samuel’s Checkers Playing Program, resulted in impractical expectations and guarantees and was followed by the first AI Winter as funding dried up. [5] [6] A second boom (1969-1986) accompanied the rise of professional systems, their guarantee of recording business knowledge, and a passionate corporate accept. [7] [8] That boom, and some early successes, e.g., with XCON at DEC, was followed once again by later on frustration. [8] Problems with difficulties in knowledge acquisition, preserving large knowledge bases, and brittleness in dealing with out-of-domain issues developed. Another, 2nd, AI Winter (1988-2011) followed. [9] Subsequently, AI scientists concentrated on dealing with underlying problems in managing unpredictability and in understanding acquisition. [10] Uncertainty was attended to with formal methods such as concealed Markov models, Bayesian thinking, and statistical relational learning. [11] [12] Symbolic maker finding out resolved the understanding acquisition problem with contributions consisting of Version Space, Valiant’s PAC knowing, Quinlan’s ID3 decision-tree learning, case-based learning, and inductive reasoning shows to learn relations. [13]

Neural networks, a subsymbolic technique, had actually been pursued from early days and reemerged strongly 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 considered as successful up until about 2012: “Until Big Data became prevalent, the general consensus in the Al neighborhood was that the so-called neural-network method was hopeless. Systems just didn’t work that well, compared to other methods. … A transformation was available in 2012, when a number of individuals, including a team of researchers dealing with Hinton, exercised a way to use the power of GPUs to immensely increase the power of neural networks.” [16] Over the next a number of years, deep knowing had spectacular success in managing vision, speech acknowledgment, speech synthesis, image generation, and device translation. However, given that 2020, as fundamental problems with predisposition, explanation, coherence, and robustness ended up being more apparent with deep learning techniques; an increasing variety of AI scientists have called for integrating the very best of both the symbolic and neural network techniques [17] [18] and dealing with locations that both approaches have problem with, such as sensible thinking. [16]

A brief history of symbolic AI to the present day follows listed below. Period and titles are drawn from Henry Kautz’s 2020 AAAI Robert S. Engelmore Memorial Lecture [19] and the longer Wikipedia post on the History of AI, with dates and titles differing a little for increased clarity.

The very first AI summer season: unreasonable vitality, 1948-1966

Success at early efforts in AI took place in 3 main areas: synthetic neural networks, knowledge representation, and heuristic search, contributing to high expectations. This section sums up Kautz’s reprise of early AI history.

Approaches inspired by human or animal cognition or behavior

Cybernetic techniques attempted to replicate the feedback loops between animals and their environments. A robotic turtle, with sensing units, motors for driving and guiding, and 7 vacuum tubes for control, based on a preprogrammed neural net, was constructed as early as 1948. This work can be viewed as an early precursor to later work in neural networks, support knowing, and situated robotics. [20]

A crucial early symbolic AI program was the Logic theorist, composed by Allen Newell, Herbert Simon and Cliff Shaw in 1955-56, as it was able to prove 38 elementary theorems from Whitehead and Russell’s Principia Mathematica. Newell, Simon, and Shaw later on generalized this work to develop a domain-independent issue solver, GPS (General Problem Solver). GPS resolved problems represented with official operators via state-space search utilizing means-ends analysis. [21]

During the 1960s, symbolic methods attained great success at mimicing intelligent habits in structured environments such as game-playing, symbolic mathematics, and theorem-proving. AI research was focused in four institutions in the 1960s: Carnegie Mellon University, Stanford, MIT and (later on) University of Edinburgh. Every one established its own style of research. Earlier methods based upon cybernetics or artificial neural networks were abandoned or pressed 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, along with cognitive science, operations research study and management science. Their research study team utilized the outcomes of mental experiments to establish programs that simulated the techniques that people utilized to fix problems. [22] [23] This custom, focused at Carnegie Mellon University would ultimately culminate in the advancement of the Soar architecture in the center 1980s. [24] [25]

Heuristic search

In addition to the extremely specialized domain-specific kinds of knowledge that we will see later used in expert systems, early symbolic AI researchers found another more basic application of understanding. These were called heuristics, general rules that direct a search in promising directions: “How can non-enumerative search be useful when the underlying issue is greatly difficult? The method promoted by Simon and Newell is to use heuristics: fast algorithms that might stop working on some inputs or output suboptimal options.” [26] Another crucial advance was to find a method to use these heuristics that ensures a service will be found, if there is one, not enduring the occasional fallibility of heuristics: “The A * algorithm provided a general frame for total and ideal heuristically assisted search. A * is used as a subroutine within almost every AI algorithm today however is still no magic bullet; its warranty of completeness is purchased the cost of worst-case exponential time. [26]

Early work on understanding representation and reasoning

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

Modeling formal thinking with reasoning: the “neats”

Unlike Simon and Newell, John McCarthy felt that machines did not require to simulate the precise mechanisms of human thought, but could rather look for the essence of abstract thinking and analytical with reasoning, [27] no matter whether individuals used the exact same algorithms. [a] His laboratory at Stanford (SAIL) concentrated on utilizing official logic to fix a wide variety of issues, consisting of understanding representation, planning and knowing. [31] Logic was also the focus of the work at the University of Edinburgh and in other places in Europe which led to the advancement of the programs language Prolog and the science of reasoning shows. [32] [33]

Modeling implicit sensible knowledge with frames and scripts: the “scruffies”

Researchers at MIT (such as Marvin Minsky and Seymour Papert) [34] [35] [6] discovered that fixing tough problems in vision and natural language processing needed advertisement hoc solutions-they argued that no basic and basic concept (like reasoning) would capture all the aspects of intelligent habits. Roger Schank described their “anti-logic” techniques as “scruffy” (instead of the “neat” paradigms at CMU and Stanford). [36] [37] Commonsense understanding bases (such as Doug Lenat’s Cyc) are an example of “shabby” AI, considering that they should be built by hand, one complicated idea at a time. [38] [39] [40]

The first AI winter: crushed dreams, 1967-1977

The very first AI winter was a shock:

During the first AI summertime, numerous people thought that machine intelligence could be attained in just a couple of years. The Defense Advance Research Projects Agency (DARPA) introduced programs to support AI research to use AI to solve problems of national security; in specific, to automate the translation of Russian to English for intelligence operations and to develop self-governing tanks for the battleground. Researchers had begun to recognize that accomplishing AI was going to be much more difficult than was supposed a decade earlier, but a mix of hubris and disingenuousness led many university and think-tank scientists to accept funding with promises of deliverables that they ought to have understood they might not fulfill. By the mid-1960s neither useful natural language translation systems nor self-governing tanks had been created, and a significant reaction set in. New DARPA leadership canceled existing AI funding programs.

Outside of the United States, the most fertile ground for AI research study was the UK. The AI winter in the UK was spurred on not so much by dissatisfied military leaders as by rival academics who saw AI researchers as charlatans and a drain on research study funding. A professor of used mathematics, Sir James Lighthill, was commissioned by Parliament to evaluate the state of AI research in the nation. The report specified that all of the problems being dealt with in AI would be much better handled by researchers from other disciplines-such as applied mathematics. The report likewise claimed that AI successes on toy issues might never scale to real-world applications due to combinatorial explosion. [41]

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

Knowledge-based systems

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

Edward Feigenbaum stated:

– “In the understanding lies the power.” [44]
to describe that high performance in a specific domain needs both general and extremely domain-specific understanding. Ed Feigenbaum and Doug Lenat called this The Knowledge Principle:

( 1) The Knowledge Principle: if a program is to carry out an intricate job well, it must understand a good deal about the world in which it runs.
( 2) A possible extension of that concept, called the Breadth Hypothesis: there are two extra abilities needed for smart behavior in unexpected scenarios: drawing on progressively basic understanding, and analogizing to particular however remote knowledge. [45]

Success with specialist systems

This “understanding transformation” led to the development and release of professional systems (introduced by Edward Feigenbaum), the very first commercially effective type of AI software. [46] [47] [48]

Key specialist systems were:

DENDRAL, which discovered the structure of natural particles from their chemical formula and mass spectrometer readings.
MYCIN, which identified bacteremia – and recommended further laboratory tests, when essential – by analyzing lab outcomes, client history, and doctor observations. “With about 450 guidelines, MYCIN was able to perform along with some experts, and significantly better than junior doctors.” [49] INTERNIST and CADUCEUS which took on internal medication medical diagnosis. Internist tried to record the know-how of the chairman of internal medicine at the University of Pittsburgh School of Medicine while CADUCEUS could eventually diagnose as much as 1000 different illness.
– GUIDON, which demonstrated how an understanding base built for expert issue resolving could be repurposed for mentor. [50] XCON, to configure VAX computer systems, a then tiresome process that might use up to 90 days. XCON lowered the time to about 90 minutes. [9]
DENDRAL is thought about the very first specialist system that count on knowledge-intensive analytical. It is explained below, by Ed Feigenbaum, from a Communications of the ACM interview, Interview with Ed Feigenbaum:

One of individuals at Stanford interested in computer-based designs of mind was Joshua Lederberg, the 1958 Nobel Prize winner in genes. When I informed him I wanted an induction “sandbox”, he said, “I have simply the one for you.” His lab was doing mass spectrometry of amino acids. The concern was: how do you go from taking a look 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 great at heuristic search techniques, and he had an algorithm that was great at producing the chemical problem space.

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 first-rate experts in mass spectrometry. We began to include to their knowledge, inventing knowledge of engineering as we went along. These experiments totaled up to titrating DENDRAL more and more understanding. The more you did that, the smarter the program became. We had great results.

The generalization was: in the knowledge lies the power. That was the big concept. In my career that is the huge, “Ah ha!,” and it wasn’t the way AI was being done formerly. Sounds simple, however it’s probably AI’s most effective generalization. [51]

The other expert systems discussed above came after DENDRAL. MYCIN exemplifies the timeless specialist system architecture of a knowledge-base of guidelines coupled to a symbolic thinking mechanism, including using certainty aspects to manage uncertainty. GUIDON reveals how a specific knowledge base can be repurposed for a 2nd application, tutoring, and is an example of a smart tutoring system, a specific sort of knowledge-based application. Clancey revealed that it was not sufficient simply to use MYCIN’s guidelines for direction, however that he also needed to include rules for discussion management and trainee modeling. [50] XCON is considerable due to the fact that of the countless dollars it conserved DEC, which set off the specialist system boom where most all major corporations in the US had skilled systems groups, to catch corporate competence, preserve it, and automate it:

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

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

Architecture of knowledge-based and professional systems

A key component of the system architecture for all professional systems is the understanding base, which shops realities and rules for analytical. [53] The simplest technique for a professional system understanding base is just a collection or network of production guidelines. Production rules connect signs in a relationship comparable to an If-Then statement. The professional system processes the guidelines to make deductions and to identify what extra info it requires, i.e. what questions to ask, utilizing human-readable symbols. For example, OPS5, CLIPS and their successors Jess and Drools run in this style.

Expert systems can run in either a forward chaining – from evidence to conclusions – or backward chaining – from objectives to required data and prerequisites – manner. Advanced knowledge-based systems, such as Soar can also perform meta-level thinking, that is reasoning about their own reasoning in terms of deciding how to fix issues and keeping an eye on the success of analytical methods.

Blackboard systems are a 2nd sort of knowledge-based or professional system architecture. They model a neighborhood of professionals incrementally contributing, where they can, to resolve an issue. The problem is represented in several levels of abstraction or alternate views. The experts (understanding sources) volunteer their services whenever they acknowledge they can contribute. Potential analytical actions are represented on an agenda that is upgraded as the issue situation changes. A controller chooses how helpful each contribution is, and who ought to make the next analytical action. One example, the BB1 blackboard architecture [54] was initially motivated by studies of how people prepare to carry out numerous jobs in a journey. [55] An innovation of BB1 was to use the very same chalkboard model to solving its control problem, i.e., its controller carried out meta-level thinking with understanding sources that kept an eye on how well a strategy or the analytical was continuing and could change from one method to another as conditions – such as objectives or times – altered. BB1 has actually been applied in several domains: construction website preparation, intelligent tutoring systems, and real-time patient monitoring.

The 2nd AI winter season, 1988-1993

At the height of the AI boom, business such as Symbolics, LMI, and Texas Instruments were selling LISP devices specifically targeted to accelerate the development of AI applications and research study. In addition, numerous artificial intelligence business, such as Teknowledge and Inference Corporation, were selling professional system shells, training, and consulting to corporations.

Unfortunately, the AI boom did not last and Kautz finest explains the 2nd AI winter season that followed:

Many factors can be offered for the arrival of the second AI winter. The hardware companies stopped working when a lot more cost-efficient basic Unix workstations from Sun together with good compilers for LISP and Prolog came onto the marketplace. Many business implementations of expert systems were stopped when they proved too expensive to maintain. Medical expert systems never ever captured on for several reasons: the difficulty in keeping them up to date; the challenge for medical professionals to find out how to utilize a bewildering range of different specialist systems for various medical conditions; and maybe most crucially, the unwillingness of physicians to trust a computer-made medical diagnosis over their gut instinct, even for particular domains where the specialist systems could exceed an average physician. Venture capital money deserted AI practically over night. The world AI conference IJCAI hosted a massive and luxurious trade convention and countless nonacademic attendees in 1987 in Vancouver; the primary AI conference the following year, AAAI 1988 in St. Paul, was a little and strictly academic affair. [9]

Adding in more rigorous foundations, 1993-2011

Uncertain thinking

Both statistical techniques and extensions to logic were tried.

One statistical method, concealed Markov models, had already been popularized in the 1980s for speech recognition work. [11] Subsequently, in 1988, Judea Pearl popularized making use of Bayesian Networks as a sound however efficient method of managing unpredictable reasoning with his publication of the book Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. [56] and Bayesian approaches were used effectively in professional systems. [57] Even later on, in the 1990s, statistical relational learning, a technique that integrates likelihood with sensible formulas, enabled 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 support were likewise attempted. For example, non-monotonic thinking might be used with reality upkeep systems. A fact upkeep system tracked presumptions and justifications for all reasonings. It enabled reasonings to be withdrawn when presumptions were discovered out to be inaccurate or a contradiction was derived. Explanations might be provided for a reasoning by explaining which guidelines were used to create it and then continuing through underlying reasonings and rules all the method back to root presumptions. [58] Lofti Zadeh had presented a various type of extension to deal with the representation of uncertainty. For example, in deciding how “heavy” or “high” a man is, there is often no clear “yes” or “no” response, and a predicate for heavy or tall would rather return values in between 0 and 1. Those worths represented to what degree the predicates held true. His fuzzy reasoning even more supplied a means for propagating combinations of these values through rational solutions. [59]

Artificial intelligence

Symbolic machine discovering methods were examined to address the understanding acquisition bottleneck. Among the earliest is Meta-DENDRAL. Meta-DENDRAL used a generate-and-test strategy to produce possible guideline hypotheses to test versus spectra. Domain and job knowledge lowered the number of candidates tested to a workable size. Feigenbaum described Meta-DENDRAL as

… the culmination of my imagine the early to mid-1960s relating to 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 used layers of understanding to steer and prune the search. That understanding got in there because we talked to individuals. But how did individuals get the knowledge? By looking at countless spectra. So we wanted a program that would look at countless spectra and infer the knowledge of mass spectrometry that DENDRAL could use to fix private hypothesis development issues. We did it. We were even able to publish new understanding of mass spectrometry in the Journal of the American Chemical Society, offering credit only in a footnote that a program, Meta-DENDRAL, actually did it. We had the ability to do something that had been a dream: to have a computer program developed a brand-new and publishable piece of science. [51]

In contrast to the knowledge-intensive method of Meta-DENDRAL, Ross Quinlan created a domain-independent method to analytical category, decision tree knowing, beginning initially with ID3 [60] and then later on extending its capabilities to C4.5. [61] The decision trees developed are glass box, interpretable classifiers, with human-interpretable classification rules.

Advances were made in understanding artificial intelligence theory, too. Tom Mitchell presented version space knowing which describes learning as an explore an area of hypotheses, with upper, more general, and lower, more particular, boundaries encompassing all viable hypotheses constant with the examples seen so far. [62] More formally, Valiant presented Probably Approximately Correct Learning (PAC Learning), a framework for the mathematical analysis of artificial intelligence. [63]

Symbolic maker learning included more than discovering by example. E.g., John Anderson offered a cognitive model of human knowing where skill practice results in a collection of guidelines from a declarative format to a procedural format with his ACT-R cognitive architecture. For instance, a student may discover to use “Supplementary angles are 2 angles whose procedures sum 180 degrees” as a number of different procedural guidelines. E.g., one rule may state that if X and Y are supplementary and you know X, then Y will be 180 – X. He called his method “understanding compilation”. ACT-R has been utilized effectively to design elements of human cognition, such as discovering and retention. ACT-R is likewise utilized in intelligent tutoring systems, called cognitive tutors, to successfully teach geometry, computer programming, and algebra to school kids. [64]

Inductive reasoning programming was another approach to finding out that allowed logic programs to be manufactured from input-output examples. E.g., Ehud Shapiro’s MIS (Model Inference System) could synthesize Prolog programs from examples. [65] John R. Koza applied genetic algorithms to program synthesis to develop genetic shows, which he used to manufacture LISP programs. Finally, Zohar Manna and Richard Waldinger supplied a more basic method to program synthesis that synthesizes a practical program in the course of proving its requirements to be proper. [66]

As an option to logic, Roger Schank introduced case-based reasoning (CBR). The CBR technique laid out in his book, Dynamic Memory, [67] focuses initially on keeping in mind crucial problem-solving cases for future usage and generalizing them where appropriate. When confronted with a brand-new issue, CBR retrieves the most comparable previous case and adjusts it to the specifics of the current issue. [68] Another option to reasoning, genetic algorithms and hereditary programming are based upon an evolutionary design of learning, where sets of guidelines are encoded into populations, the guidelines govern the habits of individuals, and selection of the fittest prunes out sets of unsuitable rules over many generations. [69]

Symbolic artificial intelligence was used to discovering principles, guidelines, heuristics, and analytical. Approaches, besides those above, include:

1. Learning from direction or advice-i.e., taking human direction, postured as guidance, and identifying how to operationalize it in specific circumstances. For example, in a game of Hearts, discovering precisely how to play a hand to “prevent taking points.” [70] 2. Learning from exemplars-improving performance by accepting subject-matter expert (SME) feedback throughout training. When analytical fails, querying the professional to either learn a new exemplar for problem-solving or to learn a brand-new description regarding exactly why one exemplar is more relevant than another. For example, the program Protos found out to detect ringing in the ears cases by connecting with an audiologist. [71] 3. Learning by analogy-constructing problem solutions based on comparable problems seen in the past, and after that modifying their options to fit a new situation or domain. [72] [73] 4. Apprentice knowing systems-learning unique solutions to issues by observing human analytical. Domain knowledge describes why unique options are correct and how the option can be generalized. LEAP found out how to design VLSI circuits by observing human designers. [74] 5. Learning by discovery-i.e., producing tasks to perform experiments and after that gaining from the outcomes. Doug Lenat’s Eurisko, for instance, learned heuristics to beat human gamers 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 gained from sequences of standard analytical actions. Good macro-operators streamline analytical 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 approach has been compared to deep learning as complementary “… with parallels having been drawn numerous times by AI researchers in between Kahneman’s research on human reasoning and decision making – shown in his book Thinking, Fast and Slow – and the so-called “AI systems 1 and 2″, which would in concept be designed by deep learning and symbolic reasoning, respectively.” In this view, symbolic thinking is more apt for deliberative reasoning, preparation, 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 attempts to integrate neural and symbolic architectures in a manner that addresses strengths and weak points of each, in a complementary fashion, in order to support robust AI capable of reasoning, discovering, and cognitive modeling. As argued by Valiant [77] and lots of others, [78] the reliable building and construction of rich computational cognitive models requires the combination of sound symbolic thinking and effective (maker) learning designs. Gary Marcus, similarly, argues that: “We can not construct abundant cognitive models in a sufficient, automatic method without the triumvirate of hybrid architecture, abundant anticipation, and sophisticated methods for reasoning.”, [79] and in particular: “To construct a robust, knowledge-driven method to AI we need to have the equipment of symbol-manipulation in our toolkit. Excessive of useful 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 such abstract understanding dependably is the apparatus of symbol manipulation. ” [80]

Henry Kautz, [19] Francesca Rossi, [81] and Bart Selman [82] have likewise argued for a synthesis. Their arguments are based upon a requirement to deal with the 2 sort of thinking gone over 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, step-by-step, and explicit. System 1 is the kind utilized for pattern recognition while System 2 is far much better matched for preparation, deduction, and deliberative thinking. In this view, deep learning finest designs the very first sort of thinking while symbolic thinking best designs the 2nd kind and both are required.

Garcez and Lamb explain research study in this location as being continuous for a minimum of the past twenty years, [83] dating from their 2002 book on neurosymbolic knowing systems. [84] A series of workshops on neuro-symbolic thinking has actually been held every year because 2005, see http://www.neural-symbolic.org/ for details.

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 a number of considerable results. Over the last years, neural symbolic systems have been shown capable of getting rid of the so-called propositional fixation of neural networks, as McCarthy (1988) put it in action to Smolensky (1988 ); see likewise (Hinton, 1990). Neural networks were shown efficient in representing modal and temporal reasonings (d’Avila Garcez and Lamb, 2006) and fragments 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 adaptation, visual intelligence, ontology learning, and computer video games. [78]

Approaches for integration are varied. Henry Kautz’s taxonomy of neuro-symbolic architectures, in addition to some examples, follows:

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

Many crucial research questions stay, such as:

– What is the very best way to incorporate neural and symbolic architectures? [87]- How should symbolic structures be represented within neural networks and extracted from them?
– How should sensible understanding be learned and reasoned about?
– How can abstract knowledge that is hard to encode logically be dealt with?

Techniques and contributions

This section provides an introduction of techniques and contributions in an overall context leading to many other, more comprehensive short articles in Wikipedia. Sections on Artificial Intelligence and Uncertain Reasoning are covered earlier in the history section.

AI shows languages

The key AI shows language in the US during the last symbolic AI boom period was LISP. LISP is the second earliest programs language after FORTRAN and was produced in 1958 by John McCarthy. LISP provided the very first read-eval-print loop to support fast program advancement. Compiled functions could be freely blended with analyzed functions. Program tracing, stepping, and breakpoints were likewise supplied, in addition to the ability to change values or functions and continue from breakpoints or errors. It had the first self-hosting compiler, suggesting that the compiler itself was originally written in LISP and after that ran interpretively to assemble the compiler code.

Other crucial innovations originated by LISP that have actually spread out to other programming languages consist of:

Garbage collection
Dynamic typing
Higher-order functions
Recursion
Conditionals

Programs were themselves data structures that other programs could operate on, enabling the easy meaning of higher-level languages.

In contrast to the US, in Europe the essential AI programming language during that exact same period was Prolog. Prolog supplied a built-in store of realities and clauses that could be queried by a read-eval-print loop. The shop could serve as a knowledge base and the stipulations could serve as rules or a restricted kind of reasoning. As a subset of first-order reasoning Prolog was based on Horn stipulations with a closed-world assumption-any facts not understood were thought about false-and an unique name assumption for primitive terms-e.g., the identifier barack_obama was thought about to describe exactly one things. Backtracking and unification are built-in to Prolog.

Alain Colmerauer and Philippe Roussel are credited as the inventors of Prolog. Prolog is a kind of reasoning programming, which was created by Robert Kowalski. Its history was also affected by Carl Hewitt’s PLANNER, an assertional database with pattern-directed invocation of techniques. For more detail see the section on the origins of Prolog in the PLANNER article.

Prolog is also a type of declarative programming. The logic stipulations that explain programs are straight interpreted to run the programs specified. No specific series of actions is needed, as is the case with necessary programs languages.

Japan promoted Prolog for its Fifth Generation Project, meaning to construct special hardware for high efficiency. Similarly, LISP makers were constructed to run LISP, but as the 2nd AI boom turned to bust these companies might not take on new workstations that could now run LISP or Prolog natively at equivalent speeds. See the history section for more information.

Smalltalk was another influential AI shows language. For instance, it presented metaclasses and, along with Flavors and CommonLoops, influenced the Common Lisp Object System, or (CLOS), that is now part of Common Lisp, the current basic Lisp dialect. CLOS is a Lisp-based object-oriented system that enables several inheritance, in addition to incremental extensions to both classes and metaclasses, therefore offering a run-time meta-object protocol. [88]

For other AI programs languages see this list of programs languages for expert system. Currently, Python, a multi-paradigm shows language, is the most popular programming language, partly due to its comprehensive plan library that supports data science, natural language processing, and deep learning. Python consists of a read-eval-print loop, functional elements such as higher-order functions, and object-oriented programs that consists of metaclasses.

Search

Search occurs in many sort of issue resolving, including preparation, constraint 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 provision 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 reasoning

Multiple different techniques to represent knowledge and after that reason with those representations have actually been examined. Below is a fast overview of approaches to understanding representation and automated thinking.

Knowledge representation

Semantic networks, conceptual graphs, frames, and reasoning are all techniques to modeling knowledge such as domain understanding, problem-solving knowledge, and the semantic meaning of language. Ontologies design key ideas 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 realities extracted from Wikipedia with WordNet synsets. The Disease Ontology is an example of a medical ontology presently being utilized.

Description reasoning is a logic for automated classification of ontologies and for discovering inconsistent classification information. 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 reasoning is more general than description logic. The automated theorem provers talked about listed below can show theorems in first-order logic. Horn clause logic is more limited than first-order logic and is utilized in logic shows languages such as Prolog. Extensions to first-order reasoning include temporal reasoning, to manage time; epistemic logic, to reason about representative knowledge; modal reasoning, to handle possibility and requirement; and probabilistic reasonings to handle reasoning and possibility together.

Automatic theorem showing

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

Prover9.
ACL2.
Vampire.

Prover9 can be utilized in conjunction with the Mace4 design checker. ACL2 is a theorem prover that can handle evidence by induction and is a descendant of the Boyer-Moore Theorem Prover, also referred to as Nqthm.

Reasoning in knowledge-based systems

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

Forward chaining inference engines are the most common, and are seen in CLIPS and OPS5. Backward chaining happens in Prolog, where a more limited logical representation is used, Horn Clauses. Pattern-matching, specifically unification, is used in Prolog.

A more flexible sort of analytical takes place when thinking about what to do next occurs, rather than simply selecting one of the readily available actions. This sort of meta-level thinking is utilized in Soar and in the BB1 chalkboard architecture.

Cognitive architectures such as ACT-R may have additional abilities, such as the ability to compile often utilized understanding into higher-level pieces.

Commonsense thinking

Marvin Minsky first proposed frames as a method of translating common visual circumstances, such as a workplace, and Roger Schank extended this idea to scripts for common routines, such as dining out. Cyc has attempted to record beneficial common-sense understanding and has “micro-theories” to deal with specific sort of domain-specific thinking.

Qualitative simulation, such as Benjamin Kuipers’s QSIM, [90] approximates human thinking about ignorant physics, such as what happens when we warm a liquid in a pot on the range. We anticipate it to heat and potentially boil over, despite the fact that we might not know its temperature level, its boiling point, or other details, such as air pressure.

Similarly, Allen’s temporal interval algebra is a simplification of thinking about time and Region Connection Calculus is a simplification of thinking about spatial relationships. Both can be resolved with constraint solvers.

Constraints and constraint-based reasoning

Constraint solvers perform a more restricted kind of reasoning than first-order logic. They can streamline sets of spatiotemporal restrictions, such as those for RCC or Temporal Algebra, together with resolving other type of puzzle issues, such as Wordle, Sudoku, cryptarithmetic problems, and so on. Constraint reasoning programs can be used to solve scheduling issues, for example with restraint managing guidelines (CHR).

Automated planning

The General Problem Solver (GPS) cast preparation as analytical used means-ends analysis to develop plans. STRIPS took a various method, viewing planning as theorem proving. Graphplan takes a least-commitment technique to preparation, rather than sequentially selecting actions from a preliminary state, working forwards, or a goal state if working backwards. Satplan is a technique to planning where a preparation issue is minimized to a Boolean satisfiability issue.

Natural language processing

Natural language processing concentrates on treating language as data to carry out tasks such as recognizing subjects without always comprehending the desired significance. Natural language understanding, in contrast, constructs a meaning representation and uses that for more processing, such as addressing questions.

Parsing, tokenizing, spelling correction, part-of-speech tagging, noun and verb expression chunking are all elements of natural language processing long managed by symbolic AI, however because improved by deep learning methods. In symbolic AI, discourse representation theory and first-order logic have actually been utilized to represent sentence significances. Latent semantic analysis (LSA) and specific semantic analysis also supplied vector representations of files. In the latter case, vector elements are interpretable as ideas called by Wikipedia short articles.

New deep learning techniques based upon Transformer designs have now eclipsed these earlier symbolic AI methods and achieved cutting edge efficiency 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 meaning of the vector parts is nontransparent.

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 textbook on expert system is organized to show representative architectures of increasing sophistication. [91] The sophistication of representatives differs from basic reactive representatives, to those with a model of the world and automated preparation capabilities, potentially a BDI agent, i.e., one with beliefs, desires, and objectives – or alternatively a reinforcement learning design found out over time to choose actions – as much as a mix of alternative architectures, such as a neuro-symbolic architecture [87] that consists of deep knowing for understanding. [92]

In contrast, a multi-agent system includes multiple agents that interact among themselves with some inter-agent communication language such as Knowledge Query and Manipulation Language (KQML). The representatives require not all have the very same internal architecture. Advantages of multi-agent systems consist of the ability to divide work among the representatives and to increase fault tolerance when agents are lost. Research problems include how agents reach agreement, distributed problem fixing, multi-agent knowing, multi-agent planning, and dispersed constraint optimization.

Controversies occurred from early in symbolic AI, both within the field-e.g., between logicists (the pro-logic “neats”) and non-logicists (the anti-logic “scruffies”)- and in between those who embraced AI but declined symbolic approaches-primarily connectionists-and those outside the field. Critiques from exterior of the field were mostly from thinkers, on intellectual grounds, but also from funding firms, specifically during the 2 AI winter seasons.

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

Limitations were discovered in using simple first-order logic to reason about vibrant domains. Problems were found both with concerns to enumerating the preconditions for an action to prosper and in offering axioms for what did not alter after an action was performed.

McCarthy and Hayes introduced the Frame Problem in 1969 in the paper, “Some Philosophical Problems from the Standpoint of Expert System.” [93] An easy example occurs in “proving that one individual might enter conversation with another”, as an axiom asserting “if a person has a telephone he still has it after searching for a number in the telephone directory” would be required for the reduction to prosper. Similar axioms would be required for other domain actions to specify what did not change.

A comparable problem, called the Qualification Problem, happens in attempting to mention the preconditions for an action to prosper. A boundless number of pathological conditions can be envisioned, e.g., a banana in a tailpipe could avoid a car from running properly.

McCarthy’s approach to repair the frame problem was circumscription, a kind of non-monotonic reasoning where reductions could be made from actions that require just define what would change while not having to explicitly define whatever that would not change. Other non-monotonic logics offered truth maintenance systems that modified beliefs resulting in contradictions.

Other ways of dealing with more open-ended domains included probabilistic reasoning systems and device knowing to find out new principles and guidelines. McCarthy’s Advice Taker can be viewed as an inspiration here, as it might integrate new understanding provided by a human in the type of assertions or rules. For instance, speculative symbolic device discovering systems explored the ability to take high-level natural language guidance and to translate it into domain-specific actionable rules.

Similar to the problems in dealing with dynamic domains, sensible reasoning is also challenging to catch in formal reasoning. Examples of common-sense reasoning include implicit reasoning about how people think or basic knowledge of daily occasions, items, and living creatures. This kind of understanding is considered approved and not viewed as noteworthy. Common-sense reasoning is an open location of research study and challenging both for symbolic systems (e.g., Cyc has tried to catch key parts of this understanding over more than a decade) and neural systems (e.g., self-driving cars and trucks that do not know not to drive into cones or not to hit pedestrians walking a bicycle).

McCarthy saw his Advice Taker as having common-sense, however his definition of sensible was different than the one above. [94] He defined a program as having good sense “if it instantly deduces for itself an adequately large class of instant consequences of anything it is informed and what it already knows. “

Connectionist AI: philosophical challenges and sociological conflicts

Connectionist methods include earlier work on 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 methods, such as Transformers, GANs, and other work in deep learning.

Three philosophical positions [96] have actually been laid out amongst connectionists:

1. Implementationism-where connectionist architectures execute the abilities for symbolic processing,
2. Radical connectionism-where symbolic processing is turned down totally, and connectionist architectures underlie intelligence and are completely adequate to describe it,
3. Moderate connectionism-where symbolic processing and connectionist architectures are seen as complementary and both are needed for intelligence

Olazaran, in his sociological history of the debates within the neural network community, described the moderate connectionism consider as essentially suitable with present research in neuro-symbolic hybrids:

The third and last position I want to examine here is what I call the moderate connectionist view, a more eclectic view of the current dispute between connectionism and symbolic AI. Among the researchers who has 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 safeguarded hybrid (partly symbolic, partially connectionist) systems. He claimed that (at least) 2 type of theories are needed in order to study and design 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 reasoning, and generative symbol control procedures) the symbolic paradigm uses sufficient designs, and not only “approximations” (contrary to what extreme connectionists would claim). [97]

Gary Marcus has actually claimed that the animus in the deep learning community against symbolic techniques now might be more sociological than philosophical:

To believe that we can merely abandon symbol-manipulation is to suspend shock.

And yet, for the most part, that’s how most current AI earnings. Hinton and many others have tried hard to eliminate signs altogether. The deep knowing hope-seemingly grounded not a lot in science, however in a sort of historical grudge-is that smart behavior will emerge purely from the confluence of huge data and deep knowing. Where classical computers and software solve jobs by defining sets of symbol-manipulating rules committed to particular tasks, such as editing a line in a word processor or performing a calculation in a spreadsheet, neural networks usually attempt to solve tasks by statistical approximation and gaining from examples.

According to Marcus, Geoffrey Hinton and his coworkers have actually been emphatically “anti-symbolic”:

When deep knowing reemerged in 2012, it was with a sort of take-no-prisoners mindset that has identified many of the last years. By 2015, his hostility towards all things symbols had totally taken shape. He provided a talk at an AI workshop at Stanford comparing symbols to aether, one of science’s greatest errors.

…

Ever since, his anti-symbolic project has actually just increased in intensity. In 2016, Yann LeCun, Bengio, and Hinton composed a manifesto for deep learning in one of science’s essential journals, Nature. It closed with a direct attack on symbol control, calling not for reconciliation however for outright replacement. Later, Hinton informed an event of European Union leaders that investing any more money in symbol-manipulating techniques was “a huge mistake,” comparing it to purchasing internal combustion engines in the period of electric cars. [98]

Part of these disagreements might be because of uncertain terms:

Turing award winner Judea Pearl provides a review of machine knowing which, regrettably, conflates the terms artificial intelligence and deep knowing. Similarly, when Geoffrey Hinton describes symbolic AI, the connotation of the term tends to be that of professional systems dispossessed of any capability to learn. Making use of the terminology is in need of clarification. Machine learning is not confined to association guideline mining, c.f. the body of work on symbolic ML and relational knowing (the differences to deep knowing being the option of representation, localist sensible instead of distributed, and the non-use of gradient-based knowing algorithms). Equally, symbolic AI is not practically production rules written by hand. A proper definition of AI concerns understanding representation and reasoning, self-governing multi-agent systems, planning and argumentation, along with knowing. [99]

Situated robotics: the world as a design

Another critique of symbolic AI is the embodied cognition technique:

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

Rodney Brooks invented behavior-based robotics, one approach to embodied cognition. Nouvelle AI, another name for this approach, is deemed an alternative to both symbolic AI and connectionist AI. His technique rejected representations, either symbolic or dispersed, as not just unnecessary, but as harmful. Instead, he created the subsumption architecture, a layered architecture for embodied representatives. Each layer attains a different purpose and needs to function in the real life. For instance, the very first robot he describes in Intelligence Without Representation, has three layers. The bottom layer translates finder sensing units to prevent objects. The middle layer causes the robotic to wander around when there are no barriers. The leading layer causes the robot to go to more distant locations for further expedition. Each layer can temporarily inhibit or suppress a lower-level layer. He slammed AI scientists for defining AI issues for their systems, when: “There is no tidy division in between perception (abstraction) and reasoning in the real world.” [101] He called his robots “Creatures” and each layer was “composed of a fixed-topology network of easy limited state makers.” [102] In the Nouvelle AI technique, “First, it is extremely crucial to check the Creatures we integrate in the real life; i.e., in the very same world that we humans live in. It is dreadful to fall under the temptation of testing them in a simplified world first, even with the finest intentions of later transferring activity to an unsimplified world.” [103] His focus on real-world testing was in contrast to “Early operate in AI focused on games, geometrical problems, symbolic algebra, theorem proving, and other formal systems” [104] and using the blocks world in symbolic AI systems such as SHRDLU.

Current views

Each approach-symbolic, connectionist, and behavior-based-has advantages, however has been slammed by the other approaches. Symbolic AI has been slammed as disembodied, liable to the credentials issue, and bad in handling the perceptual problems where deep learning excels. In turn, connectionist AI has been slammed as poorly fit for deliberative step-by-step issue resolving, including knowledge, and handling preparation. Finally, Nouvelle AI stands out in reactive and real-world robotics domains but has actually been slammed for troubles in including learning and understanding.

Hybrid AIs including several of these techniques are currently considered as the course forward. [19] [81] [82] Russell and Norvig conclude that:

Overall, Dreyfus saw locations where AI did not have total answers and said that Al is therefore difficult; we now see a lot of these very same areas going through continued research and development resulting in increased capability, not impossibility. [100]

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

Notes

^ McCarthy once stated: “This is AI, so we do not care if it’s mentally real”. [4] McCarthy reiterated 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 expert system: one aimed at producing smart habits despite how it was accomplished, and the other targeted at modeling intelligent processes discovered in nature, especially human ones.”, [29] Stuart Russell and Peter Norvig wrote “Aeronautical engineering texts do not specify the goal of their field as making ‘machines that fly so precisely like pigeons that they can deceive even other pigeons.'” [30] Citations

^ Garnelo, Marta; Shanahan, Murray (October 2019). “Reconciling deep knowing with symbolic expert system: representing objects 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 learning with symbolic expert system: representing items 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 Postal 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.
^ Lenat, Douglas B; Feigenbaum, Edward A (1988 ). “On the limits of knowledge”. Proceedings of the International Workshop on Expert System for Industrial Applications: 291-300. doi:10.1109/ AIIA.1988.13308. S2CID 11778085.
^ 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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^ Bareiss, Ray; Porter, Bruce; Wier, Craig. “Chapter 4: Protos: An Exemplar-Based Learning Apprentice”. In Michalski, Carbonell & Mitchell (1986 ), pp. 112-139.
^ Carbonell, Jaime. “Chapter 5: Learning by Analogy: Formulating and Generalizing Plans from Past Experience”. In Michalski, Carbonell & Mitchell (1983 ), pp. 137-162.
^ Carbonell, Jaime. “Chapter 14: Derivational Analogy: A Theory of Reconstructive Problem Solving and Expertise Acquisition”. In Michalski, Carbonell & Mitchell (1986 ), pp. 371-392.
^ Mitchell, Tom; Mabadevan, Sridbar; Steinberg, Louis. “Chapter 10: LEAP: A Learning Apprentice for VLSI Design”. In Kodratoff & Michalski (1990 ), pp. 271-289.
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^ Garcez & Lamb 2020, p. 2.
^ Garcez et al. 2002.
^ Rocktäschel, Tim; Riedel, Sebastian (2016 ). “Learning Knowledge Base Inference with Neural Theorem Provers”. Proceedings of the fifth Workshop on Automated Knowledge Base Construction. San Diego, CA: Association for Computational Linguistics. pp. 45-50. doi:10.18653/ v1/W16 -1309. Retrieved 2022-08-06.
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